Effects of nuclear explosions

The effects of a nuclear explosion on its immediate vicinity are typically much more destructive and multifaceted than those caused by conventional explosives. In most cases, the energy released from a nuclear weapon detonated within the lower atmosphere can be approximately divided into four basic categories:
Depending on the design of the weapon and the location in which it is detonated, the energy distributed to any one of these categories may be significantly higher or lower. The physical blast effect is created by the coupling of immense amounts of energy, spanning the electromagnetic spectrum, with the surroundings. The environment of the explosion (e.g. submarine, ground burst, air burst, or exo-atmospheric) determines how much energy is distributed to the blast and how much to radiation. In general, surrounding a bomb with denser media, such as water, absorbs more energy and creates more powerful shockwaves while at the same time limiting the area of its effect. When a nuclear weapon is surrounded only by air, lethal blast and thermal effects proportionally scale much more rapidly than lethal radiation effects as explosive yield increases. This bubble is faster than the speed of sound. The physical damage mechanisms of a nuclear weapon (blast and thermal radiation) are identical to those of conventional explosives, but the energy produced by a nuclear explosion is usually millions of times more powerful per unit mass and temperatures may briefly reach the tens of millions of degrees.
Energy from a nuclear explosion is initially released in several forms of penetrating radiation. When there is surrounding material such as air, rock, or water, this radiation interacts with and rapidly heats the material to an equilibrium temperature (i.e. so that the matter is at the same temperature as the fuel powering the explosion). This causes vaporization of the surrounding material, resulting in its rapid expansion. Kinetic energy created by this expansion contributes to the formation of a shockwave which expands spherically from the center. Intense thermal radiation at the hypocenter forms a nuclear fireball which, if the explosion is low enough in altitude, is often associated with a mushroom cloud. In a high-altitude burst, where the density of the atmosphere is low, more energy is released as ionizing gamma radiation and X-rays than as an atmosphere-displacing shockwave.
In 1942, there was some initial speculation among the scientists developing the first nuclear weapons in the Manhattan Project that a large enough nuclear explosion might ignite the Earth's atmosphere. This notion concerned the nuclear reaction of two atmospheric nitrogen atoms forming carbon and an oxygen atom, with an associated release of energy. The scientists hypothesized that this energy would heat up the remaining atmospheric nitrogen enough to keep the reaction going until all nitrogen atoms were consumed, thereby burning all of the Earth's atmosphere (which is composed of nearly 80% diatomic nitrogen) in one single massive combustion event. Hans Bethe was assigned the task of studying this hypothesis from the project's earliest days, and eventually concluded that combustion of the entire atmosphere was not possible: the cooling of the fireball due to an inverse Compton effect all but guaranteed that such a scenario would not become a reality. Richard Hamming, a mathematician, was asked to make a similar calculation just before the first nuclear test, with the same result. Nevertheless, the notion has persisted as a rumor for many years and was the source of apocalyptic gallows humor at the Trinity test.
Direct effects.
Blast damage.
The high temperatures and radiation cause gas to move outward radially in a thin, dense shell called "the hydrodynamic front". The front acts like a piston that pushes against and compresses the surrounding medium to make a spherically expanding shock wave. At first, this shock wave is inside the surface of the developing fireball, which is created in a volume of air heated by the explosion's "soft" X-rays. Within a fraction of a second, the dense shock front obscures the fireball and continues to move past it, now expanding outwards, free from the fireball, causing a reduction of light emanating from a nuclear detonation. Eventually, the shock wave dissipates to the point where the light becomes visible again giving rise to the characteristic double flash due to the shock wave–fireball interaction. It is this unique feature of nuclear explosions that is exploited when verifying that an atmospheric nuclear explosion has occurred and not simply a large conventional explosion, with radiometer instruments known as Bhangmeters capable of determining the nature of explosions.
For air bursts at or near sea-level, 50–60% of the explosion's energy goes into the blast wave, depending on the size and the yield of the bomb. As a general rule, the blast fraction is higher for low yield weapons. Furthermore, it decreases at high altitudes because there is less air mass to absorb radiation energy and convert it into a blast. This effect is most important for altitudes above 30  km, corresponding to less than 1 percent of sea-level air density.
The effects of a moderate rain storm during an Operation Castle nuclear explosion was found to dampen, or reduce, peak pressure levels by approximately 15% at all ranges.
Much of the destruction caused by a nuclear explosion is due to blast effects. Most buildings, except reinforced or blast-resistant structures, will suffer moderate damage when subjected to overpressures of only 35.5 kilopascals (kPa) (5.15 pounds-force per square inch or 0.35 atm).
Data obtained from the Japanese surveys found that was sufficient to destroy all wooden and brick residential structures. This can reasonably be defined as the pressure capable of producing severe damage.
The blast wind at sea level may exceed one thousand km/h, or ~300 m/s, approaching the speed of sound in air. The range for blast effects increases with the explosive yield of the weapon and also depends on the burst altitude. Contrary to what one might expect from geometry, the blast range is not maximal for surface or low altitude blasts but increases with altitude up to an "optimum burst altitude" and then decreases rapidly for higher altitudes. This is due to the nonlinear behavior of shock waves. When the blast wave from an air burst reaches the ground it is reflected. Below a certain reflection angle, the reflected wave and the direct wave merge and form a reinforced horizontal wave, this is known as the 'Mach stem' (named after Ernst Mach) and is a form of constructive interference.
 This constructive interference is the phenomenon responsible for the bumps or 'knees' in the above overpressure range graph.
For each goal overpressure, there is a certain optimum burst height at which the blast range is maximized over ground targets. In a typical air burst, where the blast range is maximized to produce the greatest range of severe damage, i.e. the greatest range that ~ of pressure is extended over, is a GR/ground range of 0.4 km for 1 kiloton (kt) of TNT yield; 1.9 km for 100 kt; and 8.6 km for 10 megatons (Mt) of TNT. The optimum height of burst to maximize this desired severe ground range destruction for a 1 kt bomb is 0.22  km; for 100 kt, 1  km; and for 10 Mt, 4.7  km.
Two distinct, simultaneous phenomena are associated with the blast wave in the air:
Most of the material damage caused by a nuclear air burst is caused by a combination of the high static overpressures and the blast winds. The long compression of the blast wave weakens structures, which are then torn apart by the blast winds. The compression, vacuum and drag phases together may last several seconds or longer, and exert forces many times greater than the strongest hurricane.
Acting on the human body, the shock waves cause pressure waves through the tissues. These waves mostly damage junctions between tissues of different densities (bone and muscle) or the interface between tissue and air. Lungs and the abdominal cavity, which contain air, are particularly injured. The damage causes severe hemorrhaging or air embolisms, either of which can be rapidly fatal. The overpressure estimated to damage lungs is about 70 kPa. Some eardrums would probably rupture around 22 kPa (0.2 atm) and half would rupture between 90 and 130 kPa (0.9 to 1.2 atm).
Blast winds: The drag energies of the blast winds are proportional to the cubes of their velocities multiplied by the durations. These winds may reach several hundred kilometers per hour.
Thermal radiation.
Nuclear weapons emit large amounts of thermal radiation as visible, infrared, and ultraviolet light, to which the atmosphere is largely transparent. This is known as "Flash". The chief hazards are burns and eye injuries. On clear days, these injuries can occur well beyond blast ranges, depending on weapon yield. Fires may also be started by the initial thermal radiation, but the following high winds due to the blast wave may put out almost all such fires, unless the yield is very high, where the range of thermal effects vastly outranges blast effects, as observed from explosions in the multi-megaton range. This is because the intensity of the blast effects drops off with the third power of distance from the explosion, while the intensity of radiation effects drops off with the second power of distance. This results in the range of thermal effects increasing markedly more than blast range as higher and higher device yields are detonated. Thermal radiation accounts for between 35–45% of the energy released in the explosion, depending on the yield of the device. In urban areas, the extinguishing of fires ignited by thermal radiation may matter little, as in a surprise attack fires may also be started by blast-effect-induced electrical shorts, gas pilot lights, overturned stoves, and other ignition sources, as was the case in the breakfast-time bombing of Hiroshima. Whether or not these secondary fires will in turn themselves be snuffed out as modern noncombustible brick and concrete buildings collapse in on themselves from the same blast wave is uncertain, not least of which, because of the masking effect of modern city landscapes on thermal and blast transmission are continually examined.
When combustible frame buildings were blown down in Hiroshima and Nagasaki, they did not burn as rapidly as they would have done had they remained standing. The noncombustible debris produced by the blast frequently covered and prevented the burning of combustible material.
Fire experts suggest that unlike Hiroshima, due to the nature of modern U.S.  city design and construction, a firestorm in modern times is unlikely after a nuclear detonation. This does not exclude fires from being started, but means that these fires will not form into a firestorm, due largely to the differences between modern building materials and those used in World War II-era Hiroshima.
There are two types of eye injuries from the thermal radiation of a weapon:
Flash blindness is caused by the initial brilliant flash of light produced by the nuclear detonation. More light energy is received on the retina than can be tolerated, but less than is required for irreversible injury. The retina is particularly susceptible to visible and short wavelength infrared light since this part of the electromagnetic spectrum is focused by the lens on the retina. The result is bleaching of the visual pigments and temporary blindness for up to 40 minutes.
A retinal burn resulting in permanent damage from scarring is also caused by the concentration of direct thermal energy on the retina by the lens. It will occur only when the fireball is actually in the individual's field of vision and would be a relatively uncommon injury. Retinal burns may be sustained at considerable distances from the explosion. The height of burst and apparent size of the fireball, a function of yield and range will determine the degree and extent of retinal scarring. A scar in the central visual field would be more debilitating. Generally, a limited visual field defect, which will be barely noticeable, is all that is likely to occur.
When thermal radiation strikes an object, part will be reflected, part transmitted, and the rest absorbed. The fraction that is absorbed depends on the nature and color of the material. A thin material may transmit a lot. A light-colored object may reflect much of the incident radiation and thus escape damage, like anti-flash white paint. The absorbed thermal radiation raises the temperature of the surface and results in scorching, charring, and burning of wood, paper, fabrics, etc. If the material is a poor thermal conductor, the heat is confined to the surface of the material.
The actual ignition of materials depends on how long the thermal pulse lasts and the thickness and moisture content of the target. Near ground zero where the energy flux exceeds 125 J/cm2, what can burn, will. Farther away, only the most easily ignited materials will flame. Incendiary effects are compounded by secondary fires started by the blast wave effects such as from upset stoves and furnaces.
In Hiroshima on August 6, 1945, a tremendous firestorm developed within 20 minutes after detonation and destroyed many more buildings and homes, built out of predominantly 'flimsy' wooden materials. A firestorm has gale-force winds blowing in towards the center of the fire from all points of the compass. It is not peculiar to nuclear explosions, having been observed frequently in large forest fires and following incendiary raids during World War II. Despite fires destroying a large area of the city of Nagasaki, no true firestorm occurred in the city, even though a higher yielding weapon was used. Many factors explain this seeming contradiction, including a different time of bombing than Hiroshima, terrain, and crucially, a lower fuel loading/fuel density in the city than that of Hiroshima.
As thermal radiation travels, more or less, in a straight line from the fireball (unless scattered) any opaque object will produce a protective shadow that provides protection from the flash burn. Depending on the properties of the underlying surface material, the exposed area outside the protective shadow will be either burnt to a darker color, such as charring wood, or a brighter color, such as asphalt. If such a weather phenomenon as fog or haze is present at the point of the nuclear explosion, it scatters the flash, with radiant energy then reaching burn sensitive substances from all directions. Under these conditions, opaque objects are therefore less effective than they would otherwise be without scattering, as they demonstrate maximum shadowing effect in an environment of perfect visibility and therefore zero scatterings. Similar to a foggy or overcast day, although there are few if any, shadows produced by the sun on such a day, the solar energy that reaches the ground from the sun's infrared rays is nevertheless considerably diminished, due to it being absorbed by the water of the clouds and the energy also being scattered back into space. Analogously, so too is the intensity at a range of burning flash energy attenuated, in units of J/cm2, along with the slant/horizontal range of a nuclear explosion, during fog or haze conditions. So despite any object that casts a shadow being rendered ineffective as a shield from the flash by fog or haze, due to scattering, the fog fills the same protective role, but generally only at the ranges that survival in the open is just a matter of being protected from the explosion's flash energy.
The thermal pulse also is responsible for warming the atmospheric nitrogen close to the bomb and causing the creation of atmospheric NOx smog components. This, as part of the mushroom cloud, is shot into the stratosphere where it is responsible for dissociating ozone there, in exactly the same way as combustion NOx compounds do. The amount created depends on the yield of the explosion and the blast's environment. Studies done on the total effect of nuclear blasts on the ozone layer have been at least tentatively exonerating after initial discouraging findings.
Indirect effects.
Electromagnetic pulse.
Gamma rays from a nuclear explosion produce high energy electrons through Compton scattering. For high altitude nuclear explosions, these electrons are captured in the Earth's magnetic field at altitudes between twenty and forty kilometers where they interact with the Earth's magnetic field to produce a coherent nuclear electromagnetic pulse (NEMP) which lasts about one millisecond. Secondary effects may last for more than a second.
The pulse is powerful enough to cause moderately long metal objects (such as cables) to act as antennas and generate high voltages due to interactions with the electromagnetic pulse. These voltages can destroy unshielded electronics. There are no known biological effects of EMP. The ionized air also disrupts radio traffic that would normally bounce off the ionosphere.
Electronics can be shielded by wrapping them completely in conductive material such as metal foil; the effectiveness of the shielding may be less than perfect. Proper shielding is a complex subject due to a large number of variables involved. Semiconductors, especially integrated circuits, are extremely susceptible to the effects of EMP due to the close proximity of the PN junctions, but this is not the case with thermionic tubes (or valves) which are relatively immune to EMP. A Faraday cage does not offer protection from the effects of EMP unless the mesh is designed to have holes no bigger than the smallest wavelength emitted from a nuclear explosion.
Large nuclear weapons detonated at high-altitudes also cause geomagnetically induced current in very long electrical conductors. The mechanism by which these geomagnetically induced currents are generated is entirely different from the gamma-ray induced pulse produced by Compton electrons.
Radar blackout.
The heat of the explosion causes air in the vicinity to become ionized, creating the fireball. The free electrons in the fireball affect radio waves, especially at lower frequencies. This causes a large area of the sky to become opaque to radar, especially those operating in the VHF and UHF frequencies, which is common for long-range early warning radars. The effect is less for higher frequencies in the microwave region, as well as lasting a shorter time – the effect falls off both in strength and the affected frequencies as the fireball cools and the electrons begin to re-form onto free nuclei.
A second blackout effect is caused by the emission of beta particles from the fission products. These can travel long distances, following the Earth's magnetic field lines. When they reach the upper atmosphere they cause ionization similar to the fireball, but over a wider area. Calculations demonstrate that one megaton of fission, typical of a two megaton H-bomb, will create enough beta radiation to blackout an area across for five minutes. Careful selection of the burst altitudes and locations can produce an extremely effective radar-blanking effect.
The physical effects giving rise to blackouts are those that also cause EMP, which itself can cause power blackouts. The two effects are otherwise unrelated, and the similar naming can be confusing.
Ionizing radiation.
About 5% of the energy released in a nuclear air burst is in the form of ionizing radiation: neutrons, gamma rays, alpha particles and electrons moving at speeds up to the speed of light. Gamma rays are high energy electromagnetic radiation; the others are particles that move slower than light. The neutrons result almost exclusively from the fission and fusion reactions, while the initial gamma radiation includes that arising from these reactions as well as that resulting from the decay of short-lived fission products.
The intensity of initial nuclear radiation decreases rapidly with distance from the point of burst because the radiation spreads over a larger area as it travels away from the explosion (the inverse-square law). It is also reduced by atmospheric absorption and scattering.
The character of the radiation received at a given location also varies with distance from the explosion. Near the point of the explosion, the neutron intensity is greater than the gamma intensity, but with increasing distance the neutron-gamma ratio decreases. Ultimately, the neutron component of the initial radiation becomes negligible in comparison with the gamma component. The range for significant levels of initial radiation does not increase markedly with weapon yield and, as a result, the initial radiation becomes less of a hazard with increasing yield. With larger weapons, above 50 kt (200 TJ), blast and thermal effects are so much greater in importance that prompt radiation effects can be ignored.
The neutron radiation serves to transmute the surrounding matter, often rendering it radioactive. When added to the dust of radioactive material released by the bomb itself, a large amount of radioactive material is released into the environment. This form of radioactive contamination is known as nuclear fallout and poses the primary risk of exposure to ionizing radiation for a large nuclear weapon.
Details of nuclear weapon design also affect neutron emission: the gun-type assembly Hiroshima bomb leaked far more neutrons than the implosion-type 21 kt Nagasaki bomb because the light hydrogen nuclei (protons) predominating in the exploded TNT molecules (surrounding the core of the Nagasaki bomb) slowed down neutrons very efficiently while the heavier iron atoms in the steel nose forging of the Hiroshima bomb scattered neutrons without absorbing much neutron energy.
It was found in early experimentation that normally most of the neutrons released in the cascading chain reaction of the fission bomb are absorbed by the bomb case. Building a bomb case of materials which transmitted rather than absorbed the neutrons could make the bomb more intensely lethal to humans from prompt neutron radiation. This is one of the features used in the development of the neutron bomb.
Earthquake.
The pressure wave from an underground explosion will propagate through the ground and cause a minor earthquake. Theory suggests that a nuclear explosion could trigger fault rupture and cause a major quake at distances within a few tens of kilometers from the shot point.
Summary of the effects.
The following table summarizes the most important effects of single nuclear explosions under ideal, clear skies, weather conditions. Tables like these are calculated from nuclear weapons effects scaling laws. Advanced computer modelling of real-world conditions and how they impact on the damage to modern urban areas has found that most scaling laws are too simplistic and tend to overestimate nuclear explosion effects. As it is only simplistic and unclassified scaling laws that are commonly encountered, that do not take important things like varying land topography into account to ease calculation time and equation length. The scaling laws that were used to produce the table below, assume among other things, a perfectly level target area, no attenuating effects from urban terrain masking, e.g. skyscraper shadowing, and no enhancement effects from reflections and tunneling by city streets.
As a point of comparison in the chart below, the most likely nuclear weapons to be used against countervalue city targets in a global nuclear war are in the sub-megaton range. Weapons of yields from 100 to 475 kilotons have become the most numerous in the US and Russian nuclear arsenals; for example, the warheads equipping the Russian Bulava submarine-launched ballistic missile (SLBM) have a yield of 150 kilotons. US examples are the [[W76]] and [[W88]] warheads, with the lower yield W76 being over twice as numerous as the W88 in the US nuclear arsenal.
1
2
Further complicating matters, under global nuclear war scenarios, with conditions similar to that during the [[Cold War]], major strategically important cities, like [[Moscow]], and [[Washington, D.C.|Washington]] are likely to be hit not once, but numerous times from sub megaton [[multiple independently targetable re-entry vehicles]], in a [[cluster bomb]] or "cookie-cutter" configuration. It has been reported that during the height of the Cold War in the 1970s Moscow was targeted by up to 60 warheads. The reasons that the cluster bomb concept is preferable in the targeting of cities is twofold, the first is down to the fact that large singular warheads are much easier to neutralize as both tracking and successful interception by [[A-35 anti-ballistic missile system|anti-ballistic missile system]]s than it is when several smaller incoming warheads are approaching. This [[strength in numbers]] advantage to lower yield warheads is further compounded by such warheads tending to move at higher incoming speeds, due to their smaller, more slender [[physics package]] size, assuming both nuclear weapon designs are the same (a design exception being the advanced [[W88]]). The second reason for this cluster bomb, or ‘layering’ (using repeated hits by accurate low yield weapons), is that this tactic along with limiting the risk of failure, also reduces individual bomb yields, and therefore reduces the possibility of any serious collateral damage to non-targeted nearby civilian areas, including that of neighboring countries. This concept was pioneered by [[Philip J. Dolan]] and others.
Other phenomena.
[[Image:Nukecloud.png|thumb|left|250 px|Mushroom cloud height depending on yield for ground bursts. 0 = Approx. altitude at which a commercial aircraft operates1 = [[Fat Man]]2 = [[Castle Bravo]]]]
[[Gamma rays]] from the nuclear processes preceding the true explosion may be partially responsible for the following fireball, as they may superheat nearby air and/or other material. The vast majority of the energy that goes on to form the fireball is in the soft [[X-ray]] region of the electromagnetic spectrum, with these X-rays being produced by the [[inelastic collisions]] of the high-speed fission and fusion products. It is these reaction products and not the gamma rays which contain most of the energy of the nuclear reactions in the form of [[kinetic energy]]. This kinetic energy of the fission and fusion fragments is converted into internal and then radiation energy by approximately following the process of [[blackbody radiation]] emitting in the soft X-ray region. As a result of numerous inelastic collisions, part of the kinetic energy of the fission fragments is converted into internal and radiation energy. Some of the electrons are removed entirely from the atoms, thus causing ionization, others are raised to higher energy (or excited) states while still remaining attached to the nuclei. Within an extremely short time, perhaps a hundredth of a microsecond or so, the weapon residues consist essentially of completely and partially stripped (ionized) atoms, many of the latter being in excited states, together with the corresponding free electrons. The system then immediately emits electromagnetic (thermal) radiation, the nature of which is determined by the temperature. Since this is of the order of 107 degrees, most of the energy emitted within a microsecond or so is in the soft X-ray region. To understand this one must remember that temperature depends on the average internal energy/heat of the particles in a certain volume, and internal energy or heat is due to [[kinetic energy]].
For an explosion in the atmosphere, the fireball quickly expands to maximum size, and then begins to cool as it rises like a balloon through [[buoyancy]] in the surrounding air. As it does so it takes on the flow pattern of a [[vortex ring]] with incandescent material in the vortex core as seen in certain photographs. This effect is known as a [[mushroom cloud]].
Sand will fuse into glass if it is close enough to the nuclear fireball to be drawn into it, and is thus heated to the necessary temperatures to do so; this is known as [[trinitite]].
At the explosion of nuclear bombs lightning discharges sometimes occur.
Smoke trails are often seen in photographs of nuclear explosions. These are not from the explosion; they are left by [[sounding rockets]] launched just prior to detonation. These trails allow observation of the blast's normally invisible shock wave in the moments following the explosion.
The heat and airborne debris created by a nuclear explosion can cause rain; the debris is thought to do this by acting as [[cloud condensation nuclei]]. During the city [[firestorm]] which followed the Hiroshima explosion, drops of water were recorded to have been about the size of [[Marble (toy)|marbles]]. This was termed "black rain", and has served as the source of a [[Black Rain (novel)|book and film by the same name]]. Black rain is not unusual following large fires and is commonly produced by [[pyrocumulus cloud]]s during large forest fires. The rain directly over Hiroshima on that day is said to have begun around 9 a.m. with it covering a wide area from the [[hypocenter]] to the north-west, raining heavily for one hour or more in some areas. The rain directly over the city may have carried [[neutron activation|neutron activated]] building material combustion products, but it did not carry any appreciable nuclear weapon debris or fallout, although this is generally to the contrary to what other less technical sources state. The "oily" black [[soot]] particles, are a characteristic of [[incomplete combustion]] in the city firestorm.
The element [[einsteinium]] was discovered when analyzing nuclear fallout.
A side-effect of the Pascal-B nuclear test during [[Operation Plumbbob#Missing steel bore cap|Operation Plumbbob]] may have resulted in the first man-made object launched into space. The so-called "thunder well" effect from the underground explosion may have launched a metal cover plate into space at six times Earth's [[escape velocity]], although the evidence remains subject to debate.
Survivability.
This is highly dependent on factors such as if one is indoors or out, the size of the explosion, the proximity to the explosion, and to a lesser degree the direction of the wind carrying fallout.
Death is highly likely and radiation poisoning is almost certain if one is caught in the open with no terrain or building masking effects within a radius of 0–3 km from a 1 megaton airburst, and the [[LD50|50% chance of death]] from the blast extends out to ~8  km from the same 1 megaton atmospheric explosion.
To highlight the variability in the real world, and the effect that being indoors can make, despite the lethal radiation and blast zone extending well past her position at Hiroshima, Akiko Takakura survived the effects of a 16 kt atomic bomb at a distance of 300 meters from the hypocenter, with only minor injuries, due mainly to her position in the lobby of the Bank of Japan, a [[reinforced concrete]] building, at the time. In contrast, the unknown person sitting outside, fully exposed, on the steps of the Sumitomo Bank, next door to the Bank of Japan, received lethal third-degree burns and was then likely killed by the blast, in that order, within two seconds.
With medical attention, radiation exposure is survivable to 200 rems of acute dose exposure. If a group of people is exposed to a 50 to 59 rems acute (within 24 hours) radiation dose, none will get radiation sickness. If the group is exposed to 60 to 180 rems, 50% will become sick with radiation poisoning. If medically treated, all of the 60–180 rems group will survive. If the group is exposed to 200 to 450 rems, most if not all of the group will become sick. 50% of the 200–450 rems group will die within two to four weeks, even with medical attention. If the group is exposed to 460 to 600 rems, 100% of the group will get radiation poisoning. 50% of the 460–600 rems group will die within one to three weeks. If the group is exposed to 600 to 1000 rems, 50% will die in one to three weeks. If the group is exposed to 1,000 to 5,000 rems, 100% of the group will die within 2 weeks. At 5,000 rems, 100% of the group will die within 2 days.
External links.
[[Category:Nuclear weapons]]
[[Category:Nuclear physics]]
[[Category:Articles containing video clips]]
[[sv:Kärnexplosion]]


Geoffrey Malcolm Copland

Geoffrey Malcolm Copland (born 28 June 1942) is a British physicist and former vice-chancellor of the University of Westminster.
Life and career.
Copland was educated at Fitzmaurice Grammar School, Bradford-on-Avon, and went up to Merton College, Oxford in 1960 to read Physics. After taking a first class undergraduate degree in 1963, he remained at Merton whilst studying for his DPhil, which he completed in 1967.
Following his doctorate, Copland spent two years at Yale University, before returning to the UK in 1969 to become a Researcher and Lecturer in Physics at Queen Mary College. In 1971 he joined Queen Elizabeth College as a Lecturer in Physics, a post he held until 1980. In 1981 he was made Dean of Studies at Goldsmiths College, then in 1987 he moved to become Deputy Rector at the Polytechnic of Central London (which later became the University of Westminster), becoming its Rector and Vice-Chancellor in 1996. Since 2007 he has been a consultant on higher education, and has held a range of academic and industry positions.
He was made a Fellow of the Royal Society of Arts in 1991, and awarded a CBE in 2007, for services to higher education. He has a main-belt asteroid 9193 Geoffreycopland, discovered on 10 March 1992 by Duncan Steel at Siding Spring Observatory, named after him.
Copland has been twice married, firstly in 1967 to Janet Mary Todd, with whom he had a son and a daughter; their marriage was dissolved in 1985, and that year Copland remarried, to Dorothy Joy Harrison.


DISORT

DISORT (Discrete Ordinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium) - general and versatile plane-parallel radiative transfer program applicable to problems from the ultraviolet to the radar regions of the electromagnetic spectrum.
DISORT is used in many atmospheric radiative transfer codes including , MODTRAN, RRTM and SBDART.
References.
K. Stamnes, SC. Tsay, W. Wiscombe and K. Jayaweera, Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media, Appl Opt 27 (1988) (12), pp. 2502–2509.
Z. Lin, S. Stamnes., Z. Jin, I. Laszlo, SC. Tsay, W. Wiscombe, and K. Stamnes. Improved discrete ordinate solutions in the presence of an anisotropically reflecting lower boundary: Upgrades of the DISORT computational tool. Journal of Quantitative Spectroscopy and Radiative Transfer (2015) (157), pp. 119–134.
External links.
LLLab DISORT Website, includes link to download *
Second version of the "Radiative Transfer in the Atmosphere and Ocean" book website


David Klyshko

David Nikolaevich Klyshko (Давид Николаевич Клышко), (1929—2000) was a Russian physicist and professor. A highly regarded Physics professor at Moscow State University, was known for his imperative approach for Quantum Optics understanding. His most known contributions were in the field of quantum electronics and quantum information science.
His Habilitation thesis on the topic of spontaneous parametric down-conversion, ""Multi-quantum and multi-particle transitions in radio spectroscopy and quantum radiophysics"," was published in 1972. Upon release, the thesis was widely recognized as a breakthrough in multi-particle transitions.
Throughout the 1970s, Klyshko presented several more important theoretical contributions including the development of spontaneous parametric down-conversion theory, entanglement-based quantum imaging, nonlinear transformations in quantum optics, and the advanced wave model for describing correlations in photon interference experiments.


Stavros Tavoularis

Stavros Tavoularis from the University of Ottawa, was awarded the status of Fellow in the American Physical Society, after they were nominated by their Division of Fluid Dynamics in 2007, for "contributions to turbulence, turbulent mixing, vortex dynamics, aerodynamics, thermo-hydraulics, bio-fluid dynamics, and design of flow apparatus and instrumentation. Also, for contributions to education in fluid dynamics and for promoting international collaboration and understanding."


Partition function (mathematics)

The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution. The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated probability measure, the Gibbs measure, has the Markov property. This means that the partition function occurs not only in physical systems with translation symmetry, but also in such varied settings as neural networks (the Hopfield network), and applications such as genomics, corpus linguistics and artificial intelligence, which employ Markov networks, and Markov logic networks. The Gibbs measure is also the unique measure that has the property of maximizing the entropy for a fixed expectation value of the energy; this underlies the appearance of the partition function in maximum entropy methods and the algorithms derived therefrom.
The partition function ties together many different concepts, and thus offers a general framework in which many different kinds of quantities may be calculated. In particular, it shows how to calculate expectation values and Green's functions, forming a bridge to Fredholm theory. It also provides a natural setting for the information geometry approach to information theory, where the Fisher information metric can be understood to be a correlation function derived from the partition function; it happens to define a Riemannian manifold.
When the setting for random variables is on complex projective space or projective Hilbert space, geometrized with the Fubini–Study metric, the theory of quantum mechanics and more generally quantum field theory results. In these theories, the partition function is heavily exploited in the path integral formulation, with great success, leading to many formulas nearly identical to those reviewed here. However, because the underlying measure space is complex-valued, as opposed to the real-valued simplex of probability theory, an extra factor of "i" appears in many formulas. Tracking this factor is troublesome, and is not done here. This article focuses primarily on classical probability theory, where the sum of probabilities total to one.
Definition.
Given a set of random variables formula_1 taking on values formula_2, and some sort of potential function or Hamiltonian formula_3, the partition function is defined as
The function "H" is understood to be a real-valued function on the space of states formula_5, while formula_6 is a real-valued free parameter (conventionally, the inverse temperature). The sum over the formula_2 is understood to be a sum over all possible values that each of the random variables formula_1 may take. Thus, the sum is to be replaced by an integral when the formula_1 are continuous, rather than discrete. Thus, one writes
for the case of continuously-varying formula_1.
When "H" is an observable, such as a finite-dimensional matrix or an infinite-dimensional Hilbert space operator or element of a C-star algebra, it is common to express the summation as a trace, so that
When "H" is infinite-dimensional, then, for the above notation to be valid, the argument must be trace class, that is, of a form such that the summation exists and is bounded.
The number of variables formula_1 need not be countable, in which case the sums are to be replaced by functional integrals. Although there are many notations for functional integrals, a common one would be
Such is the case for the partition function in quantum field theory.
A common, useful modification to the partition function is to introduce auxiliary functions. This allows, for example, the partition function to be used as a generating function for correlation functions. This is discussed in greater detail below.
The parameter β.
The role or meaning of the parameter formula_6 can be understood in a variety of different ways. In classical thermodynamics, it is an inverse temperature. More generally, one would say that it is the variable that is conjugate to some (arbitrary) function formula_16 of the random variables formula_17. The word "conjugate" here is used in the sense of conjugate generalized coordinates in Lagrangian mechanics, thus, properly formula_6 is a Lagrange multiplier. It is not uncommonly called the generalized force. All of these concepts have in common the idea that one value is meant to be kept fixed, as others, interconnected in some complicated way, are allowed to vary. In the current case, the value to be kept fixed is the expectation value of formula_16, even as many different probability distributions can give rise to exactly this same (fixed) value.
For the general case, one considers a set of functions formula_20 that each depend on the random variables formula_1. These functions are chosen because one wants to hold their expectation values constant, for one reason or another. To constrain the expectation values in this way, one applies the method of Lagrange multipliers. In the general case, maximum entropy methods illustrate the manner in which this is done.
Some specific examples are in order. In basic thermodynamics problems, when using the canonical ensemble, the use of just one parameter formula_6 reflects the fact that there is only one expectation value that must be held constant: the free energy (due to conservation of energy). For chemistry problems involving chemical reactions, the grand canonical ensemble provides the appropriate foundation, and there are two Lagrange multipliers. One is to hold the energy constant, and another, the fugacity, is to hold the particle count constant (as chemical reactions involve the recombination of a fixed number of atoms).
For the general case, one has
with formula_24 a point in a space.
For a collection of observables formula_25, one would write
As before, it is presumed that the argument of tr is trace class.
The corresponding Gibbs measure then provides a probability distribution such that the expectation value of each formula_25 is a fixed value. More precisely, one has
with the angle brackets formula_29 denoting the expected value of formula_25, and formula_31 being a common alternative notation. A precise definition of this expectation value is given below.
Although the value of formula_6 is commonly taken to be real, it need not be, in general; this is discussed in the section Normalization below. The values of formula_6 can be understood to be the coordinates of points in a space; this space is in fact a manifold, as sketched below. The study of these spaces as manifolds constitutes the field of information geometry.
Symmetry.
The potential function itself commonly takes the form of a sum:
where the sum over "s" is a sum over some subset of the power set "P"("X") of the set formula_35. For example, in statistical mechanics, such as the Ising model, the sum is over pairs of nearest neighbors. In probability theory, such as Markov networks, the sum might be over the cliques of a graph; so, for the Ising model and other lattice models, the maximal cliques are edges.
The fact that the potential function can be written as a sum usually reflects the fact that it is invariant under the action of a group symmetry, such as translational invariance. Such symmetries can be discrete or continuous; they materialize in the correlation functions for the random variables (discussed below). Thus a symmetry in the Hamiltonian becomes a symmetry of the correlation function (and vice versa).
This symmetry has a critically important interpretation in probability theory: it implies that the Gibbs measure has the Markov property; that is, it is independent of the random variables in a certain way, or, equivalently, the measure is identical on the equivalence classes of the symmetry. This leads to the widespread appearance of the partition function in problems with the Markov property, such as Hopfield networks.
As a measure.
The value of the expression
can be interpreted as a likelihood that a specific configuration of values formula_37 occurs in the system. Thus, given a specific configuration formula_37,
is the probability of the configuration formula_37 occurring in the system, which is now properly normalized so that formula_41, and such that the sum over all configurations totals to one. As such, the partition function can be understood to provide a measure (a probability measure) on the probability space; formally, it is called the Gibbs measure. It generalizes the narrower concepts of the grand canonical ensemble and canonical ensemble in statistical mechanics.
There exists at least one configuration formula_37 for which the probability is maximized; this configuration is conventionally called the ground state. If the configuration is unique, the ground state is said to be non-degenerate, and the system is said to be ergodic; otherwise the ground state is degenerate. The ground state may or may not commute with the generators of the symmetry; if commutes, it is said to be an invariant measure. When it does not commute, the symmetry is said to be spontaneously broken.
Conditions under which a ground state exists and is unique are given by the Karush–Kuhn–Tucker conditions; these conditions are commonly used to justify the use of the Gibbs measure in maximum-entropy problems.
Normalization.
The values taken by formula_6 depend on the mathematical space over which the random field varies. Thus, real-valued random fields take values on a simplex: this is the geometrical way of saying that the sum of probabilities must total to one. For quantum mechanics, the random variables range over complex projective space (or complex-valued projective Hilbert space), where the random variables are interpreted as probability amplitudes. The emphasis here is on the word "projective", as the amplitudes are still normalized to one. The normalization for the potential function is the Jacobian for the appropriate mathematical space: it is 1 for ordinary probabilities, and "i" for Hilbert space; thus, in quantum field theory, one sees formula_44 in the exponential, rather than formula_45. The partition function is very heavily exploited in the path integral formulation of quantum field theory, to great effect. The theory there is very nearly identical to that presented here, aside from this difference, and the fact that it is usually formulated on four-dimensional space-time, rather than in a general way.
Expectation values.
The partition function is commonly used as a probability-generating function for expectation values of various functions of the random variables. So, for example, taking formula_6 as an adjustable parameter, then the derivative of formula_47 with respect to formula_6
gives the average (expectation value) of "H". In physics, this would be called the average energy of the system.
Given the definition of the probability measure above, the expectation value of any function "f" of the random variables "X" may now be written as expected: so, for discrete-valued "X", one writes
The above notation is strictly correct for a finite number of discrete random variables, but should be seen to be somewhat 'informal' for continuous variables; properly, the summations above should be replaced with the notations of the underlying sigma algebra used to define a probability space. That said, the identities continue to hold, when properly formulated on a measure space.
Thus, for example, the entropy is given by
The Gibbs measure is the unique statistical distribution that maximizes the entropy for a fixed expectation value of the energy; this underlies its use in maximum entropy methods.
Information geometry.
The points formula_6 can be understood to form a space, and specifically, a manifold. Thus, it is reasonable to ask about the structure of this manifold; this is the task of information geometry.
Multiple derivatives with regard to the Lagrange multipliers gives rise to a positive semi-definite covariance matrix
This matrix is positive semi-definite, and may be interpreted as a metric tensor, specifically, a Riemannian metric. Equipping the space of lagrange multipliers with a metric in this way turns it into a Riemannian manifold. The study of such manifolds is referred to as information geometry; the metric above is the Fisher information metric. Here, formula_6 serves as a coordinate on the manifold. It is interesting to compare the above definition to the simpler Fisher information, from which it is inspired.
That the above defines the Fisher information metric can be readily seen by explicitly substituting for the expectation value:
where we've written formula_56 for formula_57 and the summation is understood to be over all values of all random variables formula_58. For continuous-valued random variables, the summations are replaced by integrals, of course.
Curiously, the Fisher information metric can also be understood as the flat-space Euclidean metric, after appropriate change of variables, as described in the main article on it. When the formula_6 are complex-valued, the resulting metric is the Fubini–Study metric. When written in terms of mixed states, instead of pure states, it is known as the Bures metric.
Correlation functions.
By introducing artificial auxiliary functions formula_60 into the partition function, it can then be used to obtain the expectation value of the random variables. Thus, for example, by writing
one then has
as the expectation value of formula_63. In the path integral formulation of quantum field theory, these auxiliary functions are commonly referred to as source fields.
Multiple differentiations lead to the connected correlation functions of the random variables. Thus the correlation function formula_64 between variables formula_65 and formula_63 is given by:
Gaussian integrals.
For the case where "H" can be written as a quadratic form involving a differential operator, that is, as
then partition function can be understood to be a sum or integral over Gaussians. The correlation function formula_64 can be understood to be the Green's function for the differential operator (and generally giving rise to Fredholm theory). In the quantum field theory setting, such functions are referred to as propagators; higher order correlators are called n-point functions; working with them defines the effective action of a theory.
When the random variables are anti-commuting Grassmann numbers, then the partition function can be expressed as a determinant of the operator "D". This is done by writing it as a Berezin integral (also called Grassmann integral).
General properties.
Partition functions are used to discuss critical scaling, universality and are subject to the renormalization group.


Wesley L. Harris

Wesley L. Harris is an American physicist currently the C.S. Draper Professor of Aeronautics and Astronautics at Massachusetts Institute of Technology and has been awarded honorary doctorates by Milwaukee School of Engineering, Lane College and Old Dominion University.


Leonard T. Troland

Leonard Thompson Troland (1889–1932) was an American physicist, psychologist and psychical researcher.
Career.
Troland graduated in 1912 from the Massachusetts Institute of Technology with a degree in biochemistry. He then studied psychology at Harvard University, where he obtained a Ph.D. in 1915. He worked for a year as a Harvard Travelling fellow at the General Electric Nela research lab. He served as a member of committees of the National Research Council on vision and aviation psychology. At Harvard, he gave advanced courses in psychology, and he followed up his 1926 book "The Mystery of Mind" with "Fundamentals in Human Motivation" in 1928. At the same time he was chief engineer of the Technicolor Motion Picture Corporation of California and was appointed Director of research at Technicolor in 1925.
He was elected to serve as president of the Optical Society of America from 1922 to 1923.
He gave his name to the troland (symbol Td), the unit of "conventional retinal illuminance". It is meant as a method for correcting photometric measurements of luminance values impinging on the human eye by scaling them by the effective pupil size.
The National Academy of Sciences gives an award on his behalf.
In 1932, he fell to his death from Mount Wilson.
Psychical research.
Troland took interest in psychical research and had carried out experiments in telepathy at Harvard University which were reported in 1917. He was one of the first scientists to use a machine in this type of experiment instead of a human experimenter. The machine consisted of a lamp which when triggered would light either of two square blocks. The agent would attempt to perceive the light in one room while the receiver would use a switch to identify which lamp had been lit in the other room. Troland discovered that the subjects had produced below chance expectations.


Nora Berrah

Nora Berrah is an Algerian physicist who studies how light and matter interact. She is a professor at the University of Connecticut, where she previously was chair of the physics department.
Berrah earned a diploma in physics in 1979 from the University of Algiers.
She completed her PhD in 1987 from the University of Virginia.
She worked from Argonne National Laboratory from 1987 to 1992,
and became a professor at Western Michigan University in 1999.
She moved to the University of Connecticut in 2014.
Berrah was elected as a fellow of the American Physical Society in 1999. In 2014 she won the Davisson–Germer Prize in Atomic or Surface Physics "for pioneering experiments on the interaction of atoms, molecules, negative ions and clusters with ionizing vacuum ultraviolet and soft x-ray photons".. She was elected to the American Association for the Advancement of Science (AAAS)in 2018 and her citation is for “For distinguished contributions to the field of molecular dynamics, particularly for pioneering non-linear science using x-rays free electron lasers and spectroscopy using synchrotron light sources”.
She was elected to the American Academy of Arts and Sciences in 2019.


Joseph Incandela

Joseph "Joe" Incandela is an American particle physicist, a professor of physics at the University of California, Santa Barbara and currently based at CERN, where he spent two years as the spokesperson for the Compact Muon Solenoid experiment at the Large Hadron Collider.
Biography.
Incandela received his PhD from the University of Chicago in 1986. He worked on the UA2 experiment at CERN to study the recently discovered W and Z bosons before searching for charged Higgs bosons. He then moved back to the US in 1991 to work at FNAL, where he led the construction and design of silicon detectors and co-led the search for the top quark using lifetime tagging of b quark jets. This channel had the strongest contribution to the top quark discovery in 1995. Since 1997 he has been involved with the Large Hadron Collider at CERN, initially leading the construction of a large part of the tracking system for the Compact Muon Solenoid (CMS) experiment. In 2011 he was elected to be the spokesperson for the CMS experiment.
On July 4, 2012, Incandela announced the discovery of the Higgs Boson.
Incandela was succeeded as CMS spokesperson by Tiziano Camporesi in January 2014. Profile article on Incandela back at UCSB.


God and the New Physics

God and the New Physics is a 1984 scientific book written by English scientist Paul Davies.
Overview.
The book deals fundamentally with cosmology although throughout the text several sciences are mentioned, such as: physics, mathematics, neurology, and philosophy. It deals with a wide variety of philosophical problems, such as the nature of God, miracles, free will, time, and consciousness. Davies seeks to explain the changing roles of religion and science, and the way in which physics is giving insights into what were once considered solely religious or philosophical questions.
The book is written at a level which makes it suitable for all kinds of readers, from experts to beginners.


Optical microsphere

Optical microspheres (photonic atoms) are one of the types of optical microresonators (also microcavities) employed commonly in photonic research; they provide high quality factor up to 1011. These optical resonators are used for active and passive photonic applications such as microlaser cavities and filters among many experiments that take advantage of very high levels of light confined on a small structure.


Society of X-Ray Technology

The Society of X-Ray Technology was a British professional association for work with X-rays.
History.
The Institute of X-Ray Engineers was formed in 1944 in Liverpool, soon after changing its name to the Society of X-Ray Technology.
In the mid-1980s it was one of 51 societies in the new Engineering Council, in group four.
Merger.
In 1990 it joined the Institute of Hospital Engineers, which became the Institute of Hospital Engineering and Estate Management, which is now the Institute of Healthcare Engineering and Estate Management.
Function.
It published a journal, "The Journal of X-ray Technology", twice a year and arranged lectures.
Structure.
Those belonging to the organisation were physicists, radiographers, engineers and technicians.


Pressure head

In fluid mechanics, pressure head is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container. It may also be called static pressure head or simply static head (but not "static head pressure").
Mathematically this is expressed as:
where
Note that in this equation, the pressure term may be gauge pressure or absolute pressure, depending on the design of the container and whether it is open to the ambient air or sealed without air.
Head equation.
Pressure head is a component of hydraulic head, in which it is combined with elevation head. When considering dynamic (flowing) systems, there is a third term needed: velocity head. Thus, the three terms of "velocity head", "elevation head", and "pressure head" appear in the head equation derived from the Bernoulli equation for incompressible fluids:
where
Practical uses for pressure head.
Fluid flow is measured with a wide variety of instruments. The venturi meter in the diagram on the left shows two columns of a measurement fluid at different heights. The height of each column of fluid is proportional to the pressure of the fluid. To demonstrate a classical measurement of pressure head, we could hypothetically replace the working fluid with another fluid having different physical properties.
For example, if the original fluid was water and we replaced it with mercury at the same pressure, we would expect to see a rather different value for pressure head. In fact the specific weight of water is 9.8 kN/m3 and the specific weight of mercury is 133 kN/m3. So, for any particular measurement of pressure head, the height of a column of water will be about [133/9.8 = 13.6] 13.6 times taller than a column of mercury would be. So if a water column meter reads "13.6 cm H2O", then an equivalent measurement is "1.00 cm Hg".
This example demonstrates why there is some confusion surrounding pressure head and its relationship to pressure. Scientists frequently use columns of water (or mercury) to measure pressure (manometric pressure measurement), since for a given fluid, pressure head is proportional to pressure. Measuring pressure in units of "mm of mercury" or "inches of water" makes sense for instrumentation, but these raw measurements of head must frequently be converted to more convenient pressure units using the equations above to solve for pressure.
In summary pressure head is a measurement of length, which can be converted to the units of pressure (force per unit area), as long as strict attention is paid to the density of the measurement fluid and the local value of g.
Implications for gravitational anomalies on formula_12.
We would normally use pressure head calculations in areas in which formula_6 is constant. However, if the gravitational field fluctuates, we can prove that pressure head fluctuates with it.
Applications.
Static.
A mercury barometer is one of the classic uses of static pressure head. Such barometers are an enclosed column of mercury standing vertically with gradations on the tube. The lower end of the tube is bathed in a pool of mercury open to the ambient to measure the local atmospheric pressure. The reading of a mercury barometer (in mm of Hg, for example) can be converted into an absolute pressure using the above equations.
If we had a column of mercury 767 mm high, we could calculate the atmospheric pressure as (767 mm)•(133 kN/m3) = 102 kPa. See the torr, millimeter of mercury, and pascal (unit) articles for barometric pressure measurements at standard conditions.
Differential.
The venturi meter and manometer is a common type of flow meter which can be used in many fluid applications to convert differential pressure heads into volumetric flow rate, linear fluid speed, or mass flow rate using Bernoulli's principle. The reading of these meters (in inches of water, for example) can be converted into a differential, or gauge pressure, using the above equations.
Velocity head.
The pressure of a fluid is different when it flows than when it is not flowing. This is why static pressure and dynamic pressure are never the same in a system in which the fluid is in motion. This pressure difference arises from a change in fluid velocity that produces velocity head, which is a term of the Bernoulli equation that is zero when there is no bulk motion of the fluid. In the picture on the right, the pressure differential is entirely due to the change in velocity head of the fluid, but it can be measured as a pressure head because of the Bernoulli principle. If, on the other hand, we could measure the velocity of the fluid, the pressure head could be calculated from the velocity head. See the Derivations of Bernoulli equation.


Mikhail Lukin

Mikhail Lukin (); born 10 October 1971) is a Russian theoretical and experimental physicist and a professor at Harvard University. He was elected a member of the National Academy of Sciences in 2018.
Early life.
Lukin was born in Moscow, Russia. He studied physics and mathematics at MIPT which he graduated in 1993. Following the graduation, he joined Texas A&M University where he wrote a research paper titled "Quantum Coherence and Interference in Optics and Laser Spectroscopy" which he used for his Ph.D. thesis. Between this and 1994 he was a visiting scientist to Max Planck Institute of Quantum Optics in Garching, Germany. Later on he became a postdoc at Texas A&M University and then became a fellow, and later joint director, of the Institute for Theoretical Atomic and Molecular Physics a division of Harvard–Smithsonian Center for Astrophysics. In 2001 he became an assistant professor at Harvard and three years later became its professor.
Research.
In 2005 he proposed an idea to use quantum computing mail rather than Email which is already used by both Harvard and Boston Universities. He and Vladan Vuletic experimentally confirmed a new type of matter in which photonic molecules can be used to create a lightsaber-like technology.
In a 2013 interview with "The Harvard Crimson" he explained that he observed the matter the same way as it is in the movies, but unlike the movies the objects don't pass through each other but rather behave like solid objects.
Lukin is a Fellow of the Optical Society of America.


Matthew Headrick

Matthew Peter Headrick (born ca. 1973) is Associate Professor of Physics at Brandeis University. He received his PhD from Harvard University in 2002 under Shiraz Minwalla and his A.B from Princeton University in 1994. Headrick is known for his contributions to the quantum information perspective on holography.
Headrick is notable as the 1990 winner of the Intel (then Westinghouse) Science Talent Search while a high school student at the University of Chicago Laboratory Schools, an event that generated intense media coverage. He appeared on talk shows including "Today". In response to the award, then-Illinois Gov. Thompson declared a "Matthew Headrick Day" and the US House of Representatives also made a proclamation.


Institute of Applied Physics, National Academy of Sciences of Ukraine

The Institute of Applied Physics, National Academy of Sciences of Ukraine, was established by the Decree of the Presidium of NAS Ukraine from 21.11.1991 No. 299 on the base of the Sumy branch of the Institute of Metallophysics to enlarge the fundamental and applied investigations in nuclear technology. The initiative belongs to Volodymyr Yu. Storizhko, the current director of the IAP NAS Ukraine, academician of NAS Ukraine and co-scholars from the National Scientific Center “Khar’kov Physical-Technical Institute”, NAS Ukraine. The idea of the first academic institute in Sumy region was industriously supported by B.Ye. Paton, the President of NAS Ukraine and V.G. Barjakhtar, the first Vice-President NAS Ukraine, academician of NAS Ukraine. The IAP NAS Ukraine is a part of the Department of Nuclear Physics and Power Engineering, NAS Ukraine.
Scientific schools.
The investigations are being performed by 116 researchers including 1 academician of NAS Ukraine, 3 corresponding members of NAS Ukraine, 12 Doctors of Science and 36 PhDs.
Structure of the Institute.
Much work is being done in skilled experts training. Together with Sumy Pedagogical Institute the IAP has established an IAP profile chair of advanced physical sciences for young skilled experts to be trained. A specialized Board of Studies on theses defence is created and the Interagency Board of Studies on Scientific Instrument Making led by academician V.Yu. Storizhko is working on the basis of the IAP.


Microcanonical ensemble

In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time.
The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: ), the system's volume (symbol: ), as well as the total energy in the system (symbol: ). Each of these is assumed to be constant in the ensemble. For this reason, the microcanonical ensemble is sometimes called the ensemble.
In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at . All other microstates are given a probability of zero. Since the probabilities must add up to 1, the probability is the inverse of the number of microstates within the range of energy,
The range of energy is then reduced in width until it is infinitesimally narrow, still centered at . In the limit of this process, the microcanonical ensemble is obtained.
Applicability.
Because of its connection with the elementary assumptions of equilibrium statistical mechanics (particularly the postulate of a priori equal probabilities), the microcanonical ensemble is an important conceptual building block in the theory. It is sometimes considered to be the fundamental distribution of equilibrium statistical mechanics. It is also useful in some numerical applications, such as molecular dynamics. On the other hand, most nontrivial systems are mathematically cumbersome to describe in the microcanonical ensemble, and there are also ambiguities regarding the definitions of entropy and temperature. For these reasons, other ensembles are often preferred for theoretical calculations.
The applicability of the microcanonical ensemble to real-world systems depends on the importance of energy fluctuations, which may result from interactions between the system and its environment as well as uncontrolled factors in preparing the system. Generally, fluctuations are negligible if a system is macroscopically large, or if it is manufactured with precisely known energy and thereafter maintained in near isolation from its environment. In such cases the microcanonical ensemble is applicable. Otherwise, different ensembles are more appropriate—such as the canonical ensemble (fluctuating energy) or the grand canonical ensemble (fluctuating energy and particle number).
Properties.
Thermodynamic quantities.
The fundamental thermodynamic potential of the microcanonical ensemble is entropy. There are at least three possible definitions, each given in terms of the phase volume function , which counts the total number of states with energy less than (see the Precise expressions section for the mathematical definition of ):
In the microcanonical ensemble, the temperature is a derived quantity rather than an external control parameter. It is defined as the derivative of the chosen entropy with respect to energy. For example, one can define the "temperatures" and as follows:
Like entropy, there are multiple ways to understand temperature in the microcanonical ensemble. More generally, the correspondence between these ensemble-based definitions and their thermodynamic counterparts is not perfect, particularly for finite systems.
The microcanonical pressure and chemical potential are given by:
Phase transitions.
Under their strict definition, phase transitions correspond to nonanalytic behavior in the thermodynamic potential or its derivatives. Using this definition, phase transitions in the microcanonical ensemble can occur in systems of any size. This contrasts with the canonical and grand canonical ensembles, for which phase transitions can occur only in the thermodynamic limit—i.e., in systems with infinitely many degrees of freedom. Roughly speaking, the reservoirs defining the canonical or grand canonical ensembles introduce fluctuations that "smooth out" any nonanalytic behavior in the free energy of finite systems. This smoothing effect is usually negligible in macroscopic systems, which are sufficiently large that the free energy can approximate nonanalytic behavior exceedingly well. However, the technical difference in ensembles may be important in the theoretical analysis of small systems.
Information entropy.
For a given mechanical system (fixed , ) and a given range of energy, the uniform distribution of probability over microstates (as in the microcanonical ensemble) maximizes the ensemble average .
Thermodynamic analogies.
Early work in statistical mechanics by Ludwig Boltzmann led to his eponymous entropy equation for a system of a given total energy, , where is the number of distinct states accessible by the system at that energy. Boltzmann did not elaborate too deeply on what exactly constitutes the set of distinct states of a system, besides the special case of an ideal gas. This topic was investigated to completion by Josiah Willard Gibbs who developed the generalized statistical mechanics for arbitrary mechanical systems, and defined the microcanonical ensemble described in this article. Gibbs investigated carefully the analogies between the microcanonical ensemble and thermodynamics, especially how they break down in the case of systems of few degrees of freedom. He introduced two further definitions of microcanonical entropy that do not depend on - the volume and surface entropy described above. (Note that the surface entropy differs from the Boltzmann entropy only by an -dependent offset.)
The volume entropy and associated form a close analogy to thermodynamic entropy and temperature. It is possible to show exactly that
( is the ensemble average pressure) as expected for the first law of thermodynamics. A similar equation can be found for the surface (Boltzmann) entropy and its associated , however the "pressure" in this equation is a complicated quantity unrelated to the average pressure.
The microcanonical and are not entirely satisfactory in their analogy to temperature. Outside of the thermodynamic limit, a number of artefacts occur.
The preferred solution to these problems is avoid use of the microcanonical ensemble. In many realistic cases a system is thermostatted to a heat bath so that the energy is not precisely known. Then, a more accurate description is the canonical ensemble or grand canonical ensemble, both of which have complete correspondence to thermodynamics.
Precise expressions for the ensemble.
The precise mathematical expression for a statistical ensemble depends on the kind of mechanics under consideration—quantum or classical—since the notion of a "microstate" is considerably different in these two cases. In quantum mechanics, diagonalization provides a discrete set of microstates with specific energies. The classical mechanical case involves instead an integral over canonical phase space, and the size of microstates in phase space can be chosen somewhat arbitrarily.
To construct the microcanonical ensemble, it is necessary in both types of mechanics to first specify a range of energy. In the expressions below the function formula_6 (a function of , peaking at with width ) will be used to represent the range of energy in which to include states. An example of this function would be
or, more smoothly,
Quantum mechanical.
A statistical ensemble in quantum mechanics is represented by a density matrix, denoted by formula_9. The microcanonical ensemble can be written using bra–ket notation, in terms of the system's energy eigenstates and energy eigenvalues. Given a complete basis of energy eigenstates , indexed by , the microcanonical ensemble is
where the are the energy eigenvalues determined by formula_11 (here is the system's total energy operator, i. e., Hamiltonian operator). The value of is determined by demanding that formula_9 is a normalized density matrix, and so
The state volume function (used to calculate entropy) is given by
The microcanonical ensemble is defined by taking the limit of the density matrix as the energy width goes to zero, however a problematic situation occurs once the energy width becomes smaller than the spacing between energy levels. For very small energy width, the ensemble does not exist at all for most values of , since no states fall within the range. When the ensemble does exist, it typically only contains one (or two) states, since in a complex system the energy levels are only ever equal by accident (see random matrix theory for more discussion on this point). Moreover, the state-volume function also increases only in discrete increments, and so its derivative is only ever infinite or zero, making it difficult to define the density of states. This problem can be solved by not taking the energy range completely to zero and smoothing the state-volume function, however this makes the definition of the ensemble more complicated, since it becomes then necessary to specify the energy range in addition to other variables (together, an ensemble).
Classical mechanical.
In classical mechanics, an ensemble is represented by a joint probability density function defined over the system's phase space. The phase space has generalized coordinates called , and associated canonical momenta called .
The probability density function for the microcanonical ensemble is:
where
Again, the value of is determined by demanding that is a normalized probability density function:
This integral is taken over the entire phase space. The state volume function (used to calculate entropy) is defined by
As the energy width is taken to zero, the value of decreases in proportion to as .
Based on the above definition, the microcanonical ensemble can be visualized as an infinitesimally thin shell in phase space, centered on a constant-energy surface. Although the microcanonical ensemble is confined to this surface, it is not necessarily uniformly distributed over that surface: if the gradient of energy in phase space varies, then the microcanonical ensemble is "thicker" (more concentrated) in some parts of the surface than others. This feature is an unavoidable consequence of requiring that the microcanonical ensemble is a steady-state ensemble.
Examples.
Ideal gas.
The fundamental quantity in the microcanonical ensemble is formula_18, which is equal to the phase space volume compatible with given formula_19. From formula_20, all thermodynamic quantities can be calculated. For an ideal gas, the energy is independent of the particle positions, which therefore contribute a factor of formula_21 to formula_20. The momenta, by contrast, are constrained to a formula_23-dimensional (hyper-)spherical shell of radius formula_24; their contribution is equal to the surface volume of this shell. The resulting expression for formula_20 is:
where formula_27 is the gamma function, and the factor formula_28 has been included to account for the indistinguishability of particles (see Gibbs paradox). In the large formula_29 limit, the Boltzmann entropy formula_30 is
This is also known as the Sackur–Tetrode equation.
The temperature is given by
which agrees with analogous result from the kinetic theory of gases. Calculating the pressure gives the ideal gas law:
Finally, the chemical potential formula_34 is
Ideal gas in a uniform gravitational field.
The microcanonical phase volume can also be calculated explicitly for an ideal gas in a uniform gravitational field.
The results are stated below for a 3-dimensional ideal gas of formula_29 particles, each with mass formula_37, confined in a thermally isolated container that is infinitely long in the "z"-direction and has constant cross-sectional area formula_38. The gravitational field is assumed to act in the minus "z" direction with strength formula_39. The phase volume formula_40 is
where formula_42 is the total energy, kinetic plus gravitational.
The gas density formula_43 as a function of height formula_44 can be obtained by integrating over the phase volume coordinates. The result is:
Similarly, the distribution of the velocity magnitude formula_46 (averaged over all heights) is
The analogues of these equations in the canonical ensemble are the barometric formula and the Maxwell–Boltzmann distribution, respectively. In the limit formula_48, the microcanonical and canonical expressions coincide; however, they differ for finite formula_29. In particular, in the microcanonical ensemble, the positions and velocities are not statistically independent. As a result, the kinetic temperature, defined as the average kinetic energy in a given volume formula_50, is nonuniform throughout the container:
By contrast, the temperature is uniform in the canonical ensemble, for any formula_29.


Hermanus Haga

Herman Haga (Oldeboorn, 24 January 1852 – Zeist, 11 September 1936) was a Dutch physicist.
Career.
Haga studied physics from 1871 to 1876 at the University of Leiden. He received his PhD with thesis "Over de absorptie van stralende warmte door waterdamp" (On the absorption of radiant heat by water vapor) under the direction of Pieter L. Rijke. From 1886 to 1921 Haga was professor of physics at the University of Groningen, where he designed and oversaw the building of a new physics laboratory, opened in 1892. From 1900 Haga was also the rector of the University of Gronigen. He performed experiments on the voltage of the Weston cell; these experiments lead to the modern definition of the volt. With Cornelis Wind, Haga passed X-rays through a 15-micrometer slit as a source with a V-shaped narrowing slit as a target. The target slit was 27 micrometers at the opening and nearly 0 micrometers at the output. Haga and Wind interpreted a diffuse broadening of the X-rays emitted at the narrower end of the slit as a diffraction pattern.
Haga was one of the founders of the "Nederlandse Natuurkundige Vereniging" (Dutch Physics Association). In addition to Cornelis Harm Wind (1867–1911), Haga's doctoral students include the crystallographer Pieter Terpstra (1886–1973) and Ekko Oosterhuis (1886–1966), who was the second scientist to join the "Philips Natuurkundig Laboratorium".
In 1896 Haga became a member of the Royal Netherlands Academy of Arts and Sciences.


Superoperator

In physics, a superoperator is a linear operator acting on a vector space of linear operators.
Sometimes the term refers more specially to a completely positive map which preserves or does not increase the trace of its argument. This specialized meaning is used extensively in the field of quantum computing, especially quantum programming, as they characterise mappings between density matrices.
The use of the super- prefix here is in no way related to its other use in mathematical physics. That is to say superoperators have no connection to supersymmetry and superalgebra which are extensions of the usual mathematical concepts defined by extending the ring of numbers to include Grassmann numbers. Since superoperators are themselves operators the use of the super- prefix is used to distinguish them from the operators upon which they act.
Left/Right Multiplication.
Defining the left and right multiplication superoperators by formula_1 and formula_2 respectively one can express the commutator as
formula_3
Next we vectorize the matrix formula_4 which is the mapping
formula_5
The matrix representation of formula_6 is then calculated by using the same mapping
formula_7
indicating that formula_8. Similarly one can show that formula_9. These representations allows us to calculate things like eigenvalues associated to superoperators. These eigenvalues are particularly useful in the field of open quantum systems, where the real parts of the Lindblad superoperator's eigenvalues will indicate whether a quantum system will relax or not.
Example von Neumann Equation.
In quantum mechanics the Schrödinger Equation, formula_10 expresses the time evolution of the state vector formula_11 by the action of the Hamiltonian formula_12 which is an operator mapping state vectors to state vectors.
In the more general formulation of John von Neumann, statistical states and ensembles are expressed by density operators rather than state vectors.
In this context the time evolution of the density operator is expressed via the von Neumann equation in which density operator is acted upon by a superoperator formula_13 mapping operators to operators. It is defined by taking the commutator with respect to the Hamiltonian operator:
formula_14
where
formula_15
As commutator brackets are used extensively in QM this explicit superoperator presentation of the Hamiltonian's action is typically omitted.
Example Derivatives of Functions on the Space of Operators.
When considering an operator valued function of operators formula_16 as for example when we define the quantum mechanical Hamiltonian of a particle as a function of the position and momentum operators, we may (for whatever reason) define an “Operator Derivative” formula_17
as a superoperator mapping an operator to an operator.
For example, if formula_18 then its operator derivative is the superoperator defined by:
formula_19
This “operator derivative” is simply the Jacobian matrix of the function (of operators) where one simply treats the operator input and output as vectors and expands the space of operators in some basis. The Jacobian matrix is then an operator (at one higher level of abstraction) acting on that vector space (of operators).
See also.
Lindblad superoperator


John Powell (physicist)

Dr John Alfred Powell FRSE FIEE FRSA (1923–1996) was a 20th-century British physicist and company director. His most important creation was the EMI body scanner.
Life.
Powell was born on 4 November 1923 in Islip near Oxford, the son of Algernon Powell and his wife Constance Elsie Honour. From the tiny primary school he won a scholarship to be educated at Bicester County School in Oxfordshire.
In the Second World War he joined as an apprentice in the Royal Air Force based at RAF Halton in 1939, but was invalided out in 1941. He found a place assisting at Clarendon Laboratory at Oxford, and (taking several night-classes to improve his qualifications) then won a place at Oxford University studying Physics. Gaining an honours degree (MA) he then returned to Clarendon Laboratories where he gained a doctorate (PhD). In 1952 he received a Post Doctorate Research Fellowship taking him to Ottawa in Canada.
In 1954 he returned to Britain working on semi-conductor research at Marconi Research Laboratories in Chelmsford. In 1957 he moved to Texas Instruments in Bedford as Senior Product Engineer, devising a way to create cheap germanium crystals. This brought him rapid promotion, rising to Assistant Managing Director for Northern Europe and in 1968 became Vice President. This was based in Dallas, Texas. He determined to return to Britain, albeit to a lower position. After a search for a suitable position he became Group Technical Director for EMI. His work here critically led to the development of the EMI brain scanner, which represented a major advancement in being able to view the brain. He persuaded EMI to create a new company to develop this product, EMI Medical Industries, which created a turnover of £100 million per annum. The company went on to create a body scanner and to dominate the world medical scanning market. His services made him an Honorary Fellow of the British Institute of Radiology.
In 1972 he additionally took on a role at Nuclear Enterprises Ltd as Director, rising to Chairman in 1976. This role at this time brought him into a degree of conflict with public opinion. This perhaps robbed him of what would otherwise be an expected knighthood.
In 1978 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Robert William Pringle, William Ewart John Farvis, Robert Allan Smith, James Cameron Gould, D M McCallum and Thomas Diery Patten.
He died on New Year's Eve, 31 December 1996.
Family.
In 1949 he married Zena Beatrice Steventon. They had two children, Garth and Ashley.