Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.

New non-reorientational optical nonlinear effect in MBBA

A new effect producing self-focusing of light in a nematic MBBA film is reported. This effect produces a static diffraction pattern composed of circular rings which is different from the ones arising from self-focusing previously reported. The influence of the cell thickness, the optical intensity, and the wavelength is studied. Once the nematic is distorted by a láser beam, the effect produced in other light beam passing through the modified región is independent of its polarization. This isotropic behavior shows that a molecular reorientation has not been produced. The origin of this effect seems to be the same of that of the effect which produces a randomly oscillating diffraction pattern previously reported by our group. Some possible causes such as thermal indexing, convective instabilities and self-induced transparency are discussed.

Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Automated wordlength optimization framework for multi-source statistical interval-based analysis of nonlinear systems with control-flow structures

El uso de aritmética de punto fijo es una opción de diseño muy extendida en sistemas con fuertes restricciones de área, consumo o rendimiento. Para producir implementaciones donde los costes se minimicen sin impactar negativamente en la precisión de los resultados debemos llevar a cabo una asignación cuidadosa de anchuras de palabra. Encontrar la combinación óptima de anchuras de palabra en coma fija para un sistema dado es un problema combinatorio NP-hard al que los diseñadores dedican entre el 25 y el 50 % del ciclo de diseño. Las plataformas hardware reconfigurables, como son las FPGAs, también se benefician de las ventajas que ofrece la aritmética de coma fija, ya que éstas compensan las frecuencias de reloj más bajas y el uso más ineficiente del hardware que hacen estas plataformas respecto a los ASICs. A medida que las FPGAs se popularizan para su uso en computación científica los diseños aumentan de tamaño y complejidad hasta llegar al punto en que no pueden ser manejados eficientemente por las técnicas actuales de modelado de señal y ruido de cuantificación y de optimización de anchura de palabra. En esta Tesis Doctoral exploramos distintos aspectos del problema de la cuantificación y presentamos nuevas metodologías para cada uno de ellos: Las técnicas basadas en extensiones de intervalos han permitido obtener modelos de propagación de señal y ruido de cuantificación muy precisos en sistemas con operaciones no lineales. Nosotros llevamos esta aproximación un paso más allá introduciendo elementos de Multi-Element Generalized Polynomial Chaos (ME-gPC) y combinándolos con una técnica moderna basada en Modified Affine Arithmetic (MAA) estadístico para así modelar sistemas que contienen estructuras de control de flujo. Nuestra metodología genera los distintos caminos de ejecución automáticamente, determina las regiones del dominio de entrada que ejercitarán cada uno de ellos y extrae los momentos estadísticos del sistema a partir de dichas soluciones parciales. Utilizamos esta técnica para estimar tanto el rango dinámico como el ruido de redondeo en sistemas con las ya mencionadas estructuras de control de flujo y mostramos la precisión de nuestra aproximación, que en determinados casos de uso con operadores no lineales llega a tener tan solo una desviación del 0.04% con respecto a los valores de referencia obtenidos mediante simulación. Un inconveniente conocido de las técnicas basadas en extensiones de intervalos es la explosión combinacional de términos a medida que el tamaño de los sistemas a estudiar crece, lo cual conlleva problemas de escalabilidad. Para afrontar este problema presen tamos una técnica de inyección de ruidos agrupados que hace grupos con las señales del sistema, introduce las fuentes de ruido para cada uno de los grupos por separado y finalmente combina los resultados de cada uno de ellos. De esta forma, el número de fuentes de ruido queda controlado en cada momento y, debido a ello, la explosión combinatoria se minimiza. También presentamos un algoritmo de particionado multi-vía destinado a minimizar la desviación de los resultados a causa de la pérdida de correlación entre términos de ruido con el objetivo de mantener los resultados tan precisos como sea posible. La presente Tesis Doctoral también aborda el desarrollo de metodologías de optimización de anchura de palabra basadas en simulaciones de Monte-Cario que se ejecuten en tiempos razonables. Para ello presentamos dos nuevas técnicas que exploran la reducción del tiempo de ejecución desde distintos ángulos: En primer lugar, el método interpolativo aplica un interpolador sencillo pero preciso para estimar la sensibilidad de cada señal, y que es usado después durante la etapa de optimización. En segundo lugar, el método incremental gira en torno al hecho de que, aunque es estrictamente necesario mantener un intervalo de confianza dado para los resultados finales de nuestra búsqueda, podemos emplear niveles de confianza más relajados, lo cual deriva en un menor número de pruebas por simulación, en las etapas iniciales de la búsqueda, cuando todavía estamos lejos de las soluciones optimizadas. Mediante estas dos aproximaciones demostramos que podemos acelerar el tiempo de ejecución de los algoritmos clásicos de búsqueda voraz en factores de hasta x240 para problemas de tamaño pequeño/mediano. Finalmente, este libro presenta HOPLITE, una infraestructura de cuantificación automatizada, flexible y modular que incluye la implementación de las técnicas anteriores y se proporciona de forma pública. Su objetivo es ofrecer a desabolladores e investigadores un entorno común para prototipar y verificar nuevas metodologías de cuantificación de forma sencilla. Describimos el flujo de trabajo, justificamos las decisiones de diseño tomadas, explicamos su API pública y hacemos una demostración paso a paso de su funcionamiento. Además mostramos, a través de un ejemplo sencillo, la forma en que conectar nuevas extensiones a la herramienta con las interfaces ya existentes para poder así expandir y mejorar las capacidades de HOPLITE. ABSTRACT Using fixed-point arithmetic is one of the most common design choices for systems where area, power or throughput are heavily constrained. In order to produce implementations where the cost is minimized without negatively impacting the accuracy of the results, a careful assignment of word-lengths is required. The problem of finding the optimal combination of fixed-point word-lengths for a given system is a combinatorial NP-hard problem to which developers devote between 25 and 50% of the design-cycle time. Reconfigurable hardware platforms such as FPGAs also benefit of the advantages of fixed-point arithmetic, as it compensates for the slower clock frequencies and less efficient area utilization of the hardware platform with respect to ASICs. As FPGAs become commonly used for scientific computation, designs constantly grow larger and more complex, up to the point where they cannot be handled efficiently by current signal and quantization noise modelling and word-length optimization methodologies. In this Ph.D. Thesis we explore different aspects of the quantization problem and we present new methodologies for each of them: The techniques based on extensions of intervals have allowed to obtain accurate models of the signal and quantization noise propagation in systems with non-linear operations. We take this approach a step further by introducing elements of MultiElement Generalized Polynomial Chaos (ME-gPC) and combining them with an stateof- the-art Statistical Modified Affine Arithmetic (MAA) based methodology in order to model systems that contain control-flow structures. Our methodology produces the different execution paths automatically, determines the regions of the input domain that will exercise them, and extracts the system statistical moments from the partial results. We use this technique to estimate both the dynamic range and the round-off noise in systems with the aforementioned control-flow structures. We show the good accuracy of our approach, which in some case studies with non-linear operators shows a 0.04 % deviation respect to the simulation-based reference values. A known drawback of the techniques based on extensions of intervals is the combinatorial explosion of terms as the size of the targeted systems grows, which leads to scalability problems. To address this issue we present a clustered noise injection technique that groups the signals in the system, introduces the noise terms in each group independently and then combines the results at the end. In this way, the number of noise sources in the system at a given time is controlled and, because of this, the combinato rial explosion is minimized. We also present a multi-way partitioning algorithm aimed at minimizing the deviation of the results due to the loss of correlation between noise terms, in order to keep the results as accurate as possible. This Ph.D. Thesis also covers the development of methodologies for word-length optimization based on Monte-Carlo simulations in reasonable times. We do so by presenting two novel techniques that explore the reduction of the execution times approaching the problem in two different ways: First, the interpolative method applies a simple but precise interpolator to estimate the sensitivity of each signal, which is later used to guide the optimization effort. Second, the incremental method revolves on the fact that, although we strictly need to guarantee a certain confidence level in the simulations for the final results of the optimization process, we can do it with more relaxed levels, which in turn implies using a considerably smaller amount of samples, in the initial stages of the process, when we are still far from the optimized solution. Through these two approaches we demonstrate that the execution time of classical greedy techniques can be accelerated by factors of up to ×240 for small/medium sized problems. Finally, this book introduces HOPLITE, an automated, flexible and modular framework for quantization that includes the implementation of the previous techniques and is provided for public access. The aim is to offer a common ground for developers and researches for prototyping and verifying new techniques for system modelling and word-length optimization easily. We describe its work flow, justifying the taken design decisions, explain its public API and we do a step-by-step demonstration of its execution. We also show, through an example, the way new extensions to the flow should be connected to the existing interfaces in order to expand and improve the capabilities of HOPLITE.

Compensation of biased excitation effects for MLS-based nonlinear systems' identification

MLS-based identification of nonlinear systems is largely affected by deviations in the excitation signal amenable to the combined effect of DC-offset and an arbitrary gain. These induce orthogonality loss in the MLS filter bank output, thus invalidating the underlying identification construction. In this paper we present a correction algorithm to derive the corrected Volterra kernels from the biased estimations provided by the standard MLS-based procedure.

Variation in per capita interaction strength: Thresholds due to nonlinear dynamics and nonequilibrium conditions

I measured the strength of interaction between a marine herbivore and its growing resource over a realistic range of absolute and relative abundances. The herbivores (hermit crabs: Pagurus spp.) have slow and/or weak functional and numerical responses to epiphytic diatoms (Isthmia nervosa), which show logistic growth in the absence of consumers. By isolating this interaction in containers in the field, I mimicked many of the physical and biological variables characteristic of the intertidal while controlling the densities of focal species. The per capita effects of consumers on the population dynamics of their resource (i.e., interaction strength) were defined by using the relationship between hermit crab density and proportional change in the resource. When this relationship is fit by a Weibull function, a single parameter distinguishes constant interaction strength from one that varies as a function of density. Constant interaction strength causes the proportion of diatoms to fall linearly or proportionally as hermit crab density increases whereas per capita effects that increase with density cause an accelerating decline. Although many mathematical models of species interactions assume linear dynamics and invariant parameters, at least near equilibrium, the per capita effects of hermit crabs on diatoms varied substantially, apparently crossing a threshold from weak to strong when consumption exceeded resource production. This threshold separates a domain of coexistence from one of local extinction of the resource. Such thresholds may help explain trophic cascades, resource compensation, and context-dependent interaction strengths, while indicating a way to predict trophic effects, despite nonlinearities, as a function of vital rates.

Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions

The propagation of inhomogeneous, weakly nonlinear waves is considered in a cochlear model having two degrees of freedom that represent the transverse motions of the tectorial and basilar membranes within the organ of Corti. It is assumed that nonlinearity arises from the saturation of outer hair cell active force generation. I use multiple scale asymptotics and treat nonlinearity as a correction to a linear hydroelastic wave. The resulting theory is used to explain experimentally observed features of the response of the cochlear partition to a pure tone, including: the amplification of the response in a healthy cochlea vs a dead one; the less than linear growth rate of the response to increasing sound pressure level; and the amount of distortion to be expected at high and low frequencies at basal and apical locations, respectively. I also show that the outer hair cell nonlinearity generates retrograde waves.

Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia

This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (ΔpO2) in the breathing gas. For a step change of ΔpO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and ΔpO2, which can be written as P(t-t1 | ΔpO2). An effective method does not exist to examine the nonlinear function P(t-t1 | ΔpO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.

The two-dimensional IR nonlinear spectroscopy of a cyclic penta-peptide in relation to its three-dimensional structure

A form of two-dimensional (2D) vibrational spectroscopy, which uses two ultrafast IR laser pulses, is used to examine the structure of a cyclic penta-peptide in solution. Spectrally resolved cross peaks occur in the off-diagonal region of the 2D IR spectrum of the amide I region, analogous to those in 2D NMR spectroscopy. These cross peaks measure the coupling between the different amide groups in the structure. Their intensities and polarizations relate directly to the three-dimensional structure of the peptide. With the help of a model coupling Hamiltonian, supplemented by density functional calculations, the spectra of this penta-peptide can be regenerated from the known solution phase structure. This 2D-IR measurement, with an intrinsic time resolution of less than 1 ps, could be used in all time regimes of interest in biology.

Nonlinear-dynamical arrhythmia control in humans

Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.

Linear and nonlinear pathways of spectral information transmission in the cochlear nucleus

At the level of the cochlear nucleus (CN), the auditory pathway divides into several parallel circuits, each of which provides a different representation of the acoustic signal. Here, the representation of the power spectrum of an acoustic signal is analyzed for two CN principal cells—chopper neurons of the ventral CN and type IV neurons of the dorsal CN. The analysis is based on a weighting function model that relates the discharge rate of a neuron to first- and second-order transformations of the power spectrum. In chopper neurons, the transformation of spectral level into rate is a linear (i.e., first-order) or nearly linear function. This transformation is a predominantly excitatory process involving multiple frequency components, centered in a narrow frequency range about best frequency, that usually are processed independently of each other. In contrast, type IV neurons encode spectral information linearly only near threshold. At higher stimulus levels, these neurons are strongly inhibited by spectral notches, a behavior that cannot be explained by level transformations of first- or second-order. Type IV weighting functions reveal complex excitatory and inhibitory interactions that involve frequency components spanning a wider range than that seen in choppers. These findings suggest that chopper and type IV neurons form parallel pathways of spectral information transmission that are governed by two different mechanisms. Although choppers use a predominantly linear mechanism to transmit tonotopic representations of spectra, type IV neurons use highly nonlinear processes to signal the presence of wide-band spectral features.

A few selected applications of surface nonlinear optical spectroscopy.

As a second-order nonlinear optical process, sum-frequency generation is highly surface-specific and accordingly has been developed into a very powerful and versatile surface spectroscopic tool. It has found many unique applications in different disciplines and thus provided many exciting new research opportunities in surface and surface-related science. Selected examples are discussed here to illustrate the power of the technique.

Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy.

Intrinsic, three-dimensionally resolved, microscopic imaging of dynamical structures and biochemical processes in living preparations has been realized by nonlinear laser scanning fluorescence microscopy. The search for useful two-photon and three-photon excitation spectra, motivated by the emergence of nonlinear microscopy as a powerful biophysical instrument, has now discovered a virtual artist's palette of chemical indicators, fluorescent markers, and native biological fluorophores, including NADH, flavins, and green fluorescent proteins, that are applicable to living biological preparations. More than 25 two-photon excitation spectra of ultraviolet and visible absorbing molecules reveal useful cross sections, some conveniently blue-shifted, for near-infrared absorption. Measurements of three-photon fluorophore excitation spectra now define alternative windows at relatively benign wavelengths to excite deeper ultraviolet fluorophores. The inherent optical sectioning capability of nonlinear excitation provides three-dimensional resolution for imaging and avoids out-of-focus background and photodamage. Here, the measured nonlinear excitation spectra and their photophysical characteristics that empower nonlinear laser microscopy for biological imaging are described.