Chapter 4
N3: Naval Needs, NRL Capabilities, and Nonlinear Science Research Opportunities

This chapter provides a detailed set of specific areas in which naval needs, NRL capabilities (existing or potential), and nonlinear science research concepts and techniques dovetail in such a manner that significant and, in some cases, rapid progress can be made in areas of vital interest to the future of the Navy. These specific problem areas are grouped into six sections: (1) signal and image processing, (2) robotics and adaptive control, (3) turbulent and reacting flows, (4) sonar: shallow-water acoustics, (5) lasers and nonlinear optics, and (6) materials science.

Signal and Image Processing

Image Processing and Target Recognition

Image processing to recognize patterns is important for a wide variety of tasks in vision and signal processing, including recognition of typed and handwritten text, sound identification, and target recognition. Training machines to recognize patterns from a series of examples is equally important. Both problems are very difficult and have consumed the efforts of researchers in academia, industry, and the military for many years. Aided by an exponential increase in computer power, we are now in a position to see some of the first interesting applications of these techniques.

Pattern recognition is important for a variety of problems of interest to the Navy, including the recognition of visual patterns in images, as well as the recognition of temporal patterns in sonar signals and communications. These techniques are important both for reconnaissance, pattern-change recognition over long time scales and for target recognition and acquisition on much shorter time scales. The most commonly used techniques are intelligent signal processing to emphasize characteristic features such as edges or narrow band noise. Nonlinear dynamics is already proving useful in some of these applications. Techniques developed to recognize and characterize chaotic attractors can be used to gain information about simple chaotic noise sources and to predict the future of simple chaotic signals. This class of techniques could potentially allow recognition of certain types of sonar signals that do not have sharp spectral features. Neural networks constitute a class of nonlinear adaptive systems that can be used for problems in temporal signal processing and spatial pattern recognition. Demonstrated applications include the recognition of simple speech and of handwritten numerals. The advantages of neural networks are that they are fully parallel and potentially very fast, and so can provide possible improvements for some of these applications.

Visual pattern recognition is essentially a problem in nonlinear optimization: a noisy and distorted image is correlated with a stored template, which is scaled, rotated, and shifted to obtain the best match. The error function is typically highly nonlinear with many subsidiary minima in addition to the global best fit, and the design of efficient fitting routines is a complex nonlinear problem. Machine learning from examples is an equally difficult problem. Each training pattern typically is characterized by a vector in a high-dimensional space of possible attributes; clusters of vectors are associated with like patterns. In order to generalize to patterns outside the training set, it is necessary to develop an effective technique to draw surfaces around these clusters. The geometry is typically complicated, and the choice of surfaces is again a difficult problem in nonlinear optimization theory.

Most pattern recognition is currently accomplished via a collection of ad hoc techniques, and it is often not clear how well these techniques really work or how well they generalize to other problems. In handwriting



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Chapter 4 N3: Naval Needs, NRL Capabilities, and Nonlinear Science Research Opportunities This chapter provides a detailed set of specific areas in which naval needs, NRL capabilities (existing or potential), and nonlinear science research concepts and techniques dovetail in such a manner that significant and, in some cases, rapid progress can be made in areas of vital interest to the future of the Navy. These specific problem areas are grouped into six sections: (1) signal and image processing, (2) robotics and adaptive control, (3) turbulent and reacting flows, (4) sonar: shallow-water acoustics, (5) lasers and nonlinear optics, and (6) materials science. Signal and Image Processing Image Processing and Target Recognition Image processing to recognize patterns is important for a wide variety of tasks in vision and signal processing, including recognition of typed and handwritten text, sound identification, and target recognition. Training machines to recognize patterns from a series of examples is equally important. Both problems are very difficult and have consumed the efforts of researchers in academia, industry, and the military for many years. Aided by an exponential increase in computer power, we are now in a position to see some of the first interesting applications of these techniques. Pattern recognition is important for a variety of problems of interest to the Navy, including the recognition of visual patterns in images, as well as the recognition of temporal patterns in sonar signals and communications. These techniques are important both for reconnaissance, pattern-change recognition over long time scales and for target recognition and acquisition on much shorter time scales. The most commonly used techniques are intelligent signal processing to emphasize characteristic features such as edges or narrow band noise. Nonlinear dynamics is already proving useful in some of these applications. Techniques developed to recognize and characterize chaotic attractors can be used to gain information about simple chaotic noise sources and to predict the future of simple chaotic signals. This class of techniques could potentially allow recognition of certain types of sonar signals that do not have sharp spectral features. Neural networks constitute a class of nonlinear adaptive systems that can be used for problems in temporal signal processing and spatial pattern recognition. Demonstrated applications include the recognition of simple speech and of handwritten numerals. The advantages of neural networks are that they are fully parallel and potentially very fast, and so can provide possible improvements for some of these applications. Visual pattern recognition is essentially a problem in nonlinear optimization: a noisy and distorted image is correlated with a stored template, which is scaled, rotated, and shifted to obtain the best match. The error function is typically highly nonlinear with many subsidiary minima in addition to the global best fit, and the design of efficient fitting routines is a complex nonlinear problem. Machine learning from examples is an equally difficult problem. Each training pattern typically is characterized by a vector in a high-dimensional space of possible attributes; clusters of vectors are associated with like patterns. In order to generalize to patterns outside the training set, it is necessary to develop an effective technique to draw surfaces around these clusters. The geometry is typically complicated, and the choice of surfaces is again a difficult problem in nonlinear optimization theory. Most pattern recognition is currently accomplished via a collection of ad hoc techniques, and it is often not clear how well these techniques really work or how well they generalize to other problems. In handwriting

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recognition, new systems have claimed efficiencies greater than 90 percent since research began, but few have been adopted for general use, because they do not work for many users. Only a few general theoretical facts are known about pattern recognition and machine learning. These include Bayes theorem, PAC (probably almost correct) learning developed by Leslie Valiant1 and others, and the Vapnik-Chervonenkis dimension for distribution-free learning.2 A general theory of pattern recognition would be highly desirable but is probably out of reach at present. In the absence of a general theory, the development of techniques to evaluate rationally and efficiently the effectiveness of ad hoc approaches should be a priority. Data Compression or Encryption Chaos is a behavior that is typically associated with unpredictable and undesirable phenomena. For example, similar but separate chaotic systems have motion that is never correlated and that is noise-like with broadband spectral densities. In the last five years, research at NRL by Pecora and coworkers3,4 has demonstrated new ways to configure coupled chaotic systems to give unexpected, but useful, behavior and has shown that the unique properties of chaotic systems permit them to accomplish things that better-behaved systems cannot. The earliest finding was that chaotic systems could be coupled to synchronize exactly their behavior in a stable, reproducible fashion. The overall motion was chaotic, but the linked systems moved in lockstep. The method for accomplishing such synchronization is remarkably simple and immediately suggests techniques to synthesize such setups. A signal (the drive) is taken from a specific part of an autonomous chaotic system and transmitted to another system (the response). The transmitted signal takes the place of that part of the response, and the remaining parts see only each other and the incoming signal as though the whole system were still in place. The remaining signals in the response synchronize with their counterparts back in the drive. Theory subsequently developed at NRL establishes the conditions under which this arrangement is stable. The synchronization approach demonstrates that a chaotic system can be broken into parts and that, by duplicating of some of those parts and linking various parts with chaotic signals, new behavior, such as synchronization, is possible. The main theme here is that the synthesis of new chaotic systems leads to interesting and potentially useful results, including the synthesis of new signals and signal processing hardware. The first drive-response approach to synchronous chaos was patented along with several elementary approaches to using such behavior in communications with chaotic drives and carriers. Amplifying the theme of synthesis, new drive-response constructs have been pursued. Several drive-response subsystems have been cascaded to give a system that can reproduce the input, chaotic drive signal, provided all the identical subsystem parts have the same parameters. This arrangement allows one to identify incoming signals uniquely. Only signals that come from the same type of chaotic circuit with the same parameters will yield matching synchronous behavior in the response receiver. This discovery of the cascading of electronic components has been patented and currently is being investigated for potential use in identifying friend-or-foe (IFF) situations. Nonautonomous, chaotic systems have been constructed using approaches similar to drive-response synchronization that allow the chaotic drive to carry phase information about the sinusoidal forcing of the transmitter and receiver. This configuration allows the receiver to follow phase changes similar to FM in the transmitter even though only chaos is broadcast. 1   Leslie Valiant, "Computational Learning Theory," Proceedings of the Fourth Annual Workshop on Computational Learning Theory, Morgan-Kaufmann, San Mateo, Calif., 1991. 2   Vladimir N. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995. 3   T.L. Carroll and L.M. Pecora, eds. Nonlinear Dynamics in Circuits, World Scientific, River Edge, N.J., 1995. 4   W.M. Ditto and L.M. Pecora, "Mastering Chaos," Sci. American, Vol. 269, No. 2, Aug. 1993, p. 78.

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The phase-following technique combines the use of return maps with signal averaging to accomplish the phase lock. The averaging makes the technique particularly robust to noise or other contamination in the drive signal. Finally, the drive signal can be filtered or transformed, both of which can be undone at the response receiver to keep the transmitter and receiver acting chaotically but in synchronization with each other. This ability to mangle a chaotic signal and recover it has potential uses in private communications. A patent has been disclosed for filtering and unfiltering synchronous, chaotic signals. Several other approaches to control and exploit chaos have been found, and two other patents are pending. Wavelets and Image Processing Approaches to image processing using traditional Fourier methods characteristically have difficulty with edges because the Fourier basis fractions are spatially extended. Recently, an approach involving basis functions of finite extent, called wavelets, has been applied successfully to image processing. Although wavelets are finite, they need not all be of the same length. It has been proven that wavelets form a mathematically complete orthogonal basis set with which to represent a two-dimensional image with arbitrary accuracy. Further, a hierarchical set of wavelets, similar to geometric fractals, can be employed to cover an area. Wavelets can form a representation of fractals. Wavelets lend themselves to very rapid image processing using parallel computers. Images containing edges can be represented using wavelets, with acceptable loss of detail, with data compressed 100:1. As mentioned above, the efficiency of image fitting is a complex nonlinear problem. Commercial ventures are using the wavelet approach encoded on a chip as a contender in the high-definition television (HDTV) compression competition. Sensors Image sensors are the first step in a system for visual pattern recognition. To reduce the communication load and improve speed, it is desirable to perform image processing in the sensor itself, before the image is read out to the rest of the system. The development of smart sensors that use distributed processing for this purpose has been actively pursued at a number of laboratories. The principles of operation make use of developments in electronic neural networks, cellular automata, and related fields. The highly parallel architectures associated with neural network approaches are well suited to rapid signal processing for pattern recognition. For example, the Caltech group has produced a silicon retina that uses on-chip processing to do spatial and temporal derivatives for moving edge detection. In more recent work, an associated company has produced a commercial chip to optically read account numbers from checks. The vision chip project at the Massachusetts Institute of Technology has developed novel charge-coupled techniques for charge-coupled device (CCD) camera chips to do on-chip smoothing and recognition of orientation. Robotics and Adaptive Control Robots Robots will be increasingly important for a wide range of applications in the military. The optimal control of robotic arms and actuators is an interesting problem in nonlinear dynamics. Robot arms typically consist of a number of rotary joints connected together, each with its own sensors and actuators; the choice of the most efficient individual motions of these joints to accomplish a single collective motion can be a surprisingly complex problem in nonlinear optimization. Training robots to accomplish specific tasks via a series of procedures or examples is also an important and active area. For example, researchers at MIT and the University of Michigan have developed systems to train robots to maintain their balance while hopping or running and to bounce balls on a paddle, and researchers at the University of Utah have developed sophisticated techniques to program body motions of robots in human form for use in Disneyworld. Nonlinear dynamics is important for problems in control of machines and target acquisition. Recent progress has been demonstrated in the stabilization of chaotically

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vibrating machines via relatively small inputs computed by means of nonlinear algorithms. Training robot arms to perform certain tasks is also important. Because most target acquisition systems operate via a deterministic mechanism or algorithm, they are also examples of nonlinear control. This subject may be particularly well suited to work at the Naval Research Laboratory. From the point of view of the seeker, one would like to develop a system that locks onto the strongest target and is difficult to spoof. However, most target acquisition systems in the field are actually relatively simple dynamical systems. A detailed study of their properties as dynamical systems may prove useful in developing effective decoy and spoofing techniques. Controlling Chaos Exciting recent developments, both in basic theory and in technological applications, of controlling chaos are discussed in Chapter 3. Most of this work has focused on chaotic systems in which there are only a few system variables. Although it is essential to establish that such low-dimensional chaotic systems can be controlled, most real-world chaotic systems—including turbulent flows and wide-aperture solid-state lasers—are not low dimensional, and controlling the high-dimensional spatio-temporal chaos they exhibit is much more challenging. Fortunately, there has been significant recent progress in this area. For example, feedback control techniques that use external observations of a few system variables to determine stabilizing parameter perturbations have been developed for controlling high-dimensional systems. Further, spatially extended systems of chaotic elements have been controlled via perturbations made to an external parameter at several spatial locations. Controlling spatio-temporal chaos is certainly an area of great importance to the Navy, and it is also one area in which in-house expertise at NRL, combined with judicious external interactions, can make a significant contribution. Interactive Numerical and Visualization Environments Numerical methods for finding approximate solutions to dynamical systems have undergone development for centuries. However, we frequently ask questions about dynamical systems that are not easily answered by the integration of individual trajectories. Rather, we want to obtain a qualitative picture that allows us to see key features of all the trajectories in a system. For example, we would like to know the size of a basin of attraction associated with a given operating point in a control system since this tells us how robust the controller is to large disturbances. Answering such questions is a computationally intensive task, one that has required constant interaction between expert and machine. Creating effective problem-solving environments for dynamical systems is an interdisciplinary challenge. One would like to make available to engineers an environment that combines several features: A simulation language (perhaps complete with graphical icons) that translates a high-level description of a device in terms of rods, joints, springs, and so forth, into machine executable code within the analytic environment described below; A computational environment for the simulation and analysis of dynamical systems—this environment should provide the user with a graphical interface that allows access to a comprehensive set of numerical algorithms for the analysis of dynamical systems; several good computational tools are available now, but standardization and further attention to software stability and maintenance are required; A scientific database manager that allows for storage and retrieval of the information generated in a study of a system; Expert systems that check the results of the analysis for consistency with

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underlying theory and give interpretations of the observed behavior; and Visualization tools that allow one to develop a better understanding of the dynamics of multidegree-of-freedom systems. The benefits of creating an environment with all of these features would be widespread. It would help especially with the design process for vehicles, spacecraft, robots, controllers, and machines of many kinds by providing the means for rapidly testing whether a proposed design meets desired specifications. There are attractive research opportunities in the development of both general computational tools for exploring nonlinear dynamical systems and tools aimed at specifying and visualizing systems within more restricted domains. The NRL is a natural environment in which to encourage and coordinate the development of these tools. Turbulent and Reacting Flows Turbulence and Drag Reduction Turbulence is the most difficult problem in all of nonlinear science and one of central importance to the Navy. The techniques of nonlinear dynamics have not evolved sufficiently to address the general problem; however, there has been significant progress in the description of certain limiting cases in which a relatively few degrees of freedom are excited. Combustion and Detonation From jet engines and rocket motors to propellants and explosive devices, combustion and detonation are crucial to the Navy's applied warfare technologies. The propagation of detonations and deflagrations involves highly nonlinear processes. From a nonlinear science perspective, premixed flames are ideal dynamical systems. The intensity of the emitted light, which is monotonic with temperature, is a dynamical variable that defines the flame front and can be used to characterize the system. Standard optical and video techniques can be used to measure the complete spatial and temporal characteristics of the dynamics. Measurements with similar spatial resolution for fluid flows would require a large number of probes, making such experiments prohibitively complicated and expensive. The theoretical research on reacting flows and combustion at NRL is competitive with the best work in this area anywhere in the world. Oran and Boris, together with others, have compiled an excellent research record.5 The principal work of this group, entitled Numerical Simulations of Reactive Flows,6 is a major contribution to the field of computational methods in combustion science. Their research topics have spanned the full range of combustion systems. They have examined the effects of gravity and heat loss on diffusion flames and have performed numerical simulations on the cellular structure of detonations. In addition, they have studied the effects of gravity in the thermodiffusive instability of both pulsating and cellular flames. They have state-of-the-art computational facilities that are equipped with graphics capabilities to simulate both the spatial and the temporal evolution of the flame front. Most importantly for the purposes of this report, they have the knowledge and the capabilities to undertake any problem in combustion dynamics. There is extensive theoretical literature on the instabilities of premixed flames, especially those arising from thermodiffusive instability. Most of this work has been analytical, but there are both ample opportunity and need for numerical simulations. Recent experimental results in burner-stabilized premixed flames have shown that these dynamical modes can be observed. A wide array of interesting modes has been found in experiments, including rotating, spinning, pulsating, and intermittent dynamics. The current theoretical effort in computational combustion at NRL is ideally suited to be a principal contributor to the study of nonlinear dynamics as this subject evolves 5   E.S. Oran and J.P. Boris, Numerical Approaches to Combustion Modeling," American Institute of Aeronautics and Astronautics, Washington, D.C., 1991. 6   E.S. Oran and J.P. Boris, Numerical Simulation of Reactive Flow, Elsevier, New York, 1987.

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toward a study of chaotic dynamics with both spatial and temporal characteristics. Combustion phenomena represent an important and interesting class of such dynamical systems. Many of the combustion problems of interest to the Navy involve instabilities that result from nonlinear processes in combustion systems. The smooth firing of rocket motors and the proper functioning of propellants rely on the ability to operate in safe parameter ranges or to suppress or control these instabilities. The problem of spikes in the operation of shuttle engines is a manifestation of this kind of problem that has plagued rocket-powered systems since their inception. For the past 10 years, nonlinear theories of premixed flame propagation have been developed. Recently they have been shown to describe much of the dynamics observed in laboratory experiments. The optical emissions associated with a combustion front can be used as a dynamical variable that characterizes both the spatial and the temporal characteristics of its dynamics. This situation creates possibilities for the development of advanced diagnostic techniques for combustion systems to detect and analyze the onset of instabilities. Sonar: Shallow Water Acoustics The use of sonar in shallow water is difficult, because sound waves do not propagate freely for long distances. Scattering can produce complicated paths for sound rays, as well as speckle similar to that observed with optical lasers. Speckle patterns for sound waves are due to the coherent interference of sound scattered to the same point through multiple paths, because of either objects and variation in sound speed within the water or scattering from surfaces. The effect is to distort the apparent position of sonar returns and to obscure them with clutter. The physical problem of multiply scattered waves in complex media is difficult but has been studied for years in the nonlinear dynamics and statistical physics communities. Much of what has been learned about the propagation of light and electron waves can be used to analyze analogous problems with sound. The propagation of sound rays in shallow water is analogous to the paths of classical particles in a scattering potential. This problem has been studied for many years in connection with ergodic theory, chaos, and basic statistical mechanics, and much is known about specific examples such as stadium-shaped billiards, as well as randomly located scatterers. The corresponding quantum problem has also been studied extensively by theorists in connection with the topic of quantum chaos, which has been explored experimentally in chemical dynamics and, recently, in semiconductor nanostructures. Because mesoscopic quantum effects are essentially wave phenomena, many of the ideas developed for mesoscopic systems can be applied to the propagation of sound waves in disordered media and in complex geometries. This area is a natural one for NRL. Enhanced backscattering analogous to weak localization should occur for sound waves emitted into random media as well as for sound waves emitted into homogeneous media, but scattered from rough surfaces. Theorists S. Feng and Patrick Lee,7 working on mesoscopic phenomena, have found unexpected correlations speckle patterns from multiply scattered waves that allow information to be gained about an object moving through a random medium, even when the object itself is not directly visible. An investigation of the applicability of these ideas to sonar is clearly worthwhile. Lasers and Nonlinear Optics Coherent High-Power Semiconductor Laser Sources The invention of the semiconductor laser diode in 1962 followed rapidly on the first observation of lasing from ruby, but early versions suffered from poor materials growth techniques and required relatively high drive currents to operate. Modern materials growth techniques (e.g., molecular beam epitaxy) revolutionized semiconductor laser design by making it possible to lay down ultrapure layers of GaAs and GaAlAs (or InP and InAsP) with 7   S. Feng and P.A. Lee, ''Mesoscopic Conductors and Correlations in Laser Speech Patterns," Science, Vol. 251, No. 4994, 8 Feb. 1991, pp. 633-639.

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layer thicknesses ranging from atomic-scale dimensions to many thousands of angstroms. The new heterojunction lasers, although highly efficient, were limited to relatively low output power due to facet damage. A potentially useful way to increase output power without encountering facet damage is to increase the effective aperture of the laser. This approach also had the advantage that a wider aperture would mean less beam divergence at the laser output; typical diode laser transverse dimensions range from 3 to 8 μm. However, increasing the aperture was soon found to be a recipe for disaster. Broad-area lasers tend to undergo strong filamentation, a highly nonlinear phenomenon. This is a manifestation of a modulational instability in which an initially smooth laser field profile breaks up into intense, chaotically spiking filaments. These filaments are nonlinear coherent structures (solitons) developing in the device and can lead to facet damage by generating localized high field intensities. Efforts to tame nonlinear filamentation have been going on for more than 10 years with very limited success. These have included the fabrication of multistripe gain and index-guided evanescently coupled semiconductor laser arrays, mixed evanescent and Bragg grating surface-emitting lasers, strongly coupled index antiguided arrays, vertical cavity surface-emitting lasers, and many more. Index-guided evanescently coupled, edge-emitting arrays are nearest-neighbor coupled nonlinear oscillators and, not surprisingly, exhibit a rich phenomenology of chaotic behaviors. Experimental investigations have been carried out on various geometries of laser arrays including multistripe gain-guided, Y-coupled index-guided laser arrays and two-dimensional grating surface-emitting lasers. The output intensity in each case was observed to show highly erratic intensity fluctuations and, in some devices, to sample several different dynamics regimes during the course of a single electrical pulse. The experimental observation of these spatio-temporal instabilities was made using a streak camera to capture the extremely rapid intensity fluctuations (200 picoseconds). It was emphasized in these experiments that either slow detection or detection of the total integrated output power of the laser can be very misleading due to an effective averaging process that smoothes the intensity-time traces. Since the goal was to build wide-aperture, high-power coherent laser sources capable of delivering their energy in a single far-field lobe, it was even more disturbing to find that most of the energy was distributed in side lobes because of the tendency of these lasers to operate in an out-of-phase mode. Despite their importance in industrial and military applications, understanding of these laser devices has not improved much over the years. They obviously are marvelously rich nonlinear dynamical systems whose full potential can be realized only by discarding oversimplified theoretical models using ad hoc parameterization. A proper theoretical framework that has useful predictive power will require full understanding of the microscopic physics of the interaction of light with semiconductor media and consideration of longitudinal and transverse inhomogeneities in the laser structure. The many spatiotemporal events occurring in these structures on widely different space and time scales—carrier diffusion, carrier-carrier scattering (50 femtoseconds), carrier-hole recombination (nanoseconds), electromagnetic field damping (picoseconds), and thermal effects (milliseconds)—characterize this as a "grand challenge" problem, requiring the full arsenal of novel high-performance computational tools and the application of sophisticated modeling and mathematical techniques of nonlinear analysis. Experiments on wide-aperture amplifiers indicate that the most efficient amplification process occurs if the external signal is off-axis by a few degrees. Similarly, injection locking of broad-area semiconductor lasers is most efficient for off-axis injection. Preliminary unpublished theoretical evidence suggests that wide-aperture lasers and amplifiers tend to support nonlinear traveling wave solutions as their natural modes. These traveling waves manifest themselves as an off-axis emission in the far field of the laser.

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The whole development of high-power, wide-aperture, coherent laser sources has been driven to such an extent by short-term technological demands that the many issues preventing their actual realization have never been brought to the attention of the nonlinear science community. This is an area of tremendous potential for nonlinear scientists at NRL and elsewhere. In particular, developing novel methods for controlling the spatiotemporal chaos in these lasers is a topic ripe for exploitation by NRL experts and their external collaborators. Bright X-Ray Sources Bright x-ray sources offer many important applications, including x-ray lithography to create structures on submicron scales; x-ray holography for time-resolved, three-dimensional images of living cells; operation within the water window for high-contrast live biological studies; surface studies (surface dislocation cell structure and crack formation); and diagnostics of high-density fusion plasmas, to name just a few. Hot, dense plasmas produced by either electrical discharge (pulsed power drivers) or laser beams, (I > 1014 W/cm2) emit x-rays efficiently. A common mode of operation involves single-pass amplified spontaneous emission (ASE), which requires large gain-length products and leads to poor spatial coherence. True lasing would require multipass configurations, and many challenges remain with regard to designing efficient reflectors that avoid damage from hot, gaseous x-ray laser media. The potential impact of nonlinear science on this emerging field is both broad and deep. Beginning with pump sources, if tabletop x-ray lasers are to be realized, challenges lie in developing subpicosecond, high-repetition-rate, short-wavelength lasers. Significant developments in higher harmonic generation in recent years (up to the sixty-fifth harmonic of 825-nm laser light in neon at an irradiance of 1 × 1015 W/cm2 has been reported) bring reasonably accessible, tunable sources closer to implementation. Understanding the subtle interplay among nonequilibrium plasma generation (in particular, the possible role of plasma turbulence, vortex generation, and mixing in limiting the length of the gain region), x-ray emission (strong refraction due to high-density gradients in plasma has a deleterious defocusing effect), and propagation (ray or wave optics) is essential. Current state-of-the-art modeling techniques utilize plasma codes (e.g., LASNEX), gain medium modeling (rate equation kinetics) including plasma density and temperature effects, and ray tracing or wave optics propagation codes. These large-scale computational approaches offer little fundamental insight into the myriad of nonlinear interactions that contribute to or detract from efficient x-ray lasing. Finally, a challenge to materials scientists is the discovery and growth of robust materials for efficient reflection of x-rays down to very short wavelengths (~5 Å) that approach the spatial periods of naturally occurring crystals. Multilayer stacks appear to offer the best solution for normal-incidence reflectors covering the 10-Å to 50-Å wavelength range. Blue-Green Lasers The Navy has particular interest in blue-green lasers because of the good optical transmission properties of the sea in that wavelength region. A major challenge, up to a few years ago, was satellite-to-submarine communication in the deep ocean. More recently, Navy concerns have emphasized operations in shallower coastal waters where the optical properties are variable and generally better toward the green. Navy desiderata, besides the wavelength region, include high power, controllability/high pulse repetition frequency (prf), modest turbidity, high efficiency, long lifetime, compact size, and low cost. Recent industrial interest in short-wavelength lasers for compact disc recording and medical applications has some of the same desiderata, but at low power. The Fibertek medium-power device operates at 532-nm wavelength and appears to be the state of the art in meeting many of these desiderata. However, Roy and coworkers8 have demonstrated that an 8   R. Roy, Z. Gills, and K. Scott Thornburg, "Controlling Chaotic Lasers," Optics and Photonics News, Vol. 5, No. 5, 1994, p. 8.

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active approach to control of laser stability, if extensible to high-power lasers (which have many modes excited) and arrays, might offer attractive possibilities for flexibility. Materials Science Novel Electronic Materials In the past two decades, technological developments in materials synthesis and nanofabrication have led to the creation of whole new classes of man-made materials with exotic and highly nonlinear electronic properties. These novel electronic materials fall into two broad classes: (1) chemically engineered materials, including conducting polymers, charge-transfer solids, organic superconductors, and high-temperature superconductors, which are produced by creative chemical synthesis or preparation; and (2) physically engineered materials, including semiconductor superlattices, quantum wells, quantum wires, and quantum dots, which are produced by molecular beam epitaxy (MBE) and electron beam lithography (EBL). Often these materials are sufficiently anisotropic in their electronic properties as to be considered quasi-two dimensional (i.e., layered, such as copper oxide-based high-Tc superconductors), quasi-one dimensional (i.e., chain-like, such as conducting polymers or quantum wires), or even so-called zero dimensional (i.e., like artificial atoms, such as quantum dots). This reduced dimensionality has several important physical consequences on the microscopic scale, including most prominently the enhancement of nonlinear effects and of the importance of residual electron-electron interactions. On the macroscopic scale, consequences include a tremendous range of effects of potential use in future electronic devices, including negative differential conductivity (and even negative absolute conductivity in response to certain time-dependent fields) and the existence of superconductivity at temperatures above that of liquid nitrogen. The possible implications for applications of interest to the Navy strongly suggest that the nonlinear science and materials efforts at NRL should be involved actively in these developments. Organic Electronic Materials: Flexible Polymer LEDs and Nonlinear Optics As one important class of novel electronic materials, consider the conducting polymers and related organics. These materials are typically quasi-one dimensional (i.e., chain-like) and consequently exhibit larger anisotropies in their conductivity and optical properties. Their quasi-one-dimensional nature also strongly enhances the role that coherent nonlinear structures are expected to play in their transport and response properties, and experimental evidence for solitons (in trans-polyacetylene), polarons and bipolarons (in many polymers), and excitons and biexcitons (also in many polymers) confirms this expectation. Understanding the interplay of these nonlinear excitations with other degrees of freedom and modeling their effects on the optical and magnetic response and transport are crucial challenges for fundamental science and are also important for technology. Several laboratories have demonstrated that polymers, such as PPV (poly(para -phenylene)vinylene), can be made into large-format, flexible, color-tunable light-emitting diodes (LEDs). In addition, several spinoff companies are preparing this technology for the marketplace. Similarly, certain conducting polymers show some of the largest nonlinear optical responses measured to date, and the ability to tune these responses further by altering the microchemistry promises still better responses. It is important for the NRL to remain abreast of developments in this field and related areas in which the nonlinear properties of electronic materials are being studied. Semiconductor Nanostructures: Chaotic Scattering and Nonlinear Electronic Devices As noted above, modern semiconductor fabrication techniques such as MBE and EBL make possible the construction of devices approaching the size of the electron wavelength. Electrons move in these mesoscopic systems as waves and exhibit a wide variety of quantum mechanical phenomena. For structures with dimensions on the order of 0.1 mm, very low temperatures (T < 10 K) are required to reach this regime. Considerable experimental and

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theoretical research in the past decade has been devoted to understanding how electrons move as waves through complex structures. Phenomena typically found in this mesoscopic regime include reproducible conductance fluctuations associated with electron wave interference analogous to laser speckle patterns. Weak localization occurs when time-reversed pairs of electron paths constructively interfere and cause enhanced backscattering and an associated decrease in conductance. Typically, the motion of electrons in quantum wires and boxes has been thought to be relatively simple. However, scattering due simply to the shape of the box or wire can produce quantum chaos, which has a strong effect on the motion of electrons. In this context, quantum chaos is simply the behavior of quantum systems that are chaotic in the classical limit. A good example is the motion of an electron through a disordered conductor, which corresponds to a pinball scattering problem in the classical limit but gives universal conductance fluctuations in mesoscopic systems. Quantum chaos has been studied theoretically for many years in connection with the foundations of statistical mechanics and chemical dynamics and, recently, in connection with electronic conduction in metals and semiconductors. Experiments have begun on actual semiconductor nanostructures made in controlled geometries. Although this work is currently done at dilution refrigerator temperatures, as the sizes of the devices become smaller, similar phenomena will eventually occur at liquid nitrogen temperatures and higher. However, in future devices with dimensions on the order of 100 Å, wave phenomena should be observable near room temperature. Although research in this area is currently basic and seemingly removed from near-term applications, a good understanding of these inherently nonlinear phenomena will be essential to the design of ultrasmall devices in the future. In high-speed electronic devices, very large electric fields are applied over short distances to move charge carriers as rapidly as possible. In this hot carrier regime, the charge carriers acquire energies much greater than in thermal equilibrium, and their velocity distribution can change dramatically. A variety of inherently nonlinear phenomena are known to occur in this nonequilibrium regime. Carriers in confined geometries, such as quantum wells, leave the well when they attain sufficient energy, causing spatial instabilities similar to the Gunn effect in GaAs. Impact ionization of carriers bound to charge centers or confined in quantum wells can also occur, as can band-to-band impact ionization. Reliable computations of these nonlinear phenomena are important for device design and characterization. Knowledge of the hot carrier distribution is essential but cannot be computed by purely analytic methods and is difficult to obtain from experiments. Fast numerical methods to compute the hot carrier distribution in actual device geometries are needed. Good design tools can be used to avoid unwanted nonlinear phenomena as well as to exploit nonlinear effects for device operation (e.g., in microwave oscillators). Structured Materials Materials Synthesis and Processing The tools needed to understand growth processes that lead to complex materials have emerged only in the last decade. These tools include nonlinear growth models, fractal analysis, and kinetic models. Application of these nonlinear concepts to materials synthesis and processing can be expected to yield new materials that will enable novel manufacturing technologies. In particular, polymer alloys, toughened ceramics, smart gels, self-reinforced composites, and porous materials can be tailored to achieve specific properties. Research aimed at correcting these properties by manipulating new, far-from-equilibrium synthetic pathways should receive high priority. The description of colloidal aggregates and branched polymers is one of the recent successes of fractal analysis. These important commodity materials have defied characterization (let alone understanding) for decades. Fractal analysis not only quantified the structure of these materials, but also led immediately to identification of kinetic growth processes as the active process leading to fractal morphologies. The panel notes parenthetically that these same kinetic growth processes must

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be controlled in the synthesis of optical fibers, which in turn support nonlinear soliton communications technology. The most promising concepts for high-performance materials involve composites. Current technology typically uses two-pot synthesis of constituents with complementary properties (reinforcing filler and matrix) followed by mechanical mixing, often involving hand lay-up. In several demonstrated cases, however, composite properties have been achieved through in situ filling via chemical reactions. These new synthetic strategies enable new manufacturing concepts including net shape processing and low-temperature synthesis of ceramics. Self-assembling materials seem to apply local rules of assembly to generate rather complicated long-range structures. These materials, as found for example in natural living organisms, would offer outstanding properties in synthetic materials if the rules of assembly could be deciphered and manipulated. Since biological systems are adaptable (local conditions modify growth rules, leading to variability), the exploitation of self-assembly could open pathways to novel agile materials whose properties are easily tuned. This is an area in which recent discoveries in fundamental nonlinear science—studies of cellular automata, neural nets, and other adaptive complex systems—should provide valuable insights. Fracture Despite the importance of fracture to almost every technology, from ancient to modern, the fundamentals of crack growth have eluded materials scientists. Although linear regions of crack growth exist, failure usually involves nonlinear processes. Classical theories introduce a velocity-dependent fracture energy to parameterize experimental data. This approach, however, has proven inadequate to account for even the qualitative aspects of crack propagation. In brittle materials, thresholds separate regions of nonpropagation, steady crack growth, and unstable growth. Unstable growth occurs at about 40 percent of the speed of sound, where the acceleration of cracks slows sharply and they emit high-frequency acoustic waves. At this point, the fracture surface shows periodic structure correlated with velocity oscillations. The time scale of the velocity oscillations is greater than the time scale on which bonds break and remains unexplained. These basic features are found in materials from network glasses to linear polymers. Recent work employing nonlinear mathematics and computer simulation accounts for the qualitative features of crack growth but still fails to account for the observed rates of crack propagation. Experiments designed to elucidate the nonlinear phenomena underlying crack growth are nearly nonexistent. Rubbery materials fail by complex processes that are also poorly understood. Crack propagation in such materials is related closely to adhesion. As opposed to brittle materials, bond breaking is a minor contributor to fracture energy. Rather, nonlinear phenomena associated with the pullout of polymer chains dominate crack propagation. Because of the complexity of polymer dynamics, the viscoelastic processes occurring over 10 decades in time are active in crack propagation. Once again, experiments designed to probe the fundamental processes underlying crack propagation are limited. Numerous attempts have been made to use fractal analysis to describe the fracture interface. This exercise has yet to lead either to conclusive evidence for fractal roughness or to insights into the fracture process. Interfaces arising from diffusion processes, on the other hand, do display fractal characteristics, but the universal nature of the diffusion process guarantees similar geometric structures despite radical differences in interface strength. Smart Materials Smart materials have duties beyond simple structural support and containment. Such materials, although nearly nonexistent in man-made structures, are abundant in living structures. Biomaterials not only heal but also perform a variety of sensing and control functions. It is not surprising that biomimetic materials are recognized as a major emerging route to new-generation materials. Although

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numerous programs are starting up, little progress has been made in imitating even the most primitive aspects of smart biomaterials. Substantial opportunities exist to model not only the nonlinear response of these complex systems but also the self-assembly processes by which they form. Currently, adaptive control is achieved through integration of structures, sensors, and actuators. All the armed services, including the Navy, have extensive programs devoted to extending these concepts to smart structures capable of responding to their environment. Sensors remain the limiting element. Nonlinear science is essential to the design of adaptive control systems. Passive-control systems based on smart materials are a logical extension of current active-control systems. Self-healing materials, for example, could extend the life of critical components. Materials that simply provide a prefailure signature would improve reliability and safety. A material that acts as its own corrosion sensors is an example. Materials with tailored sound absorption characteristics would be of obvious interest to the Navy. The ultimate passive material system would act as its own sensor. It would convert an incoming disturbance to a control signal and then respond appropriately, for example, with a shape change. Speculative systems based on magnetostrictive alloys, shape memory alloys, and piezoelectric ceramics are under study at several laboratories. Primitive examples (e.g., foam packing) of these concepts already exist.