Proper acceleration

In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero.
Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers (see three-acceleration in special relativity).
In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time.
In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant. Thus the concept is useful: (i) with accelerated coordinate systems, (ii) at relativistic speeds, and (iii) in curved spacetime.
In an accelerating rocket after launch, or even in a rocket standing at the gantry, the proper acceleration is the acceleration felt by the occupants, and which is described as g-force (which is "not" a force but rather an acceleration; see that article for more discussion of proper acceleration) delivered by the vehicle only. The "acceleration of gravity" ("force of gravity") never contributes to proper acceleration in any circumstances, and thus the proper acceleration felt by observers standing on the ground is due to the mechanical force "from the ground", not due to the "force" or "acceleration" of gravity. If the ground is removed and the observer allowed to free-fall, the observer will experience coordinate acceleration, but no proper acceleration, and thus no g-force. Generally, objects in such a fall or generally any such ballistic path (also called inertial motion), including objects in orbit, experience no proper acceleration (neglecting small tidal accelerations for inertial paths in gravitational fields). This state is also known as "zero gravity" ("zero-g") or "free-fall," and it produces a sensation of weightlessness.
Proper acceleration reduces to coordinate acceleration in an inertial coordinate system in flat spacetime (i.e. in the absence of gravity), provided the magnitude of the object's proper-velocity (momentum per unit mass) is much less than the speed of light "c". Only in such situations is coordinate acceleration "entirely" felt as a g-force (i.e. a proper acceleration, also defined as one that produces measurable weight).
In situations in which gravitation is absent but the chosen coordinate system is not inertial, but is accelerated with the observer (such as the accelerated reference frame of an accelerating rocket, or a frame fixed upon objects in a centrifuge), then g-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems. This weight, in turn, is produced by fictitious forces or "inertial forces" which appear in all such accelerated coordinate systems, in a manner somewhat like the weight produced by the "force of gravity" in systems where objects are fixed in space with regard to the gravitating body (as on the surface of the Earth).
The total (mechanical) force that is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = "m" a, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e. its weight as measured by a device like a spring scale, in vacuum, in the object's coordinate system). Thus, the proper force on an object is always equal and opposite to its measured weight.
Examples.
When holding onto a carousel that turns at constant angular velocity you experience a radially inward (centripetal) proper-acceleration due to the interaction between the handhold and your hand. This cancels the radially outward "geometric acceleration" associated with your spinning coordinate frame. This outward acceleration (from the spinning frame's perspective) will become the coordinate acceleration when you let go, causing you to fly off along a zero proper-acceleration (geodesic) path. Unaccelerated observers, of course, in their frame simply see your equal proper and coordinate accelerations vanish when you let go.
Similarly, standing on a non-rotating planet (and on earth for practical purposes) we experience an upward proper-acceleration due to the normal force exerted by the earth on the bottom of our shoes. This cancels the downward geometric acceleration due to our choice of coordinate system (a so-called shell-frame). That downward acceleration becomes coordinate if we inadvertently step off a cliff into a zero proper-acceleration (geodesic or rain-frame) trajectory.
Note that "geometric accelerations" (due to the connection term in the coordinate system's covariant derivative below) act on "every ounce of our being", while proper-accelerations are usually caused by an external force. Introductory physics courses often treat gravity's downward (geometric) acceleration as due to a mass-proportional force. This, along with diligent avoidance of unaccelerated frames, allows them to treat proper and coordinate acceleration as the same thing.
Even then if an object maintains a "constant proper-acceleration" from rest over an extended period in flat spacetime, observers in the rest frame will see the object's coordinate acceleration decrease as its coordinate velocity approaches lightspeed. The rate at which the object's proper-velocity goes up, nevertheless, remains constant.
Thus the distinction between proper-acceleration and coordinate acceleration allows one to track the experience of accelerated travelers from various non-Newtonian perspectives. These perspectives include those of accelerated coordinate systems (like a carousel), of high speeds (where proper and coordinate times differ), and of curved spacetime (like that associated with gravity on Earth).
Classical applications.
At low speeds in the inertial coordinate systems of Newtonian physics, proper acceleration simply equals the coordinate acceleration a=d2x/dt2. As reviewed above, however, it differs from coordinate acceleration if one chooses (against Newton's advice) to describe the world from the perspective of an accelerated coordinate system like a motor vehicle accelerating from rest, or a stone being spun around in a slingshot. If one chooses to recognize that gravity is caused by the curvature of spacetime (see below), proper acceleration differs from coordinate acceleration in a gravitational field.
For example, an object subjected to physical or proper acceleration ao will be seen by observers in a coordinate system undergoing constant acceleration aframe to have coordinate acceleration:
Thus if the object is accelerating with the frame, observers fixed to the frame will see no acceleration at all.
Similarly, an object undergoing physical or proper acceleration ao will be seen by observers in a frame rotating with angular velocity ω to have coordinate acceleration:
In the equation above, there are three geometric acceleration terms on the right-hand side. The first "centrifugal acceleration" term depends only on the radial position r and not the velocity of our object, the second "Coriolis acceleration" term depends only on the object's velocity in the rotating frame vrot but not its position, and the third "Euler acceleration" term depends only on position and the rate of change of the frame's angular velocity.
In each of these cases, physical or proper acceleration differs from coordinate acceleration because the latter can be affected by your choice of coordinate system as well as by physical forces acting on the object. Those components of coordinate acceleration "not" caused by physical forces (like direct contact or electrostatic attraction) are often attributed (as in the Newtonian example above) to forces that: (i) act on every ounce of the object, (ii) cause mass-independent accelerations, and (iii) don't exist from all points of view. Such geometric (or improper) forces include Coriolis forces, Euler forces, g-forces, centrifugal forces and (as we see below) gravity forces as well.
Viewed from a flat spacetime slice.
Proper-acceleration's relationships to coordinate acceleration in a specified slice of flat spacetime follow from Minkowski's flat-space metric equation ("c"d"τ")2 = ("c"d"t")2 - (dx)2. Here a single reference frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, the traveling object's clocks define proper time "τ", and the "d" preceding a coordinate means infinitesimal change. These relationships allow one to tackle various problems of "anyspeed engineering", albeit only from the vantage point of an observer whose extended map frame defines simultaneity.
Acceleration in (1+1)D.
In the unidirectional case i.e. when the object's acceleration is parallel or antiparallel to its velocity in the spacetime slice of the observer, proper acceleration α and coordinate acceleration a are related through the Lorentz factor γ by α=γ3a. Hence the change in proper-velocity w=dx/dτ is the integral of proper acceleration over map-time t i.e. Δ"w"="α"Δ"t" for constant "α". At low speeds this reduces to the well-known relation between coordinate velocity and coordinate acceleration times map-time, i.e. Δ"v"="a"Δ"t".
For constant unidirectional proper-acceleration, similar relationships exist between rapidity "η" and elapsed proper time Δ"τ", as well as between Lorentz factor "γ" and distance traveled Δ"x". To be specific:
where the various velocity parameters are related by
These equations describe some consequences of accelerated travel at high speed. For example, imagine a spaceship that can accelerate its passengers at "1 gee" (10 m/s2 or about 1.0 light year per year squared) halfway to their destination, and then decelerate them at "1 gee" for the remaining half so as to provide earth-like artificial gravity from point A to point B over the shortest possible time. For a map-distance of Δ"x"AB, the first equation above predicts a midpoint Lorentz factor (up from its unit rest value) of "γ"mid=1+"α"(Δ"x"AB/2)/c2. Hence the round-trip time on traveler clocks will be Δ"τ" = 4("c"/"α") cosh−1("γ"mid), during which the time elapsed on map clocks will be Δ"t" = 4("c"/α") sinh[cosh−1("γ"mid)].
This imagined spaceship could offer round trips to Proxima Centauri lasting about 7.1 traveler years (~12 years on Earth clocks), round trips to the Milky Way's central black hole of about 40 years (~54,000 years elapsed on earth clocks), and round trips to Andromeda Galaxy lasting around 57 years (over 5 million years on Earth clocks). Unfortunately, sustaining 1-gee acceleration for years is easier said than done, as illustrated by the maximum payload to launch mass ratios shown in the figure at right.
In curved spacetime.
In the language of general relativity, the components of an object's acceleration four-vector "A" (whose magnitude is proper acceleration) are related to elements of the four-velocity via a covariant derivative "D" with respect to proper time τ:
Here "U" is the object's four-velocity, and "Γ" represents the coordinate system's 64 connection coefficients or Christoffel symbols. Note that the Greek subscripts take on four possible values, namely 0 for the time-axis and 1-3 for spatial coordinate axes, and that repeated indices are used to indicate summation over all values of that index. Trajectories with zero proper acceleration are referred to as geodesics.
The left hand side of this set of four equations (one each for the time-like and three spacelike values of index λ) is the object's proper-acceleration 3-vector combined with a null time component as seen from the vantage point of a reference or book-keeper coordinate system in which the object is at rest. The first term on the right hand side lists the rate at which the time-like (energy/"mc") and space-like (momentum/"m") components of the object's four-velocity "U" change, per unit time "τ" on traveler clocks.
Let's solve for that first term on the right since at low speeds its spacelike components represent the coordinate acceleration. More generally, when that first term goes to zero the object's coordinate acceleration goes to zero. This yields...
Thus, as exemplified with the first two animations above, coordinate acceleration goes to zero whenever proper-acceleration is exactly canceled by the connection (or "geometric acceleration") term on the far right. "Caution:" This term may be a sum of as many as sixteen separate velocity and position dependent terms, since the repeated indices "μ" and "ν" are by convention summed over all pairs of their four allowed values.
Force and equivalence.
The above equation also offers some perspective on forces and the equivalence principle. Consider "local" book-keeper coordinates for the metric (e.g. a local Lorentz tetrad like that which global positioning systems provide information on) to describe time in seconds, and space in distance units along perpendicular axes. If we multiply the above equation by the traveling object's rest mass m, and divide by Lorentz factor "γ" = d"t"/d"τ", the spacelike components express the rate of momentum change for that object from the perspective of the coordinates used to describe the metric.
This in turn can be broken down into parts due to proper and geometric components of acceleration and force. If we further multiply the time-like component by lightspeed "c", and define coordinate velocity as v = dx/d"t", we get an expression for rate of energy change as well:
Here "a""o" is an acceleration due to proper forces and "a""g" is, by default, a geometric acceleration that we see applied to the object because of our coordinate system choice. At low speeds these accelerations combine to generate a coordinate acceleration like a=d2x/d"t"2, while for unidirectional motion "at any speed" "a""o"'s magnitude is that of proper acceleration "α" as in the section above where "α" = "γ"3"a" when "a""g" is zero. In general expressing these accelerations and forces can be complicated.
Nonetheless if we use this breakdown to describe the connection coefficient (Γ) term above in terms of geometric forces, then the motion of objects from the point of view of "any coordinate system" (at least at low speeds) can be seen as locally Newtonian. This is already common practice e.g. with centrifugal force and gravity. Thus the equivalence principle extends the local usefulness of Newton's laws to accelerated coordinate systems and beyond.
Surface dwellers on a planet.
For low speed observers being held at fixed radius from the center of a spherical planet or star, coordinate acceleration ashell is approximately related to proper acceleration ao by:
where the planet or star's Schwarzschild radius rs=2GM/c2. As our shell observer's radius approaches the Schwarzschild radius, the proper acceleration ao needed to keep it from falling in becomes intolerable.
On the other hand, for r»rs, an upward proper force of only GMm/r2 is needed to prevent one from accelerating downward. At the Earth's surface this becomes:
where g is the downward 9.8 m/s2 acceleration due to gravity, and formula_11 is a unit vector in the radially outward direction from the center of the gravitating body. Thus here an outward proper force of mg is needed to keep one from accelerating downward.
Four-vector derivations.
The spacetime equations of this section allow one to address "all deviations" between proper and coordinate acceleration in a single calculation. For example, let's calculate the Christoffel symbols:
for the far-coordinate Schwarzschild metric , where "r"s is the Schwarzschild radius 2"GM"/"c"2. The resulting array of coefficients becomes:
From this you can obtain the shell-frame proper acceleration by setting coordinate acceleration to zero and thus requiring that proper acceleration cancel the geometric acceleration of a stationary object i.e. formula_14. This does not solve the problem yet, since Schwarzschild coordinates in curved spacetime are book-keeper coordinates but not those of a local observer. The magnitude of the above proper acceleration 4-vector, namely formula_15, is however precisely what we want i.e. the upward frame-invariant proper acceleration needed to counteract the downward geometric acceleration felt by dwellers on the surface of a planet.
A special case of the above Christoffel symbol set is the flat-space spherical coordinate set obtained by setting "r"s or "M" above to zero:
From this we can obtain, for example, the centri"petal" proper acceleration needed to cancel the centri"fugal" geometric acceleration of an object moving at constant angular velocity "ω"=d"φ"/d"τ" at the equator where "θ"="π"/2. Forming the same 4-vector sum as above for the case of d"θ"/d"τ" and d"r"/d"τ" zero yields nothing more than the classical acceleration for rotational motion given above, i.e. formula_17 so that "a"o="ω"2"r". Coriolis effects also reside in these connection coefficients, and similarly arise from coordinate-frame geometry alone.


Arthur M. Poskanzer

Arthur M. Poskanzer (born 28 June 1931 in New York City) is an experimental physicist, known for his pioneering work on relativistic nuclear collisions.
Poskanzer received in 1953 his bachelor's degree in physics and chemistry from Harvard University and in 1954 his master's degree in chemistry from Columbia University. In 1957 he received his Ph.D. from Massachusetts Institute of Technology in physical chemistry. From 1957 to 1966 he was a chemist at Brookhaven National Laboratory. From 1966 he worked as a scientist as Lawrence Berkeley National Laboratory (LBL) and remained on the staff there until 2001, when he retired with emeritus status. From 1978 to 1979 he was the scientific director of Bevalac. From 1980 to 1990 he was the leader of the Plastic Ball Experimental Group, which was part of a collaboration between LBL and GSI Helmholtz Centre for Heavy Ion Research (GSI). From 1990 to 1995 he was the head of the Relativistic Collisions Program at LBL.
He is famous as one of the co-discoverers of what nuclear physicists call collective flow; this phenomenon consists of fluidic motion exhibited by nuclear matter, such as quarks and gluons, when compressed to a physical state of high temperature and high energy-density. This discovery was made during the collaboration between LBL and GSI.
For the academic year 1970/71 he was a Guggenheim Fellow at the University of Paris-Sud in Orsay. He was several times a visiting scientist at CERN (in 1979/80, in 1986/87 and in 1995/96, with the latter two visiting years each supported by Alexander von Humboldt Senior US Scientist Awards).
He married in 1954 and is the father of three children.


Horace Hearne Institute

The Horace Hearne Jr. Institute for Theoretical Physics is at Louisiana State University. The Hearne Institute is funded by a donation of two endowed chairs by Horace Hearne Jr. and the State of Louisiana, as well as additional grants from a variety of national and international granting agencies. It currently has as co-directors Jonathan Dowling and Jorge Pullin. The institute hosts faculty, postdoctoral researchers, students — as well as long- and short-term visitors — who conduct research on quantum technologies and on gravitational physics. The Hearne Institute also sponsors international workshops on quantum information theory, quantum technologies, relativity and quantum gravity.


Rama Bansil

Rama Bansil serves as Professor of Physics at Boston University, a post she has held since 1997. Although trained as a physicist, her work and professional associations are multi-disciplined, with areas of expertise encompassing biopolymer engineering, polymer engineering, photonics, nanoscience, nanobiotechnology, biophysics and biochemistry.
Academic biography.
Dr. Bansil holds a Doctorate in Physics, awarded by the University of Rochester in 1975. This followed the completion of studies at Delhi University, where she earned M.Sc. and B.Sc. degrees. After serving as a research associate at the Harvard-M.I.T. Program in Health Sciences and Technology during the 1975–1976 academic year, she began her teaching career at Boston University in 1976. Since 1997 she has served at that institution as a Professor of Physics with multiple affiliations, including the Center for Polymer Studies, the Photonics Center, the Molecular and Cell Biology and Biochemistry (MCBB) Program, the Center of Nanoscience and Nanobiotechnology, Materials Science and Engineering, and the Department of Physiology and Biophysics at Boston University's School of Medicine.
Between 2007 and 2009, on leave of absence from Boston University, she served as the Program Director, Division of Materials Research, Directorate for Mathematical and Physical Sciences, at the National Science Foundation.
Awards and honors.
Among a small number of women to enter the sciences in the early sixties, Rama Bansil won early distinction, capturing undergraduate prizes in science and winning a Vinton Hayes Fellowship to Harvard University, where she conducted postdoctoral research in 1974–1975. She was later awarded a Bunting Fellowship at Radcliffe College (1993–1994).
Dr. Bansil has been a successful applicant for more than a dozen grants from the National Science Foundation and private institutions, with total funding approaching three million dollars.
She was elected a Fellow of the American Physical Society in 2001.
Research.
In the course of her scientific career Dr. Bansil has authored or co-authored nearly one hundred publications.
The recent focus of her work has been the molecular structure of gels, the physics of gel formation, diffusion in gels and the kinetics of phase transitions and chemical reactions in gels. Her early work, prior to 2000, focused on biophysics, chemical physics, polymer physics (gelation and phase separation). Since 2000, the topics of the biophysics of mucin, and phase transitions and dynamics in block copolymers have occupied her research interests.
In her latest work, Dr. Bansil, in collaboration with her former graduate student Jonathan Celli and a team of nine other researchers, has succeeded in explaining the process through which the "H. pylori" bacterium is able to penetrate the mucous lining of the human stomach, a source of ulcers and even cancer. Those findings could have implications for the prevention and treatment of "H. pylori" infections. According to "Scienceblog": "A team of researchers from Boston University, Harvard Medical School and Massachusetts Institute of Technology recently made a discovery that changes a long held paradigm about how bacteria move through soft gels."


Christine Aidala

Christine Angela Aidala is an American high-energy nuclear physicist, Alfred P. Sloan Research Fellow and Associate Professor of Physics at the University of Michigan. She studies nucleon structure and parton dynamics in quantum chromodynamics.
Education.
She received a B.S. in Physics and a B.S. in Music from Yale University in 1999. During her undergraduate studies, she taught English and music in Milan, Italy. She earned her Ph.D. from Columbia University in 2005. During her Ph.D., she was also a Physics Associate at Brookhaven National Laboratory and worked on the OPAL Experiment at CERN.
Career and research.
Aidala was a postdoctoral researcher at University of Massachusetts Amherst, where she studied proton spin decomposition using the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. In addition to numerous research publications, she authored a review article on nucleon spin structure in the journal Reviews of Modern Physics that has been cited over 200 times.
She currently studies nucleon structure and quantum chromodynamics with her research lab at the University of Michigan. The Aidala group's work involves international collaboration to study spin-spin and spin-momentum correlations in a variety of subatomic particles. Her experiments use the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, the Main Injector at Fermilab, and the Large Hadron Collider at CERN.
In 2017, she was selected to serve on a National Academy of Sciences committee to assess the justification for a domestic electron ion collider facility in the United States.
In addition to researching subatomic particle structure, she is working on a foundational physics project deriving the standard mathematical frameworks for Hamiltonian and Lagrangian mechanics from physical assumptions.
Aidala has participated in numerous outreach activities, including Saturday Morning Physics and coordinating physics demonstrations for elementary and middle school students.
In 2013, she wrote an essay about her career path, which was published in the book "Blazing the Trail: Essays by Leading Women in Science". She has also been interviewed on this topic.
Awards and honors.
In 2015, she was awarded a Sloan Research Fellowship and was a recipient of a National Science Foundation CAREER Award in 2018.
In July 2019 she received the Presidential Early Career Award for Scientists and Engineers.


Hot mirror

A hot mirror is a specialized dielectric mirror, a dichroic filter, often employed to protect optical systems by reflecting infrared light back into a light source, while allowing visible light to pass. Hot mirrors can be designed to be inserted into the optical system at an incidence angle varying between zero and 45 degrees, and are useful in a variety of applications where the buildup of waste heat can damage components or adversely affect spectral characteristics of the illumination source. Wavelengths reflected by an infrared hot mirror range from about 750 to 1250 nanometers. By transmitting visible light wavelengths while reflecting infrared, hot mirrors can also serve as dichromatic beam splitters for specialized applications in fluorescence microscopy or optical eye tracking.
Some early digital cameras designed for visible light capture, such as the Associated Press NC2000 and Nikon Coolpix 950, were unusually sensitive to infrared radiation, and tended to produce colours that were contaminated with infrared. This was particularly problematic with scenes that contained strong sources of infrared, such as fires, although the effect could be moderated by inserting a photographic hot mirror filter into the imaging pathway. Conversely, these cameras could be used for infrared photography by inserting a cold mirror filter into the imaging pathway, most commonly by mounting the filter on the front of the lens.
New incandescent bulbs incorporate hot mirrors, increasing efficiency by redirecting unwanted infrared frequencies back to the filament.


Normalized compression distance

Normalized compression distance (NCD) is a way of measuring the similarity between two objects, be it two documents, two letters, two emails, two music scores, two languages, two programs, two pictures, two systems, two genomes, to name a few. Such a measurement should not be application dependent or arbitrary. A reasonable definition for the similarity between two objects is how difficult it is to transform them into each other.
It can be used in information retrieval and data mining for cluster analysis.
Information distance.
We assume that the objects one talks about are finite strings of 0s and 1s. Thus we mean string similarity. Every computer file is of this form, that is, if an object is a file in a computer it is of this form. One can define the information distance between strings formula_1 and formula_2 as the length of the shortest program formula_3 that computes formula_1 from formula_2 and vice versa. This shortest program is in a fixed programming language. For technical reasons one uses the theoretical notion of Turing machines. Moreover, to express the length of formula_3 one uses the notion of Kolmogorov complexity. Then, it has been shown
up to logarithmic additive terms which can be ignored. This information distance is shown to be a metric
(it satisfies the metric inequalities up to a logarithmic additive term), is universal (it minorizes
every computable distance as computed for example from features up to a constant additive term).
Normalized information distance (similarity metric).
The information distance is absolute, but if we want to express similarity, then we are more interested in relative ones. For example, if two strings of length 1,000,000 differ by 1000 bits, then we consider that those strings are relatively more similar than two strings of 1000 bits that differ by 1000 bits. Hence we need to normalize to obtain a similarity metric. This way one obtains the normalized information distance (NID),
where formula_9 is algorithmic information of formula_1 given formula_2 as input. The NID is called `the similarity metric.' since the function formula_12 has been shown to satisfy the basic requirements for a metric distance measure. However, it is not computable or even semicomputable.
Normalized compression distance.
While the NID metric is not computable, it has an abundance of applications. Simply approximating formula_13 by real-world compressors, with formula_14 is the binary length of the file formula_1 compressed with compressor Z (for example "gzip", "bzip2", "PPMZ") in order to make NID easy to apply. Vitanyi and Cilibrasi rewrote the NID to obtain the Normalized Compression Distance (NCD)
The NCD is actually a family of distances parametrized with the compressor Z. The better Z is, the closer the NCD approaches the NID, and the better the results are.
Applications.
The normalized compression distance has been used to fully automatically reconstruct language and phylogenetic trees. It can also be used for new applications of general clustering and classification of natural data in arbitrary domains, for clustering of heterogeneous data, and for anomaly detection across domains. The NID and NCD have been applied to numerous subjects, including music classification, to analyze network traffic and cluster computer worms and viruses, authorship attribution, gene expression dynamics, predicting useful versus useless stem cells, critical networks, image registration, question-answer systems.
Performance.
Researchers from the datamining community use NCD and variants as "parameter-free, feature-free" data-mining tools. One group have experimentally tested a closely related metric on a large variety of sequence benchmarks. Comparing their compression method with 51 major methods found in 7 major data-mining conferences over the past decade, they established superiority of the compression method for clustering heterogeneous data, and for anomaly detection, and competitiveness in clustering domain data.
NCD has an advantage of being robust to noise. However, although NCD appears "parameter-free", practical questions include which compressor to use in computing the NCD and other possible problems.
Comparison with the Normalized Relative Compression (NRC).
In order to measure the information of a string relative to another there is the need to rely on relative semi-distances (NRC). These are measures that do not need to respect symmetry and triangle inequality distance properties. Although the NCD and the NRC seem very similar, they address different questions. The NCD measures how similar both strings are, mostly using the information content, while the NRC indicates the fraction of a target string that cannot be constructed using information from another string. For a comparison, with application to the evolution of primate genomes, see.
Normalized Google distance.
Objects can be given literally, like the literal four-letter genome of a mouse, or the literal text of War and Peace by Tolstoy. For simplicity we take it that all meaning of the object is represented by the literal object itself. Objects can also be given by name, like "the four-letter genome of a mouse," or "the text of `War and Peace' by Tolstoy." There are also objects that cannot be given literally, but only by name, and that acquire their meaning from their contexts in background common knowledge in humankind, like "home" or "red."
We are interested in semantic similarity. Using code-word lengths obtained from the page-hit counts returned by Google from the web, we obtain a semantic distance using the NCD formula and viewing Google as a compressor useful for data mining, text comprehension, classification, and translation. The associated NCD, called the normalized Google distance (NGD) can be rewritten as
where formula_18 denotes the number of pages containing the search term formula_1, and formula_20 denotes the number of pages containing both formula_1 and formula_2,) as returned by Google or any search engine capable of returning an aggregate page count. The number formula_23 can be set to the number of pages indexed although it is more proper to count each page according to the number of search terms or phrases it contains. As rule of the thumb one can multiply the number of pages by, say, a thousand...


Guglielmo Marconi (Piccirilli)

Guglielmo Marconi is a public artwork by Attilio Piccirilli, located at the intersection of 16th and Lamont Streets, N.W., in the Mount Pleasant neighborhood of Washington, D.C., United States. It stands as a tribute to Italian inventor Guglielmo Marconi. It was paid for by public subscription and erected in 1941. The artwork was listed on both the District of Columbia Inventory of Historic Sites and the National Register of Historic Places in 2007. It is a contributing property in the Mount Pleasant Historic District. The monument was originally surveyed as part of the Smithsonian's Save Outdoor Sculpture! survey in 1994.
Description.
The sculpture features two bronze pieces. In the front is a bust of Marconi (approx. 40 x 30 x 16 in.) which sits on a rectangular Stony Creek granite base (approx. 95 x 32 x 18 in.). Behind the bust is the second bronze resting on another granite base (approx. 95 x 72 x 36 in.). The second bronze is an allegorist female figure sitting on a globe with her legs stretched out behind her. She points her proper left arm straight in front of her while her proper right arm is raised and bent at the elbow. She is naked with a small piece of drapery on her lap. According to Piccirilli she is "the Wave", representing "Marconi's contribution to science..."
The base housing the Marconi bust features the inscription on the proper left side:
On the same base's rear:
On the front of the base:
The statue is not without association to fascist art, since Marconi was strongly identified with Italian fascism, and Piccirilli's subsequent work at the Rockefeller center in New York was criticized for using language appropriated by Mussolini.
Acquisition.
The fund for the memorial was begun a year after Marconi's 1937 death. The total sculpture cost after completion was $32,555.


Lenslet

A lenslet is literally a small lens. The fact that distinguishes it from a small lens is that it is part of a lenslet array. A lenslet array consists of a set of lenslets in the same plane. Each lenslet normally has the same focal length.
It has many uses but is commonly found in Shack–Hartmann wavefront sensors and beam homogenization optics for projection systems.


Arunava Gupta

Arunava Gupta from the IBM T.J. Watson Research Center, was awarded the status of Fellow in the American Physical Society, after he was nominated by the Division of Materials Physics in 1998, for contributions to the development of pulsed laser deposition techniques, the use of this technique for the production of materials with novel physical properties, and for original contributions to the understanding of nonequilibrium film-growth mechanisms.


Louis Alan Hazeltine

Louis Alan Hazeltine (August 7, 1886 – May 24, 1964) was an engineer and physicist, the inventor of the Neutrodyne circuit, and the Hazeltine-Fremodyne Superregenerative circuit. He was the founder of the Hazeltine Corporation.
Biography.
Louis Alan Hazeltine was born in Morristown, New Jersey, in 1886 and attended the Stevens Institute of Technology in Hoboken, New Jersey, majoring in electrical engineering. He graduated in 1906 and accepted a job with General Electric corporation.
Hazeltine returned to Stevens to teach, eventually becoming chair of the electrical engineering department in 1917.
The following year he became a consultant for the United States Navy. The Navy job eventually parlayed into a position as an advisor to the U.S. government on radio broadcasting regulation, and later, a position on the National Defense Research Committee during World War II.
Hazeltine was president of the Institute of Radio Engineers in 1936.


Ultracold neutrons

Ultracold neutrons (UCN) are free neutrons which can be stored in traps made from certain materials. The storage is based on the reflection of UCN by such materials under any angle of incidence.
Properties.
The reflection is caused by the coherent strong interaction of the neutron with atomic nuclei. It can be quantum-mechanically described by an effective potential which is commonly referred to as the "Fermi pseudo potential" or the "neutron optical potential". The corresponding velocity is called the "critical velocity" of a material. Neutrons are reflected from a surface if the velocity component normal to the reflecting surface is less than or equal to the critical velocity.
As the neutron optical potential of most materials is below 300 neV, the kinetic energy of incident neutrons must not be higher than this value to be reflected under any angle of incidence, especially for normal incidence. The kinetic energy of 300 neV corresponds to a maximum velocity of 7.6 m/s or a minimum wavelength of 52 nm. As their density is usually very small, UCN can also be described as a very thin ideal gas with a temperature of 3.5 mK.
Due to the small kinetic energy of an UCN, the influence of gravitation is significant. Thus, the trajectories are parabolic. Kinetic energy of an UCN is transformed into potential (height) energy with ~102 neV/m.
The magnetic moment of the neutron, produced by its spin, interacts with magnetic fields. The total energy changes with ~60 neV/T.
History.
It was Enrico Fermi who realized first that the coherent scattering of slow neutrons would result in an effective interaction potential for neutrons traveling through matter, which would be positive for most materials. The consequence of such a potential would be the total reflection of neutrons slow enough and incident on a surface at a glancing angle. This effect was experimentally demonstrated by Fermi and Walter Henry Zinn and Fermi and Leona Marshall. The storage of neutrons with very low kinetic energies was predicted by Yakov Borisovich Zel'dovich and experimentally realized simultaneously by groups at Dubna and Munich.
UCN production.
There are various methods for the production of UCN. Such facilities have been built and are in operation:
Reflecting materials.
Any material with a positive neutron optical potential can reflect UCN. The table on the right gives an (incomplete) list of UCN reflecting materials including the height of the neutron optical potential ("VF") and the corresponding critical velocity ("vC"). The height of the neutron optical potential is isotope-specific. The highest known value of VF is measured for 58Ni: 335 neV (vC = 8.14 m/s). It defines the upper limit of the kinetic energy range of UCN.
The most widely used materials for UCN wall coatings are beryllium, beryllium oxide, nickel (including 58Ni) and more recently also diamond-like carbon (DLC).
Non-magnetic materials such as DLC are usually preferred for the use with polarized neutrons. Magnetic centers in e.g. Ni can lead to de-polarization of such neutrons upon reflection. If a material is magnetized, the neutron optical potential is different for the two polarizations, caused by
where formula_2 is the magnetic moment of the neutron and formula_3 the magnetic field created on the surface by the magnetization.
Each material has a specific loss probability per reflection,
which depends on the kinetic energy of the incident UCN ("E") and the angle of incidence ("θ"). It is caused by absorption and thermal upscattering. The loss coefficient η is energy-independent and typically of the order of 10−4 to 10−3.
Experiments with UCN.
The production, transportation and storage of UCN is currently motivated by their usefulness as a tool to determine properties of the neutron and to study fundamental physical interactions. Storage experiments have improved the accuracy or the upper limit of some neutron related physical values.
Measurement of the neutron lifetime.
Today's world average value for the neutron lifetime is formula_5, to which the experiment of Arzumanov et al. contributes strongest. Ref. measured formula_6 by storage of UCN in a material bottle covered with Fomblin oil. Using traps with different surface to volume ratios allowed them to separate storage decay time and neutron lifetime from each other. There is another result, with even smaller uncertainty, but which is not included in the World average. It was obtained by Serebrov et al., who found formula_7. Thus, the two most precisely measured values deviate by 5.6 σ.
Measurement of the neutron electric dipole moment.
The neutron electric dipole moment (nEDM) is a measure for the distribution of positive and negative charge inside the neutron. No nEDM has been found currently (Oct. 2019). Today's lowest value for the upper limit of the nEDM was measured with stored UCN (see main article).
Observation of the gravitational interactions of the neutron.
Physicists have observed quantized states of matter under the influence of gravity for the first time. Valery Nesvizhevsky of the Institut Laue-Langevin and colleagues found that cold neutrons moving in a gravitational field do not move smoothly but jump from one height to another, as predicted by quantum theory. The finding could be used to probe fundamental physics such as the equivalence principle, which states that different masses accelerate at the same rate in a gravitational field (V Nesvizhevsky "et al." 2001 Nature 415 297). UCN spectroscopy has been used to limit scenarios including dark energy, chameleon fields, and new short range forces.
Measurement of the A-coefficient of the neutron beta decay correlation.
The first reported measurement of the beta-asymmety using UCN is from a Los Alamos group in 2009. The LANSCE group published precision measurements with polarized UCN the next year. Further measuments by these groups and others have led to the current world average:


Greg Parker (physicist)

Greg Parker (b. 1954) is a British physicist. He served as a Professor of Photonics at the University of Southampton. He spent 23 years in research and lecturing.
Career.
He now runs Parker Technology. His research interests included the design and construction of Ultra High Vacuum (UHV) compatible semiconductor deposition systems, and the design and fabrication of Photonic Crystal circuits and devices. Most recently, he became interested in deep-sky imaging, macrophotography, microphotography, pin-hole camera photography and high-speed flash photography. He is the designer and developer of ultra-high speed Xenon flash equipment. His photographic work is featured on the Scientific Artist web site.
He has 13 patents on optical devices and circuits and created three successful companies. His most recent spin-out from Southampton University was Mesophotonics Ltd.
He is constructing the world's most powerful amateur deep-sky imaging system, the mini-WASP imaging array, named after the SuperWASP array built for the Wide Angle Search for Planets.
Publications.
Parker published over 120 refereed journal and conference papers, a textbook on Solid-State Physics, "Introductory Semiconductor Device Physics", a "how to" book on astrophotography "Making Beautiful Deep-Sky Images" and a large format book of deep-sky images taken from the New Forest Observatory, called "Star Vistas".
Recognition.
Parker is a Chartered Engineer, a Chartered Physicist, and a Fellow of the Institute of Physics.


Born (crater)

Born is a small lunar impact crater located near the eastern edge of the Moon, to the northeast of the prominent crater Langrenus. It was previously designated Maclaurin Y before being named by the IAU in 1979. Maclaurin itself lies to the north.
This crater is circular and generally cup-shaped, with dark patches stretching from the midpoint toward the northeastern rim. It is otherwise undistinguished.


Floyd K. Richtmyer

Floyd Karker Richtmyer (October 12, 1881 – November 7, 1939) was a physicist and educator in the United States.
Biography.
Richtmyer was born October 12, 1881, in the rural community of Cobleskill, New York.
He studied with Perley Nutting at Cornell University; both were students of Edward L. Nichols. Richtmyer graduated with his A.B. in 1904 and Ph.D. in 1910.
He taught physics at Drexel University, but returned to Cornell as instructor in 1906, where he remained for the duration of his career.
He became assistant professor of physics in 1911, full professor in 1918, and then dean of the graduate school in 1931.
He also taught summer classes at the University of California, Berkeley, Stanford University, and Columbia University.
When the new Journal of the Optical Society of America (JOSA) began in 1917, Richtmyer wrote the very first article, on page 1 of volume 1, titled "Opportunities for Research."
In 1918 and 1919, he served as OSA’s vice president, and president in 1920. In 1928, he published a very popular textbook "Introduction to Modern Physics" (with E.H.Kennard,T. Lauritsen and John N. Cooper in later revisions). In 1933, he succeeded Paul Foote as editor of JOSA, and he served until his death. He published 11 items in JOSA, mostly in the period between 1922 and 1929.
His son Robert Davis Richtmyer was also a physicist and mathematician. He had a daughter Sarah R. Richtmyer who married John T. Mann, and another son Lawson E. Richtmyer. In 1929 he was awarded the Louis E. Levy Medal of the Franklin Institute for the study of X-rays.
After his death from a coronary thrombosis on November 7, 1939, the American Association of Physics Teachers, which he had helped form, established the Richtmyer Memorial Award, which is conferred annually, and is typically given to educators who have made outstanding contributions as teachers in their fields. It is awarded to those who have not only produced important current research in physics, but to those who have, by means of communication to both students and other educators, imparted information and motivation to participants in the field. Winners deliver the Richtmyer Memorial Lecture.


Edward Greitzer

Edward M. Greitzer is an American physicist currently the H. N. Slater Professor of Aeronautics and Astronautics at Massachusetts Institute of Technology. He is a Fellow of the American Institute of Aeronautics and Astronautics, Royal Academy of Engineering and ASME. His vast research includes turbomachinery, fluid mechanics, thermodynamics, energy, internal flow, fluid systems and gas turbines and engine design.


W. Lewis Hyde

Walter Lewis Hyde (1919-2003) was an American physicist, an early contributor to the field of fiber optics. He held patents for devices used in ophthalmology, as well as a panoramic rear-view mirror for automobiles.
Originally from Minnesota, he studied physics at Harvard University. He worked at the Polaroid Corporation in the nascent field of fiber optics. He married Elizabeth Sanford Hyde, and they had six children, including Lewis Hyde. In the 1950s, he worked for the London Office of Naval Research, tracking European physics research. He went on to become the Director of Development at the American Optical Company, in Southbridge, Massachusetts, and then a professor of optics at the University of Rochester. He then changed gears to administration, and served as provost of New York University until 1972. He served as President of the Optical Society of America in 1970
He married Elizabeth Sanford, who became the President of The Woodstock Academy's Board of Trustees and helped lead The Academy's renovation and building project in the early 90s. The library and media center there is named after her.


Dan Walls

Daniel Frank Walls FRS (13 September 1942 – 12 May 1999) was a New Zealand theoretical physicist specialising in quantum optics.
Education.
Walls gained a BSc in physics and mathematics and a first class honours MSc in physics at the University of Auckland. He then went to Harvard University as a Fulbright Scholar, obtaining his PhD in 1969. He was supervised by Roy J. Glauber who was later awarded a Nobel prize in 2005.
Career and research.
After holding postdoctoral research positions in Auckland and Stuttgart, Walls became a senior lecturer in physics at the University of Waikato in 1972, where he became professor in 1980. Together with his colleague Crispin Gardiner, during the next 25 years he established a major research centre for theoretical quantum optics in New Zealand and built active and productive collaborations with groups throughout the world.
In 1987 he moved to the University of Auckland as professor of theoretical physics.
His major research interests centred on the interaction and similarities between light and atoms. He was notable for his wide-ranging expertise in relating theory to experiment, and was involved in all major efforts to understand non-classical light. A seminal paper by Walls with his first graduate student Howard Carmichael, showed how to create antibunched light, in which photons arrive at regular intervals, rather than randomly.
Walls was a pioneer in the study of ways that the particle-like nature of light (photons) could be controlled to make optical systems less susceptible to unwanted fluctuations, in particular by the use of squeezed light, a concept formulated by Carlton Caves. In squeezed light, some fluctuations can be made very small provided other fluctuations are correspondingly large.
He made major contributions to the theory of quantum measurement such as those involving Albert Einstein's"which-path" experiment, and the quantum nondemolition measurement. Walls also used a simple field theoretical approach to explain and corroborate Dirac's description of photon interference and in particular Dirac's statement "that a photon interferes only with itself."
In the later stages of his career he focused his research efforts on the theoretical aspects of the newly created state of matter, the Bose–Einstein condensate (BECs). Some of his contributions in the field include the prediction of the interference signature of quantized vortices, and the collapses and revivals of the Josephson coupled BECs.
Awards and honours.
Walls was elected a Fellow of the Royal Society (FRS) in 1992. Walls was also elected Fellow of the American Physical Society and the Royal Society of New Zealand (FRSNZ). In 1995 he was awarded the Dirac Prize for theoretical physics.
The Dodd-Walls Centre for Photonic and Quantum Technologies, a New Zealand Centre of Research excellence based in the University of Otago, was named after Jack Dodd and Dan Walls in recognition of their pioneering roles in establishing New Zealand's as an internationally recognised standing in Photonics, Quantum Optics and Ultra-Cold atoms.
Personal life.
Dan Walls had one sister. He married Fari Khoy in 1968 with whom he had one son, Mark, in 1980. This marriage ended in 1986. His partner in later years was Pamela King. Walls died of cancer at hospital, in Auckland, aged 57.


First International Statistical Congress

The First International Statistical Congress was held on September 19th, 1853 in Brussels, Belgium, with twenty-six countries in attendance. It was principally organised by Belgian astronomer and statistician Adolphe Quetelet, who envisioned a standardisation of European units of measurement to allow for collaborative research to be done between nations. The International Statistical Congress was therefore designed to create tentative guidelines for the process of unifying measurement in statistical research, and it was also aimed to establish leadership and regulations for future congresses. Although the First Congress was followed by seven further sessions across Europe between 1853 and 1876, it was unsuccessful in its initial goals to standardise all measurements across nations, as it occurred at a time when international conferences failed to overcome national interests.
Congress development.
In 1851, Queen Victoria’s husband, Prince Albert, organised the first World’s Fair held at the Great Exhibition of London. As the World’s Fair attracted scholars from different parts of Europe, Prince Albert began the task of influencing public opinion favourably towards the standardisation of international statistics. One of these scholars was the Belgian astronomer and statistician Adolphe Quetelet, who became convinced of the necessity for an international congress to unify the various methods of statistical measurement across different nations. Upon his return to Brussels, Quetelet wrote to Prince Albert expressing his desire to collaborate in the creation of an international statistical congress. Aided by members of the Belgian Statistical Commission, Quetelet and Prince Albert agreed to work together to create the First International Statistical Congress in Brussels.
The purpose of the International Statistical Congress went beyond simply standardising units of measurement throughout Europe. The founders believed that a common means of measuring, to use the same units to represent the same results, was necessary. It would allow for easier transfer of data between nations so that officials could interpret other states’ findings without previously converting them. In doing so, this would not only create a sense of unity amongst European nations, but it would also greatly increase the efficacy of statistical-based research, allowing for bigger scientific initiatives to be taken in the hopes of improving living conditions across Europe.
Attendance and roles.
States in attendance.
A total of twenty-six states and their leading statisticians participated in the Congress. Officially, the states represented were:
Administrative roles.
The first order of business for the Congress was to establish administrative roles. Ferdinand Piercot, Belgium's Minister of the Interior, was elected as President of the Congress; William Farr of England, Louis-René Villermé of France, Karl Friedrich Wilhelm Dieterici of then-Prussia, Carl Mittermaier of then-Baden, Jan Akersdyck of the Netherlands, Ramón de la Sagra of Spain, Karl von Czoernig of Austria, and Bertini of Sardinia were named Vice-Presidents. A system of publications and operations, along with an official and regular correspondence scheme between members and nations, was devised for implementation in the Congress. The Congress proceeded to appoint one person by nation responsible for receiving and reporting new national scientific developments, and lastly, created the Bulletin of the Central Statistical Commission to publish an annual newsletter of statistical communications and documents relevant to the committee.
National interests.
Despite the Congress's emphasis on international collaboration, a great portion of the conference was first spent highlighting domestic statistics and measurement processes to gain a better understanding of how best to begin standardisation. Delegates in attendance spoke of the methods in which their nations compiled statistical information. However, this was not without ulterior motives. Often, participating nations exerted their own interests to influence the agenda to varying degrees. For example, the Belgian commission expressed the need to focus on economic statistics for workers. Vienna introduced ethnographic statistics concerning demographics and populations at the encouragement of Karl von Czoernig, the director of the Habsburg’s statistical service, who believed in the viability of international demographic analysis. Furthermore, national interests directly conflicted with the gathering of statistical information. In France, statisticians were prompted to present misleading demographic statistics that would underestimate the population growth of the country as not to raise concerns among their European neighbours regarding the balance of power.
Congress accomplishments.
Organisations for standard measurement.
The Congress first decided that if a united system of information was needed in international statistics, they would have to establish a standard template for officials across nations to follow when informing the public of various statistics. As a result, the members of the Congress concluded that it was necessary to create a certain manner of tables and statements to be implemented across Europe. Likewise, they recommended that each national government establish a Central Statistical Commission, which would be uniform throughout the continent, and ensure that the standardisation of statistics by these officials would be done according to the new measures. In addition to these Central Commissions, the Congress advised that local Commissions also be established for the purpose of overcoming any local irregularities concerning the measurement process of statistics previously overlooked.
Industry and agriculture.
Collaboratively, the First International Statistical Congress took into account the nature of industries throughout European nations, including agriculture, mining, manufacturing, and commercial enterprises which consisted of import and export statistics. For agriculture specifically, censuses were designed to measure what and how much was produced, what farm equipment was used, and how many workers and animals were present; these took place once every ten years in the winter, after the annual harvests to ensure availability of farmers. Industrial censuses measured what kind of mechanical forces were prevalent in specific industries, such as hydraulics or steam power, as well as demographics like the number of workers, their salaries, and the quantity of goods produced. For example, mines would need to report the size and depth of the mine, as well as the methods of extraction, the good extracted, and how much was produced. The Congress agreed that in order to record the most precise information possible using these agricultural censuses, it was necessary to conduct surveys simultaneously and collect the results through local Commissions, at which point a final table could be created and used for comparison against other states.
Urbanisation and education.
The Congress sought to standardise certain measurements for cities and their inhabitants. In terms of demographics and population, metrics like emigration and immigration were analysed based on origin, health condition, and number of people departing from and arriving at certain nations. As well, the cause of the immigration was considered, such as political or religious reasonings. Originally, the Congress advocated that any censuses regarding immigration and emigration consist of personal details including the motive for emigration, as well as the capital which the migrant would carry with them. However, this led to conflicting discussion on the merits of asking questions that seemed to be too inquisitive, and thus the final proposed censuses avoided questions seen as overtly personal. The working class was also examined from an economic angle, through their savings and expenses from food, rent, and clothing. Here, data was gathered from one family or household every ten years in the month of December. Additionally, personal information such as Indigenous status, language spoken, religion, place of birth, education level and profession, number of rooms in one’s house, and illnesses were also included in the census.
Regarding cities themselves, studies were conducted in an attempt to compare countries’ standards of public health, criminal behaviour, and property partitioning. For property, the Congress examined different states’ measurements of who inherited property and how much was inherited after death.
Geography and navigation.
To standardise physical terrain across nations to create uniformity, the Congress proposed a system of triangulation to measure distance for each country’s map if states were able to provide an adequate, acceptable one. If not, the accepted solution was to begin with the largest possible approximation of triangulation, and gain closer results by subdividing each triangle until the resulting map was satisfactory. This process was done immediately after following surveys of land, and was subsequently followed up by closer examinations of each nation’s soil and flora.
Navigation was also a component that the Congress looked at; the participating countries agreed to keep a measure of the number of boats entering and exiting each sea, as well as the number of people and cargo aboard. It was required to do so in a manner that differentiated between classical sailboats and newer steam-powered boats.
Spread of information.
Traditionally, methods to transmit information at the time of the Congress included introductory letters, scientific correspondence, and face-to-face visits. However, the Congress coincided with growth of more modern methods of communication, such as telegrams. This allowed for a shift in the means of transmitting knowledge and further collaboration between nations. It was the hope that nations would use telegrams to produce quicker and more efficient communications between each other, but national interests prevailed over international cooperation, which adversely impacted the effect that telegrams had on statistical standardisation overall.
Aftermath.
Despite many of the major areas talked about during the First International Statistical Congress, no major progress was achieved in standardising measurement across Europe. This was partly attributed to an overall lack of cohesive communication, an inability for the Congress to gather and verify data, and a growing tension in nationalist beliefs in states. In particular, France and Germany were culprits of misrepresentation of population demographics. Moreover, nationalism played a large role in the failure of standardising statistical information across Europe; domestic governments' desire to push individual agendas overcame the desire to develop international uniformity.
The First Congress would give way to seven more International Statistical Congresses, which took place across Europe from 1855 to 1876.
These include:
In addition, after the eighth Congress, the Permanent Commission of the International Statistical Congress was created in 1872 to guide and facilitate cooperation on developing international statistics. They would assemble four times in the following eight years. The backlash to all of these iterations of the International Statistical Congress, however, mainly centred on how all states involved were ultimately unable to accomplish anything of note. In each Congress, the agenda would often be populated with topics that were desirable to certain nations and undesirable to others. As a result, collaboration could not be achieved and the Congresses failed to progress further.
Further reading.
The Permanent Commission of the International Statistical Congress (1872).
Second International Statistical Congress, Paris (1855)
Third International Statistical Congress, Vienna (1857)
Fourth International Statistical Congress, London (1860)
Fifth International Statistical Congress, Berlin (1863)
Sixth International Statistical Congress, Florence (1867)
Seventh International Statistical Congress, The Hague (1869)
Eighth International Statistical Congress, St. Petersburg (1872)


Planck (crater)

Planck is a large lunar impact crater, approximately 319 kilometers in diameter, that is located in the southern hemisphere of the Moon, on the far side as seen from the Earth. It lies to the west of the walled plain Poincaré, another enormous formation only slightly larger than Planck. Both formations are larger than the walled plain Bailly, the largest crater on the near side. Lying across the southeast rim of Planck is the crater Prandtl, to the northeast is Hildegard, and to the west is Fechner.
Description.
Like many lunar formations of this size, the outer rim has been damaged and eroded by lesser impacts, leaving a rugged ring of peaks and ridges that is notched and incised by small craters. The western rim of this walled plain is neatly overlain by a long lunar valley designated the Vallis Planck. Despite its name, however, this valley is actually radial to the walled plain Schrödinger to the south. The valley is approximately 503 kilometers in length.
The most notable feature on the interior floor of Planck is a multi-crater formation in the northern half consisting of Planck W, Planck Y, Planck Z, Planck B, and Planck A. The interior of Planck Y has been almost completely flooded by lava, leaving only a shallow perimeter. Likewise Planck Z has been flooded, although its rim is somewhat more prominent. The interior of Planck B is partly occupied by a concentric crater, and the floor contains several clefts. Parts of the remaining floor of Planck are level and smooth, at least in comparison with the surrounding terrain. This is particularly so in an arc along the northern inner wall. The southern half of the crater is somewhat more irregular, although still forming level plains in places. There are many small craters across the interior of Planck, and a few ghost-crater remnants.
Satellite craters.
By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Planck.


Ernst Emil Alexander Back

Ernst Emil Alexander Back (October 21, 1881 – June 20, 1959) was a German physicist, born in Freiburg. He attended school in Strasbourg until 1900, and from 1902 until 1906 studied law in Strasbourg, Munich, and Berlin. He then worked in the legal profession in Alsace-Lorraine until 1909, afterwards taking leave to study physics in Tübingen. He retired from the legal profession in 1912, and earned his Ph.D. in 1913. His thesis, titled "Zur Prestonschen Regel", was on the subject of what would later be called the Paschen-Back effect, and was named after Back and Friedrich Paschen.
Between 1914 and 1918 he served with the German Army during World War I. Following this conflict he became head of a Veifa-Werke laboratory in Frankfurt am Main, a company that produced electrical and X-ray equipment. In 1920 he left to become an assistant at the Physics Institute in Tübingen. He was promoted to professor in 1926 at Hohenheim University, and became a full professor in 1929. He remained at this post until 1936 when he returned to become a professor at Tübingen.
From 1926 to 1927 Samuel Abraham Goudsmit worked with Back to make the first measurement of nuclear spin and its Zeeman effect.
Back retired in 1948, and died in Munich over a decade later. The crater Back on the Moon is named in his memory.


Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default. The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time.
Definition of entropy and differential entropy.
If formula_1 is a discrete random variable with distribution given by
then the entropy of formula_1 is defined as
If formula_1 is a continuous random variable with probability density formula_6, then the differential entropy of formula_1 is defined as
The quantity formula_9 is understood to be zero whenever formula_10.
This is a special case of more general forms described in the articles Entropy (information theory), Principle of maximum entropy, and differential entropy. In connection with maximum entropy distributions, this is the only one needed, because maximizing formula_11 will also maximize the more general forms.
The base of the logarithm is not important as long as the same one is used consistently: change of base merely results in a rescaling of the entropy. Information theorists may prefer to use base 2 in order to express the entropy in bits; mathematicians and physicists will often prefer the natural logarithm, resulting in a unit of nats for the entropy.
The choice of the measure formula_12 is however crucial in determining the entropy and the resulting maximum entropy distribution, even though the usual recourse to the Lebesgue measure is often defended as "natural"
Distributions with measured constants.
Many statistical distributions of applicable interest are those for which the moments or other measurable quantities are constrained to be constants. The following theorem by Ludwig Boltzmann gives the form of the probability density under these constraints.
Continuous case.
Suppose "S" is a closed subset of the real numbers R and we choose to specify "n" measurable functions "f"1...,"f""n" and "n" numbers "a"1...,"a""n". We consider the class "C" of all real-valued random variables which are supported on "S"
(i.e. whose density function is zero outside of "S") and which satisfy
the "n" moment conditions:
If there is a member in "C" whose density function is positive everywhere in "S", and if there exists a maximal entropy distribution for "C", then its probability density "p"("x") has the following shape:
where we assume that formula_15. The constant formula_16 and the "n" Lagrange multipliers formula_17 solve the constrained optimization problem with formula_18 (this condition ensures that formula_19 integrates to unity):
Using the Karush–Kuhn–Tucker conditions, it can be shown that the optimization problem has a unique solution, because the objective function in the optimization is concave in formula_21.
Note that if the moment conditions are equalities (instead of inequalities), that is,
then the constraint condition formula_23 is dropped, making the optimization over the Lagrange multipliers unconstrained.
Discrete case.
Suppose formula_24 is a (finite or infinite) discrete subset of the reals and we choose to specify formula_25 functions "f"1...,"f""n" and "n" numbers "a"1...,"a""n". We consider the class "C" of all discrete random variables "X" which are supported on "S" and which satisfy the "n" moment conditions
If there exists a member of "C" which assigns positive probability to all members of "S" and if there exists a maximum entropy distribution for "C", then this distribution has the following shape:
where we assume that formula_28 and the constants formula_29 solve the constrained optimization problem with formula_18:
Again, if the moment conditions are equalities (instead of inequalities), then the constraint condition formula_23 is not present in the optimization.
Proof in the case of equality constraints.
In the case of equality constraints, this theorem is proved with the calculus of variations and Lagrange multipliers. The constraints can be written as
We consider the functional
where formula_35 and formula_36 are the Lagrange multipliers. The zeroth constraint ensures the second axiom of probability. The other constraints are that the measurements of the function are given constants up to order formula_25. The entropy attains an extremum when the functional derivative is equal to zero:
It is an exercise for the reader that this extremum is indeed a maximum. Therefore, the maximum entropy probability distribution in this case must be of the form (formula_39)
The proof of the discrete version is essentially the same.
Uniqueness of the maximum.
Suppose formula_41, formula_42 are distributions satisfying the expectation-constraints. Letting formula_43 and considering the distribution formula_44 it is clear that this distribution satisfies the expectation-constraints and furthermore has as support formula_45. From basic facts about entropy, it holds that formula_46. Taking limits formula_47 and formula_48 respectively yields formula_49.
It follows that a distribution satisfying the expectation-constraints and maximising entropy must necessarily have full support — "i. e." the distribution is almost everywhere positive. It follows that the maximising distribution must be an internal point in the space of distributions satisfying the expectation-constraints, that is, it must be a local extreme. Thus it suffices to show that the local extreme is unique, in order to show both that the entropy-maximising distribution is unique (and this also shows that the local extreme is the global maximum).
Suppose formula_50 are local extremes. Reformulating the above computations these are characterised by parameters formula_51 via formula_52 and similarly for formula_42, where formula_54. We now note a series of identities: Via the satisfaction of the expectation-constraints and utilising gradients/directional derivatives, one has formula_55 and similarly for formula_56. Letting formula_57 one obtains:
where formula_59 for some formula_60. Computing further one has
where formula_62 is similar to the distribution above, only parameterised by formula_63. "Assuming" that no non-trivial linear combination of the observables is almost everywhere (a.e.) constant, (which "e.g." holds if the observables are independent and not a.e. constant), it holds that formula_64 has non-zero variance, unless formula_65. By the above equation it is thus clear, that the latter must be the case. Hence formula_66, so the parameters characterising the local extrema formula_50 are identical, which means that the distributions themselves are identical. Thus, the local extreme is unique and by the above discussion, the maximum is unique—provided a local extreme actually exists.
Caveats.
Note that not all classes of distributions contain a maximum entropy distribution. It is possible that a class contain distributions of arbitrarily large entropy (e.g. the class of all continuous distributions on R with mean 0 but arbitrary standard deviation), or that the entropies are bounded above but there is no distribution which attains the maximal entropy. It is also possible that the expected value restrictions for the class "C" force the probability distribution to be zero in certain subsets of "S". In that case our theorem doesn't apply, but one can work around this by shrinking the set "S".
Examples.
Every probability distribution is trivially a maximum entropy probability distribution under the constraint that the distribution have its own entropy. To see this, rewrite the density as formula_68 and compare to the expression of the theorem above. By choosing formula_69 to be the measurable function and
to be the constant, formula_6 is the maximum entropy probability distribution under the constraint
Nontrivial examples are distributions that are subject to multiple constraints that are different from the assignment of the entropy. These are often found by starting with the same procedure formula_69 and finding that formula_74 can be separated into parts.
A table of examples of maximum entropy distributions is given in Lisman (1972) and Park & Bera (2009)
Uniform and piecewise uniform distributions.
The uniform distribution on the interval ["a","b"] is the maximum entropy distribution among all continuous distributions which are supported in the interval ["a", "b"], and thus the probability density is 0 outside of the interval. This uniform density can be related to Laplace's principle of indifference, sometimes called the principle of insufficient reason. More generally, if we're given a subdivision "a"="a"0 < "a"1 < ... < "a""k" = "b" of the interval ["a","b"] and probabilities "p"1...,"p""k" which add up to one, then we can consider the class of all continuous distributions such that
The density of the maximum entropy distribution for this class is constant on each of the intervals ["a""j"-1,"a""j"). The uniform distribution on the finite set {"x"1...,"x""n"} (which assigns a probability of 1/"n" to each of these values) is the maximum entropy distribution among all discrete distributions supported on this set.
Positive and specified mean: the exponential distribution.
The exponential distribution, for which the density function is
is the maximum entropy distribution among all continuous distributions supported in [0,∞) that have a specified mean of 1/λ.
Specified variance: the normal distribution.
The normal distribution N(μ,σ2), for which the density function is
has maximum entropy among all real-valued distributions supported on (−∞,∞) with a specified variance "σ"2 (a particular moment). Therefore, the assumption of normality imposes the minimal prior structural constraint beyond this moment. (See the differential entropy article for a derivation.)
In the case of distributions supported on [0,∞), the maximum entropy distribution depends on relationships between the first and second moments. In specific cases, it may be the exponential distribution, or may be another distribution, or may be undefinable.
Discrete distributions with specified mean.
Among all the discrete distributions supported on the set {"x"1...,"x""n"} with a specified mean μ, the maximum entropy distribution has the following shape:
where the positive constants "C" and "r" can be determined by the requirements that the sum of all the probabilities must be 1 and the expected value must be μ.
For example, if a large number "N" of dice are thrown, and you are told that the sum of all the shown numbers is "S". Based on this information alone, what would be a reasonable assumption for the number of dice showing 1, 2, ..., 6? This is an instance of the situation considered above, with {"x"1...,"x"6} = {1...,6} and μ = "S"/"N".
Finally, among all the discrete distributions supported on the infinite set formula_79 with mean μ, the maximum entropy distribution has the shape:
where again the constants "C" and "r" were determined by the requirements that the sum of all the probabilities must be 1 and the expected value must be μ. For example, in the case that "xk = k", this gives
such that respective maximum entropy distribution is the geometric distribution.
Circular random variables.
For a continuous random variable formula_82 distributed about the unit circle, the Von Mises distribution maximizes the entropy when the real and imaginary parts of the first circular moment are specified or, equivalently, the circular mean and circular variance are specified.
When the mean and variance of the angles formula_82 modulo formula_84 are specified, the wrapped normal distribution maximizes the entropy.
Maximizer for specified mean, variance and skew.
There exists an upper bound on the entropy of continuous random variables on formula_85 with a specified mean, variance, and skew. However, there is "no distribution which achieves this upper bound", because formula_86 is unbounded except when formula_87 (see Cover & Thomas (2006: chapter 12)).
However, the maximum entropy is -achievable: a distribution's entropy can be arbitrarily close to the upper bound. Start with a normal distribution of the specified mean and variance. To introduce a positive skew, perturb the normal distribution upward by a small amount at a value many larger than the mean. The skewness, being proportional to the third moment, will be affected more than the lower order moments.
Maximizer for specified mean and deviation risk measure.
Every distribution with log-concave density is a maximal entropy distribution with specified mean "μ" and Deviation risk measure "D".
In particular, the maximal entropy distribution with specified mean formula_88 and deviation formula_89 is:
Other examples.
In the table below, each listed distribution maximizes the entropy for a particular set of functional constraints listed in the third column, and the constraint that x be included in the support of the probability density, which is listed in the fourth column. Several examples (Bernoulli, geometric, exponential, Laplace, Pareto) listed are trivially true because their associated constraints are equivalent to the assignment of their entropy. They are included anyway because their constraint is related to a common or easily measured quantity. For reference, formula_96 is the gamma function, formula_97 is the digamma function, formula_98 is the beta function, and is the Euler-Mascheroni constant.


Ian Hinchliffe

Ian Hinchliffe (born 1952) is a British physicist at Lawrence Berkeley National Laboratory. He obtained his BA and his D.Phil. in physics from Oxford University.
In 1983 he became a Staff Senior Scientist at Lawrence Berkeley National Laboratory, where he served as head of the theoretical physics group from 1992 to 1999.
Trained in theoretical physics, his primary activity is with the ATLAS experiment at CERN's Large Hadron Collider, which he joined in 1996; he served as ATLAS physics coordinator in 2006–2007 and currently heads Berkeley Lab's ATLAS group. His research emphasizes the importance of experiment in testing theoretical ideas, and in driving theoretical developments aimed at understanding interactions among fundamental particles. Much of his research looks to show how the Standard Model can be tested at hadron colliders.
In 2011 Hinchliffe with Chris Quigg, Estia Eichten and Kenneth Lane won the J. J. Sakurai Prize for Theoretical Particle Physics "For their work, separately and collectively, to chart a course of the exploration of TeV scale physics using multi-TeV hadron colliders"


Jet quenching

In high-energy physics, jet quenching is a phenomenon that can occur in the collision of ultra-high-energy particles. In general, the collision of high-energy particles can produce jets of elementary particles that emerge from these collisions. Collisions of ultra-relativistic heavy-ion particle beams create a hot and dense medium comparable to the conditions in the early universe, and then these jets interact strongly with the medium, leading to a marked reduction of their energy. This energy reduction is called "jet quenching".
Physics background.
In the context of high-energy hadron collisions, quarks and gluons are collectively called partons. The jets emerging from the collisions originally consist of partons, which quickly combine to form hadrons, a process called hadronization. Only the resulting hadrons can be directly observed. The hot, dense medium produced in the collisions is also composed of partons; it is known as a quark–gluon plasma (QGP). In this realm, the laws of physics that apply are those of quantum chromodynamics (QCD).
High-energy nucleus-nucleus collisions make it possible to study the properties of the QGP medium through the observed changes in the jet fragmentation functions as compared to the unquenched case. According to QCD, high-momentum partons produced in the initial stage of a nucleus-nucleus collision will undergo multiple interactions inside the collision region prior to hadronization. In these interactions, the energy of the partons is reduced through collisional energy loss and medium-induced gluon radiation, the latter being the dominant mechanism in a QGP. The effect of jet quenching in QGP is the main motivation for studying jets as well as high-momentum particle spectra and particle correlations in heavy-ion collisions. Accurate jet reconstruction will allow measurements of the jet fragmentation functions and consequently the degree of quenching and therefore provide insight on the properties of the hot dense QGP medium created in the collisions.
Experimental evidence of jet quenching.
First evidence of parton energy loss has been observed at the Relativistic Heavy Ion Collider (RHIC) from the suppression of high-pt particles studying the nuclear modification factor and the suppression of back-to-back correlations.
In ultra-relativistic heavy-ion collisions at center-of-mass energy of 2.76 and 5.02 TeV at the Large Hadron Collider (LHC), interactions between the high-momentum parton and the hot, dense medium produced in the collisions, are expected to lead to jet quenching. Indeed, in November 2010 CERN announced the first direct observation of jet quenching, based on experiments with "heavy-ion collisions", which involved ATLAS, CMS and ALICE.


Eli Barkai

Eli Barkai is a professor of physics at Bar-Ilan University, located in Ramat-Gan, Israel.
Education.
Barkai studied physics in Tel Aviv University, completing his Ph.D in 1998. He then joined Bob Silbey at MIT for his post-doctoral studies. In 2002 he joined the faculty of Notre Dame University and in 2004 returned to Israel to Bar Ilan University where he became a full professor in 2010.
Research.
His main research is in the field of non-equilibrium statistical mechanics. In particular he helped develop the theory of
fractional kinetic equations for anomalous diffusion and relaxation, theory of single molecule spectroscopy, and weak ergodicity breaking.
Among the physical systems he studied are blinking of quantum dots, the diffusion of cold atoms in atomic traps and the diffusion of single molecules within a live cell.
Honors and awards.
Barkai has received several prizes: the Krill prize (2006, selected by the Wolf foundation), the Michael Bruno Memorial award (2009, selected by Yad Hanadiv) and the Friedrich Wilhelm Bessel Research award (2011, selected by the Alexander von Humboldt foundation).
Family.
Married to Adina Alster, daughter of Jonas Alster. Barkai has three children


5006 Teller


Leona Woods

Leona Harriet Woods (August 9, 1919 – November 10, 1986), later known as Leona Woods Marshall and Leona Woods Marshall Libby, was an American physicist who helped build the first nuclear reactor and the first atomic bomb.
At age 23, she was the youngest and only female member of the team which built and experimented with the world's first nuclear reactor (then called a "pile"), Chicago Pile-1, in a project led by her mentor Enrico Fermi. In particular, Woods was instrumental in the construction and then utilization of geiger counters for analysis during experimentation. She was the only woman present when the reactor went critical. She worked with Fermi on the Manhattan Project, and, together with her first husband John Marshall, she subsequently helped solve the problem of xenon poisoning at the Hanford plutonium production site, and supervised the construction and operation of Hanford's plutonium production reactors.
After the war, she became a fellow at Fermi's Institute for Nuclear Studies at the University of Chicago. She later worked at the Institute for Advanced Study in Princeton, New Jersey, the Brookhaven National Laboratory, and New York University, where she became a professor in 1962. Her research involved high-energy physics, astrophysics and cosmology. In 1966 she divorced Marshall and married Nobel laureate Willard Libby. She became a professor at the University of Colorado, and a staff member at RAND Corporation. In later life she became interested in ecological and environmental issues, and she devised a method of using the isotope ratios in tree rings to study climate change. She was a strong advocate of food irradiation as a means of killing harmful bacteria.
Early life.
Leona Harriet Woods was born on a farm in La Grange, Illinois on August 9, 1919, the second of five children of Weightstill Arno Woods, a lawyer, and his wife Mary Leona Holderness Woods. She had two sisters and two brothers. She graduated from Lyons Township High School in La Grange at 14, and received her BS in chemistry from the University of Chicago in 1938, at the age of 18.
After passing her qualifying exams in chemistry, she approached the Nobel Prize for Physics laureate James Franck about being his graduate student, having been impressed by a talk he gave in 1939 on Brillouin zones. Franck accepted, but told her that when he was young his professor had warned him that as a Jewish academic, he would starve to death. Franck therefore warned Woods that "You are a woman and you will starve to death." Despite the fact that Franck did not look malnourished, she took the warning seriously, and decided to instead become a graduate student of Robert Mulliken, who would one day become a Nobel laureate himself.
Mulliken allowed her to choose her own research problem, and edited the final version before it appeared in the "Physical Review". Her doctoral thesis, "On the Silicon Oxide Bands", prepared under the supervision of Mulliken and Polish chemist Stanisław Mrozowski was accepted in 1943. Mulliken, she later recalled, had twice told her "that perhaps not all he taught me was wasted." His students, she noted, "agree that this is his highest praise."
Manhattan Project.
By 1942, when she was finishing writing up her thesis, she was the youngest and last of Mulliken's pre-war students, and was working alone because all her fellow students had become involved with war work. She met Herbert Anderson, who was working for Enrico Fermi. The two would go swimming together in Lake Michigan every afternoon at 5 pm. Anderson discovered that Woods was adept with vacuum technology from her research, and as soon as her PhD was finished, he hired her to work with the boron trifluoride detectors used to measure neutron flux.
Fermi's group constructed a nuclear reactor known as Chicago Pile-1 under the stands of Stagg Field, the University's abandoned football stadium, where Woods had once played squash. Walter Zinn did not want a woman involved in the dirty work of placing the graphite blocks, but Woods had plenty of work to do with the detectors and thermocouples, and used a small stack of graphite of her own to measure the effects of a radium-beryllium source on manganese foil to obtain a measure of the neutron cross section in order to calibrate the detectors. Her skills in glassblowing were useful in constructing the neutron detectors. Woods was the only woman present when the reactor went critical, asking Fermi "When do we become scared?"
Laura Fermi remembered Woods as "a tall young girl built like an athlete, who could do a man's job and do it well. She was the only woman physicist in Enrico's group. At that time, her mother, who was also endowed with inexhaustible energy, was running a small farm near Chicago almost by herself. To relieve Mrs. Woods of some work, Leona divided her time between atoms and potatoes."
Like many scientists working on the project, Woods affected a casual attitude towards the danger posed by radiation. After a morning with Willard Libby soldering a canister containing a mixture of radium salt and beryllium metal, Woods absorbed about 200 roentgens, and her white blood cell count halved. The doctors gave her a lecture on how a woman has only a fixed number of egg cells, a proposition that Woods was skeptical of. She considered that the important thing was that the solder was done correctly. When the team moved to their new home at Argonne, Woods had a dormitory all to herself.
Woods married John Marshall in July 1943. Soon after, she fell pregnant. While she told Enrico Fermi, they agreed not to let Walter Zinn know, for fear that he would insist that she leave the reactor building. She covered up her pregnant belly with her baggy denim work clothes. She rode to work each day on an unheated Army bus, "arriving each morning barely in time to vomit before starting the day's work." The child, a boy called Peter, was born in 1944. She returned to work a few days later.
A team from Argonne was on hand for powering up the first reactor at the Hanford Site, where large reactors would produce plutonium for bombs. They watched the reactor in shifts, with John Marshall and others on the day shift, Enrico Fermi and Leona Marshall on the night shift, ending at midnight, and Don Hughes and John Wheeler on the swing shift. While the Marshalls were babysitting the reactor in Hanford, they left Peter with Leona's mother.
The reactor was powered up successfully, but after a few hours the power level dropped and the reactor shut down. Leona speculated that a water leak was the problem, rather than a radioactive poison. However, during the night the operators were able to power the reactor up again only to have it once more die away. The timings now pointed to a radioactive poison. After working through the numbers with slide rules and hand calculators, they determined the neutron cross section of the poison, which turned out to be xenon-135. Fortunately, the DuPont engineers had equipped the reactor with 50 per cent more fuel tubes than the physicists had called for, and by loading them up, they managed to get the reactor started.
Asked many years later about how she felt about her involvement in the Manhattan Project, she said:
Post-war career.
After the war, Leona Marshall returned to the University of Chicago, where she became a fellow at Fermi's Institute for Nuclear Studies. Working with the Chicago Pile 3 heavy water reactor, she found a way to 100 percent spin polarize neutron beams, and determined the refractive index of neutrons for various materials. Her second child, John Marshall III, was born in 1949. She became an assistant professor in 1953.
After Fermi died in 1954, the Marshalls separated. John Marshall returned to the Los Alamos Laboratory, while Leona, now effectively a single mother, became a fellow at the Institute for Advanced Study in Princeton, New Jersey in 1957. The following year she became a fellow at the Brookhaven National Laboratory, at a time when the focus of research in physics was shifting away from the nucleus and towards elementary particles. In 1960, she joined New York University as an associate professor of physics. She became a professor in 1962.
Three years later, she became a professor at the University of Colorado, researching high-energy physics, astrophysics and cosmology. She then became a staff member at RAND Corporation, where she worked until 1976. In 1966, she divorced John Marshall, and married Willard Libby, who had won the Nobel prize in 1960. She later joined him at UCLA, where she became a visiting professor of environmental studies, engineering, engineering archaeology, mechanical aerospace and nuclear engineering in 1973.
Now known as Leona Marshall Libby, she became interested in ecological and environmental issues, and she devised a method of using the isotope ratios of Oxygen-18 to Oxygen-16, Carbon-13 to Carbon-12, and Deuterium to Hydrogen in tree rings to study changes in temperature and rainfall patterns hundreds of years before records were kept, opening the door to the study of climate change.
Like Willard Libby, she was a strong advocate of food irradiation as a means of killing off harmful bacteria, and advocated that legal and regulatory restrictions on its use be relaxed. She proposed that, instead of it being sprayed with malathion, fruit affected by the Mediterranean fruit fly could be treated with gamma rays.
She was a prolific author, publishing over 200 scientific papers. While at RAND she wrote a paper on "Creation of an Atmosphere for the Moon" (1969). Her works include the autobiographical "" (1979), a history of early atomic research. After Libby died in 1980, she edited his papers with Rainer Berger, and published "The Life Work of Nobel Laureate Willard Libby" (1982). Her last paper, on quasi-stellar objects, appeared in 1984.
She died at St. John's Medical Center in Santa Monica, California, on November 10, 1986, from an anesthesia-induced stroke. She was survived by her sons Peter and John, and four grandchildren. She also had two stepdaughters, Janet Eva Libby and Susan Charlotte Libby from her second marriage.