reference throughout this specification to “ one embodiment ,” “ an embodiment ,” or similar language means that a particular feature , structure , or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention . thus , appearances of the phrases “ in one embodiment ,” “ in an embodiment ,” and similar language throughout this specification may , but do not necessarily , all refer to the same embodiment . furthermore , the described features , structures , or characteristics of the invention may be combined in any suitable manner in one or more embodiments . in the following description numerous specific details are provided to facilitate a thorough understanding of embodiments of the invention . one skilled in the relevant art will recognize , however , that the invention may be practiced without one or more of the specific details or with other methods , components , materials , and so forth . in other instances well - known structures , materials , or operations are not shown or described in detail to avoid obscuring aspects of the invention . the schematic method diagrams included herein are generally set forth as logical flow chart diagrams . as such , the depicted order and labeled steps are indicative of one embodiment of the presented method . other steps and methods may be conceived that are equivalent in function , logic , or effect to one or more steps , or portions thereof , of the illustrated method . additionally , the format and symbols employed are provided to explain the logical steps of the method and are understood not to limit the scope of the method . although various arrow types and line types may be employed in the flow chart diagrams , they are understood not to limit the scope of the corresponding method . indeed , some arrows or other connectors may be used to indicate only the logical flow of the method . for instance , an arrow may indicate a waiting or monitoring period of unspecified duration between enumerated steps of the depicted method . additionally , the order in which a particular method occurs may or may not strictly adhere to the order of the corresponding steps shown . fig1 a - 1c displays examples of standing wave patterns than can be generated using harmonic modulation or synthesis . as illustrated an acoustic wave 100 and its pressure field 102 are generated by a transducer 106 , transmitted through a fluid ( not shown ), and reflected from a hard surface , or reflector 108 . fig1 a displays the classic example of the square wave pattern . in this example , the node or particle levitation region 104 is unstable because of the large gradient in the pressure field at the node . 1 a diagrams a transducer ( unclamped end ) 106 , an increasing pressure gradient 102 , an unstable levitation region 104 , and a reflector ( clamped end ) 108 . the pressure field ( curved line ) is generated from an acoustic standing wave in a cavity , with harmonic modulation to produce an ideal square wave , which produces an unstable nodal or levitation region by creating a steep pressure gradient . fig1 b illustrates an embodiment of harmonic modulation to produce a modified sawtooth wave 110 , which produces a stable nodal or levitation region 112 with a flat pressure gradient 114 . the flat regions 112 at the nodes of the sawtooth wave 110 stabilize the levitation region since particles ( not shown ) would not experience a pressure gradient 102 in these regions . fig1 c illustrates an embodiment of harmonic modulation to produce an ideal spike wave 116 , which localizes the wavefield pressure 114 . sharp pressure spikes 118 may occur at the antinode positions . an embodiment of optimal levitation condition may comprise a pressure “ well ”, which could tightly confine the particles between two adjacent pressure spikes 118 . fig1 b and 1c illustrate embodiments of theoretical wavefields that would require a very large number of harmonic modes ranging to very high frequencies to produce . in practice , only a small number of harmonic modes would be necessary to produce a good approximation to an example such as the square wave in fig1 a . fig2 a - 2d illustrates an embodiment of the harmonic modulation 200 of a fundamental wave mode , fig2 a , in accordance with the present invention . as illustrated fig2 b uses two , fig2 c uses four , and fig2 d uses seven harmonic modes to produce an approximations 206 , 208 , an 210 of a square wave . the illustrated embodiment depicts a transducer 106 , a standing wave 202 , a nodal 204 region forming a levitation point and a reflector 108 for each modulation . acoustic standing waves may be generated in a confined fluid . for example , if an acoustic source is placed against one face of a cubic chamber filled with fluid , longitudinal standing waves will be generated in the fluid at frequencies which are inversely proportional to the size of the cube . if the acoustic source is emitting a single frequency , then the pressure field of the standing wave 202 may be described with a cosine wave , and the nodal 204 regions may be described as planar surfaces parallel to the cube faces . cells or particles may collect at the nodal 204 regions since the acoustic forces and pressures are zero there . however , in some cases the nodal 204 regions are not well defined since the acoustic pressure gradually increases away from the nodal 204 surface due to the pure cosine function . cells and particles with motion may therefore oscillate about the nodal 204 surface , thus creating an ill - defined nodal region 204 . acoustic waves of multiple frequencies may be used , however , to more sharply define the nodal 204 region and resulting particle structure . for example , higher - order harmonic waves may be used to modify the shape of the standing wave 202 to more tightly confine the cells and particles in the nodal 204 region . in some embodiments , the cosine waveform of the standing wave 202 may be modified with harmonics to resemble a square wave 100 , a modified sawtooth wave 110 , or a double spike structure 116 with a pressure well at the nodal 204 points . such a wave modifications may be used to create a much more narrow and well - defined nodal 204 region where the acoustic pressure steeply increases away from the nodal 204 ( zero acoustic pressure ) surface and simultaneously tightly binds the cells or particles by creating a potential well with respect to the pressure . cells and particles with motion may therefore be more tightly restricted to the nodal 204 surface , thus creating a well - defined nodal 204 region . the increased definition of the nodal 204 region may also increase its stability with respect to particle motion and the shape of the composite particle structure . for example , particles in a planar nodal 204 surface may oscillate in and out of the nodal 204 region less frequently , and the nodal 204 surface may maintain a more well - defined planar geometry . various embodiments of the technology provided herein employ acoustic or electromagnetic sources that can generate multiple , distinct frequencies . a piezoelectric transducer may have stacked piezoelectric elements . the transducers sometimes comprise piezoelectric elements of different thicknesses stacked on top of each other and , in some embodiments , electrically isolated from each other to facilitate independent electrical excitation of that element &# 39 ; s specific frequency . the different thickness of each element may tune the element to a different harmonic frequency . when driven in concert by a voltage source , the combination of elements may produce multifrequency wave fields more similar in structure to the ideal wave fields used in the computer simulations illustrated in fig3 , 7 , 8 , 9 , and 10 herein . a broadband acoustic transducer may be driven by an arbitrary waveform generator to directly produce the desired standing wave pattern . in some embodiments a broadband piezoelectric transducer used in combination with one or more narrow - band acoustic filters . the broadband transducer may be pulsed at a high pulse repetition frequency . the acoustic filters are sometimes made from acoustic metamaterials . in certain embodiments a saser ( sound amplification by stimulated emission of radiation ) is used in combination with nonlinear higher - order harmonic generation . some embodiments employ harmonic generation from the acoustic scattering of single - frequency plane waves from small orifices . various embodiments use new acoustic metamaterials that exhibit phenomena analogous to frequency mixing processes in nonlinear optics . various embodiments multifrequency electromagnetic sources comprise harmonic frequency generation in lasers , harmonic frequency generation in masers , miniaturized , multicomponent radio - frequency ( rf ) and microwave antennas with harmonic frequency capability , and the use of metamaterials as tunable narrow - band filters in combination with a broadband electromagnetic or optical source . fig3 a - 3c depict embodiments 300 of computer simulations of periodic three - dimensional channels created with square 3 a , rectangular 3 b , and hexagonal 3 c symmetries using harmonic modulation and placement of two acoustic sources at 90 ° 3 a - b , and 120 ° 3 c orientations with respect to each other in accordance with the present invention . the harmonic modulations create well - defined , multilayered channel walls , or interlaced channel structures with different channel sizes . the use of multiple sources and multiple frequencies for the acoustic waves , standing waves may be generated with a wide range of complex structures . in various embodiments , periodic three - dimensional channels may be created with square , rectangular , triangular , and rhombohedral symmetries using placement of acoustic sources at 90 ° and 120 ° orientations with respect to each other . aperiodic structures may be created using placement of acoustic sources with five - fold ( 108 °, seven - fold ) ( 128 . 57 °, and eight - fold ( 135 ° symmetries . since such symmetries cannot tile two - and three - dimensional spaces , resulting cell structures from such standing waves could be aperiodic and random , much like many tissue microstructures . in atomic structures , five - and seven - fold symmetries are incommensurate and form disordered or quasi - crystalline patterns . other positioning is sometimes employed to created other specialized patterns or structures . in certain embodiments complex structures are generated in a cell or particle suspension in a cylindrical chamber . the resulting standing waves may be described by cylindrical wave functions , and excitation of different standing wave modes could be used to create structures with axial channels clustered around the chamber &# 39 ; s axis and cuboidal chambers encircling the channels . such composite cell structures could be used to engineer lobular - type tissue microstructures such as those found in the lung ( alveoli ) or kidney ( glomeruli ). dendritic alveolar structures may be patterned using a conical confinement chamber and multiple frequencies . the standing waves may be the resonant modes of a cone , and could have conical symmetry , might follow a conical coordinate system , and be modeled and represented with conical wave functions . in some embodiments microfluidic control of cells or particles is achieved without the need for conventional microfluidic devices with fixed channels and chambers . acoustic standing wavefields may be used as a force field to confine the cells or particles to virtual channels and chambers through which they would flow . in various embodiments an acoustic wavefield structure is modified by modifying its frequency content , source positions , and phase . thus , the virtual microfluidic device may be rapidly reconfigured to perform many different functions . certain embodiments focus the antinodal regions of standing waves into spikes . such embodiments comprise acoustic cavitation in fluids , sonochemistry , sonoluminescence , tissue ablation in tissue engineering or cancer therapy , ultrasonic and electromagnetic stimulation of neurons in vivo . localized optical focusing for ultra - resolution optical microscopy , and rf or microwave focusing for heating or sensing applications . fig4 a - 4b depict an embodiment of a device 400 using acoustic levitation to produce a layer of cells 408 suspended in a liquid medium 406 in accordance with the present invention . fig4 a is a schematic line drawing depicting an embodiment of the device 400 comprising a 50 mhz - prove transducer 402 , a cylindrical well 404 , fluid 406 , a standing wave 405 , a node 204 , an antinode 407 , a cell layer 408 , a thin plastic film 410 , and a 200 khz levitation transducer 412 . fig4 b is line drawing of a photographic depiction of the device 400 demonstrating acoustic levitation of cell - mimicking buoyancy neutral microspheres 414 in water 406 in a cylindrical well 404 using an upper transducer 402 and a lower transducer 412 . the microspheres 414 form layers 416 at the standing - wave nodes . such layers 416 are necessary for probing with hf ultrasound and acquiring a coherent pulse reflection . in some embodiments the cell layer 416 can then be probed with hf ultrasound to obtain cell biomechanical properties without interfering reflections and adhesion forces due to the culture plate . the use of acoustic standing waves for the purpose of tissue engineering relies on the phenomenon of acoustic levitation . in acoustic levitation , a standing wave 405 is generated in a closed cavity 404 or acoustic region with the use of ultrasound tuned to a specific frequency conducive to forming the standing wave 405 . such a standing wave 405 has nodes 204 where the wave pressure does not vary and antinodes 407 where the wave pressure shows the greatest variation . particles 414 in the fluid ( air or liquid ) 406 are forced away from the antinodes 407 due to the changing pressure , accumulate at the nodal regions , 204 and form layers . fig4 illustrates acoustic levitation to suspend microparticles 414 and cells 408 in a fluid 406 for testing with high - frequency ( 50 mhz ) ultrasound . when applied to tissue engineering , cells 408 in a growth medium 406 ( fluid or gel ) are exposed to acoustic standing waves 405 . the cells 408 accumulate at the nodal regions 204 , where they continue to reproduce as well as release proteins and other biomolecules to adhere to each other and produce an extracellular matrix . the cell 406 layers 416 are thus organized into forming a layered tissue structure . a standing wave 405 comprised of multiple frequencies facilitates this process . to maintain the characteristics of a standing wave 405 , the frequencies may be harmonics of the fundamental or lowest standing - wave frequency . the interference pattern created by the multiple frequencies enables the modulation of the standing wave and the custom tailoring of its properties . for example , in fig4 b , the transducer 402 , 412 is being driven by a square - wave voltage pattern , which is forcing the transducer 402 , 412 to produce wave frequencies of the fundamental and first four odd harmonics . this combination of frequencies produces a nodal region 204 that is much more focused ( thinner and highly defined ) as illustrated in 4 b than that produced by the simple sine wave shown in 4 a . since the pressure gradients near the node 204 are greater in 4 b than in 4 a , the levitated microparticles 414 or cells 408 form a much more stable and defined layer 416 . fig5 a - 5c depict an embodiment of computer model 500 of the nodal focusing effect for an ultrasonic standing wave - field in accordance with the present invention . the illustrated embodiment shows the nodal focusing effect with six nodes illustrating the nodes as dark lines for a single - frequency sine wave 5 a , a square wave generated from three frequencies ( fundamental and first two odd harmonics ) 5 b , and a square wave generated from five frequencies ( fundamental and first four odd harmonics ) 5 c . the model displays the absolute values of the pressure fields and nodes for a simple sine wave driving the transducer with a single frequency 5 a , a square wave driving the transducer to emit three ultrasonic frequencies 5 b , and a square wave driving the transducer to emit five ultrasonic frequencies 5 c . as illustrated the nodal regions grow thinner and more defined with the accumulation of additional frequencies , with greater sharpness and definition of the nodes in 5 b and 5 c as compared to 5 a . other nodal patterns may be generated as well by altering the amplitudes of the harmonic frequencies . such patterns could include double or triple thin nodal layers , or thick nodal layers separated by thin antinodal regions . fig6 a - 6b depict embodiments of experimental verification 600 of the use of harmonic frequencies to modulate the standing wave and focus the nodal regions using cell - mimicking buoyancy neutral microspheres 414 in water 406 in accordance with the present invention . for fig6 a an ultrasonic transducer was driven by a sine - wave voltage source ( single frequency ). fig6 b used an ultrasonic transducer driven by a square - wave voltage source ( fundamental frequency and odd harmonics ) thus producing greater sharpness and definition of the cell layers in 6 b as compared to 6 a . buoyancy - neutral polyethylene microspheres 414 were suspended in water 406 contained in an acrylic cylinder 404 with a thin sheet of plastic 410 glued to the bottom . a 200 - khz transducer 412 was placed below the cylinder and acoustically coupled to the plastic bottom with ultrasonic gel . in fig6 a , a pure sine - wave voltage was applied to the transducer 412 , producing a single - frequency standing wave . as predicted by the model shown in fig5 a , the microspheres 414 formed thick layers 416 at the nodes , with many microspheres 414 left in suspension between the nodes 204 . in fig6 b , a square - wave voltage was applied to the transducer , producing higher harmonic frequencies . as predicted by the models shown in fig5 b and 5c , the microspheres 414 formed thinner layers at the nodes 204 , with much fewer microspheres 414 between the nodes 204 . in addition to forming thinner , more highly defined layers 416 , experiment 6 b using a square - wave voltage source produced the layers 416 more rapidly than experiment 6 a using the sine - wave voltage source . the layers 416 in 6 b were additionally more stable and persisted longer in solution . the results from the computer modeling of fig5 and the experiments here demonstrate that one - dimensional interference patterns created by standing waves of different frequencies can be used to fine - tune and improve the acoustic levitation process . the process of forming these interference patterns is also known as fourier synthesis , the ability to create any arbitrary waveform from a combination of a set of sine waves of different frequencies . for example , tissue microstructures from a laboratory animal such as a mouse are analyzed with 3d fourier analysis . the 3d microstructure of a region of tissue , such as the alveolar structure of lung , are obtained by microtoming and imaging successive slices of a sample of tissue . the image slices are then stacked by a computer program and reconstructed into a 3d representation of the tissue microstructure . finally , 3d fourier analysis is performed on the 3d image to obtain the principal spatial frequencies and their amplitudes . the ultrasonic interference patterns may be extended from one dimension to two and three dimensions as well , forming complex patterns that may be used for engineering tissues with microstructures mimicking those found in the human body . fig7 a - 7c depict embodiments of the generation 700 of complex 3d node patterns ( black lines ) using a combination of two transducers 106 , multiple frequencies , and the resulting interference patterns in accordance with the present invention . fig7 a is a schematic line drawing depicting a system 700 for creating complex 3d node patterns , the system 700 comprising a configuration of two ultrasonic transducers 106 that produce standing waves 706 in a growth medium 704 in a chamber 702 . by orienting the transducers 106 orthogonal to each other , the standing waves 706 can be made to interfere with each other to produce patterns useful for constructing biomaterials and tissues . fig7 b depicts square channels generated from two simple sine waves and the intersection of the nodal planes and is a model - generated image of how the interference patterns from two simple sine waves transmitted from the transducers 106 interfere to produce a square lattice of nodal planes ( dark lines ). growth of cells into tissue walls along this nodal lattice could produce square channels running through the microstructure . fig7 c depicts a lattice of complexly shaped channels and planes ( dark lines ) generated by using multiple harmonic frequencies from each transducer . this lattice was created using only the fundamental frequency and first three harmonics and comprises parallel channels of different shapes and sizes . an even more complex nodal microstructure may be created by adding a third transducer orthogonal to the first two . harmonic frequencies added to the ultrasonic waves could produce an enormous variety of complex nodal lattices . thus , by modulating the amplitudes of the harmonic frequencies , almost an infinite variety of tissue microstructures could be generated with the ultrasonic interference patterns . for example , such a microstructure may comprise sac - like structures interlaced with channels , much like alveoli and bronchioles in the lungs . fig8 a - 8c depicts embodiments of other types of complex node patterns ( black lines ) generated using two transducers and various combinations of harmonic frequencies in accordance with the present invention . in some embodiments , an actual tissue microstructure from the body could be analyzed using 3d fourier analysis to obtain the spatial frequencies of the structure . the amplitudes of these spatial frequencies would then be used to tune the combinations of harmonic frequencies used to generate the ultrasonic interference patterns . the method employs a holographic approach to tissue engineering by using the principle of interfering wave fields to produce realistic patterns in space . fig9 a - 9b depict an example 900 of a one - dimensional simple , single - frequency wavefield 9 a , and a two - dimensional view of a three - dimensional tissue structure 9 b engineered from the superposition of three simple standing wavefields as shown in 9 a . the light and dark areas are antinodal regions which form continuous channels running through the structure , into and out of the drawing as portrayed . the nebulous and gradually varying amplitude variations would make it difficult to predict or control the growth of tissue structures of specific sizes , shapes , and configurations . fig1 a - 10b illustrate embodiments 1000 of a complex standing waveform constructed from a specific superposition of harmonic frequencies to form sharp , distinctive pressure amplitude spikes 10 a , and the formation of a triangular lattice of channels in a three - dimensional tissue structure 10 b by the superposition of three planar complex standing waves as shown in 10 a and confined in a cavity with a hexagonal cross - section in accordance with the present invention . in 10 b , only the light regions that form the sharply defined triangular lattice are the antinodal regions which form continuous channels running through the structure , both into and out of the drawing as portrayed and across the microstructure as a triangular lattice . these antinodes correspond to the amplitude spikes in 10 a . the triangular dark areas between the light - shaded lines are nodal regions , and correspond to the regions of the waveform with low pressure amplitudes (≦ 0 . 2 ). tissue structures such as regular cell clusters ( lobules ) could form in these nodal regions . thus , in certain embodiments , complex , harmonic - modulated standing wavefield produces sharp , well - defined channels in the tissue structure that more closely resemble the structure of arteriole , capillary , and other ductal structures in tissue . the segmentation of cells into regular triangular , rectangular , or hexagonal cell clusters could also more closely resemble many tissue microstructures in the body , such as the lobules of the liver . other organ tissues could be engineered from such geometrically regular structural units , such as the alveoli and bronchioles of the lung as shown in fig1 . fig1 is a schematic line drawing of an embodiment of an engineered tissue structure 1100 for replicating the alveolar 1102 and bronchiole 1104 structures of the lung using harmonic - modulated acoustic standing wavefields in accordance with the present invention . such regular geometric structures could be produced in a manner similar to that shown in fig1 , except the interior of the hexagonal regions may be the empty alveolar 1102 and bronchiole 1104 cavities , and could therefore be generated from antinodal regions in the standing wavefield . the thin regions surrounding the alveoli may be the epithelial , elastin , and capillary walls 1106 of the alveoli 1102 and bronchioles 1104 , and could be generated by a large part from nodal regions in the standing wavefield . fig1 a - 12d depict embodiments of a complex , harmonic - modulated standing wavefields 1200 designed to produce highly localized amplitude spikes 1202 in accordance with the present invention . in some embodiments the wavefields 1200 comprise acoustic waves in fluids . the wavefields 1200 sometimes comprise stress - strain fields corresponding to acoustic waves in solids , electromagnetic fields , particle density fields ( e . g ., ions or electrons in a plasma , metal , or ionic conductor ), and the like . such spikes 1202 may be useful in tissue engineering for patterning channels and cavities in tissue constructs . in certain embodiments they could also be used for a variety of other applications such as enhancing acoustic cavitation and sonoluminescence , improving stability and fusion yields in plasmas by producing an electromagnetic pinch or containment effect , inducing high - field effects in laser cavities , or enhancing electro - acoustic and acousto - ionic effects in liquid and solid electrolytes . fig1 depicts an embodiment of a system 1300 for spatial focusing and patterning using harmonic modulation of standing wavefields in accordance with the present invention . as illustrated the embodiment comprises a wave transmitter 1302 that transmits waves at multiple frequencies ; a chamber or cavity 1304 configured to generate standing waves ; a control module 1306 to modulate the amplitudes of the individual harmonics in order to generate a desired wavefield pattern and an analysis module 1308 to calculate the amplitudes of individual harmonics corresponding to a desired wavefield pattern , material structure , or material configuration . in some embodiments the wave transmitter 1302 comprises an acoustic transducer , electromagnetic antenna , or laser . the multiple frequencies transmitted may comprise specifically a fundamental ( lowest ) frequency mode and harmonics of the fundamental frequency . in certain embodiments the wave transmitter 1302 comprises multiple wavefield sources to further focus the wavefield structure into a complex or well - defined pattern in one , two , or three dimensions . the standing waves may be planar , cylindrical , spherical , or one of the many other geometries that produce wave functions conducive to standing waves , such as spheroidal . various embodiments of the technology herein use the principle of fourier &# 39 ; s theorem to focus the nodal or antinodal regions in a standing wave , or to generate more complex node - antinode patterns in the standing wave . fourier &# 39 ; s theorem states that it is possible to construct any complex periodic vibration into a harmonic array of component frequencies . fourier &# 39 ; s theorem may therefore be used to construct periodic waves more complex than a single - frequency wave , and that can therefore more sharply focus the acoustic pressure or electromagnetic fields at the nodal or antinodal regions . in some embodiments a multifrequency , single transmitting source spatially focuses the wavefields . such a system may generate a wide range of arbitrary complex wavefield patterns , eliminating the need for a transmitter with a special shaped design or face for focusing waves . likewise this spatial focusing of the wavefields using multiple frequencies (“ frequency focusing ”), is not reliant on physical focusing elements such as lenses or mirrors . in various embodiments the generation of highly defined nodal regions may increase the stability of levitated suspensions by confining particle motion to a greater extent . the generation of more highly defined antinodal regions — spikes — which may increase the localization of wavefield intensity for the generation of high intensity phenomena such as cavitation in fluids , thermal ablation , sonochemistry , or stimulation of neurons in biological organisms . in certain embodiments wavefields of multiple frequencies and from multiple sources 1302 are used to create standing waves in a three - dimensional particle suspension . particles may be attracted to and held at the nodal regions of the standing waves . the use of multiple frequencies and sources 1302 allows the creation of sharply defined and complexly structured nodal regions . the sharp definition of the nodal regions may additionally stabilize the particle structure by suppressing particle motion and oscillations within the nodal regions . thus , in some embodiments acoustic wavefields having multiple frequencies and multiple sources are used to create standing waves that function as a virtual template for holding particles in complex , highly stable , and highly resolved patterns . computational modeling of the wavefields is sometimes used to select a set of frequencies and source locations to produce the particle structures . in some embodiments each acoustic source has the capability of generating acoustic waves comprised of a plurality of distinct frequencies . these distinct - frequency acoustic waves may form standing waves that superimpose ( sum ), creating complex standing wave structures with stable , highly defined nodal surfaces . they may also generate complex combinations of nodal surfaces forming “ double - wall ” and “ triple - wall ” features . the technology herein may further use a plurality of these multifrequency sources to generate complex geometric configurations of nodal surfaces . these configurations can then be used as virtual or acoustic - force templates for the patterning of particles in suspensions . fig1 depicts a method 1400 for spatial focusing and patterning using harmonic modulation of standing wavefields in accordance with the present invention and comprising the steps : begin 1401 , provide 1402 at least one wave transmitter , provide 1404 at least one chamber or cavity , provide 1406 at least one controller , identify 1408 at least one desired wave pattern , generate 1410 at least one standing wave according to the desired wave pattern , generate 1412 at least one additional standing wave according to the desired wave pattern , compare 1414 the resulting combined wave to the desired wave pattern , if the resulting combined wave pattern does not closely approximate the desired wave pattern then return to step 1410 , if the resulting combined wave closely approximates the desired wave pattern then fine tune 1416 the resulting combined wave to generate a fine tuned wave pattern more closely approximating the desired wave pattern , compare 1418 the fine tuned wave pattern to the desired wave pattern , if the fine tuned wave pattern does not sufficiently approximate the desired wave pattern then return to step 1416 , and if the fine tuned wave pattern sufficiently approximates the desired wave pattern then end 1420 . in certain embodiments the wave generated is an electromagnetic wave . the wave generated is sometimes an acoustical wave . in some embodiments the method spatially focuses and patterns the nodal and antinodal regions in standing wavefields by modulating the wavefields with harmonics ( waves of higher frequency where the frequency is an integer value of the lowest or fundamental frequency ). various embodiments include , but are not limited to , the generation of highly stable nodal regions for acoustic , electromagnetic , or optical levitation and manipulation of particulate matter in suspension , including biological cells , colloids , aerosols , and powders . some embodiments generate complexly structured nodal regions for patterning biological materials in tissue engineering applications or nonbiological materials in fabrication applications . the method provided may generate antinodal regions with highly - localized , high acoustic pressures for enhanced cavitation , sonoluminescence , or sonochemistry in fluids . the method sometimes generates antinodal regions with highly - localized , high acoustic pressures to create well - defined channels or cavities in biological or nonbiological materials . in certain embodiments the method generates antinodal regions with highly - localized , high electromagnetic field strengths for initiating novel physical , chemical , or biological processes . fig1 depicts a method 1500 for cellular or tissue modeling using harmonic modulation of standing wavefields for spatial focusing and patterning and comprising the steps : select 1502 a target tissue , analyze 1504 the structure of the target tissue , model 1506 a standing wavefield that mimics the structure of the target tissue , program 1508 one or more multifrequency wave transmitters to create the specified standing wavefield , provide 1510 a chamber configured to create standing waves , provide 1512 a suitable medium within the chamber , add 1514 the selected cells to the medium , apply 1516 the wavefield to the chamber , allow 1518 sufficient time for the cells to organize into the form dictated by the standing wavefield and repeating 1520 the steps for complex tissues to pattern other cell types . embodiments of this technology include , but are not limited to , the patterning of cells into realistic tissue structures for tissue engineering ; the patterning , consolidation , and bonding of particles for the fabrication of parts and devices having complex shapes ; the stabilization of cell or particle layers in acoustic standing wave chambers or channels for nondestructive testing via ultrasonic , optical , or other noninvasive means ; the refined separation of cells or particles for medical , chemical , or industrial processes ; and microfluidic control of cells or particles without the need for conventional microfluidic devices with fixed channels and chambers . the present invention may be embodied in other specific forms without departing from its spirit or essential characteristics . the described embodiments are to be considered in all respects only as illustrative and not restrictive . the scope of the invention is , therefore , indicated by the appended claims rather than by the foregoing description . all changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope .