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At least 883 records · Page 49Linked to original sources

PubMed2006

Nonlinear standing waves in 2-D acoustic resonators.

This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.

Journal Article↗

PubMed2000

Glass transition in the quenched and annealed version of the frustrated lattice gas model

In this paper we study the three-dimensional frustrated lattice gas model in the annealed version, where the disorder is allowed to evolve in time with a suitable kinetic constraint. Although the model does not exhibit any thermodynamic transition it shows a diverging peak at some characteristic time in the dynamical nonlinear susceptibility, similar to the results on the p-spin model in mean field and the Lennard-Jones mixture recently found by Donati et al. (e-print cond-mat/9905433). Comparing these results to those obtained in the model with quenched interactions, we conclude that the critical behavior of the dynamical susceptibility is reminiscent of the thermodynamic transition present in the quenched model, and signaled by the divergence of the static nonlinear susceptibility, suggesting therefore a similar mechanism also in supercooled glass-forming liquids.

Journal Article↗

PubMed2003

Community dynamics in a university environment.

Scholars have characterized academic communities of faculty, administration, and students in U.S. universities as "organized anarchies." In contrast, we offer evidence that the community structures of two representative public university systems are notably systematic by applying empirical phase-diagram techniques from the nonlinear dynamics literature to reconstruct low-dimensional deterministic behavior from historic data on the coevolution of faculty, administration, and student populations in each system. Ecological community models, fit with population data for each university, reproduce the essence of this behavior. The models offer novel explanations of how university resources obtained from enrollments and other sources are systematically partitioned among faculty, administration, and student populations interacting in shifting and well-defined community roles. This work offers empirical evidence that ecological principles, typically reserved for characterizing nonhuman interactions in biological systems, can shed light on human interactions in social systems.

Group Processes↗

PubMed2003

Automatic detection of slight parameter changes associated to complex biomedical signals using multiresolution q-entropy1.

It is well known that, from a dynamical point of view, sudden variations in physiological parameters which govern certain diseases can cause qualitative changes in the dynamics of the corresponding physiological process. The purpose of this paper is to introduce a technique that allows the automated temporal localization of slight changes in a parameter of the law that governs the nonlinear dynamics of a given signal. This tool takes, from the multiresolution entropies, the ability to show these changes as statistical variations at each scale. These variations are held in the corresponding principal component. Appropriately combining these techniques with a statistical changes detector, a complexity change detection algorithm is obtained. The relevance of the approach, together with its robustness in the presence of moderate noise, is discussed in numerical simulations and the automatic detector is applied to real and simulated biological signals.

Algorithms↗

PubMed2001

Modeling of an impact system with a drift.

A physical model to examine impact oscillators has been developed and analyzed. The model accounts for the viscoelastic impacts and is capable to mimic the dynamics of a bounded progressive motion (a drift), which is important in practical applications. The system moves forward in stick-slip phases, and its behavior may vary from periodic to chaotic motion. A nonlinear dynamic analysis reveals a complex behavior and that the largest drift is achieved when the responses switch from periodic to chaotic, after a cascade of subcritical bifurcations to period one. Based on this fact, a semianalytical solution is constructed to calculate the progression of the system for periodic regimes and to determine conditions when periodicity is lost.

Journal Article↗

PubMed1997

A dynamic neuromuscular model for describing the pendulum test of spasticity.

Both dynamic and static thresholds, as well as the gain in the stretch reflex loop, affect the sensitivity of motoneurons to muscle stretch. How the variation in each parameter will influence the mechanical behavior of patients with spasticity is not well understood because of the difficulty in experimentally isolating individual parameters. A neuromuscular dynamic model, based on the pendulum test of spasticity, has been developed to study the specific contribution of individual parameter abnormalities in stretch reflex loops to the observed mechanical abnormalities. The model contains detailed nonlinear dynamics of muscle force generation and stretch reflexes. A computer simulation of the model indicates that the stretch reflex thresholds and the gain have different influences on the leg swing in the pendulum test of spasticity. Individual changes in the static stretch reflex threshold, in the dynamic threshold, or in the gain can not stimulate the whole spectrum of spasticity severity. When simultaneous changes in all three parameters of the stretch reflex loop occur, a small variation of the gain coupled with changes in both static and dynamic thresholds can produce increasing severity of spasticity as the thresholds further decrease. The model is also successful in simulating the effect of posture changes on spasticity.

Adult↗

PubMed1976

Tracer experiment design for unique identification of nonlinear physiological systems.

The design of tracer kinetic experiments, the purpose of which is to elucidate uniquely the internal couplings of a nonlinear dynamic system, is considered for a practical class of models of physiological systems. The extent of information about the real system contained in tracer kinetic data is a central issue. Criteria for determining whether nonlinear model parameters can be estimated from small-signal, "linearizing" tracer experiments are developed and illustrated by examples. The concept of "structural identifiability" is employed in this analysis to determine which model parameters can be and which cannot be determined "uniquely" from given input-output data; a step-by-step procedure based on an extension of this concept is presented for adapting the overall approach to the experimental design problem. Estimation of unmeasurable endogenous inputs and system state variables, problems that are intimately related to parameter estimation for physiological systems, are also considered.

Kinetics↗

PubMed1991

Aging and the complexity of cardiovascular dynamics.

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Adult↗

PubMed2006

Distinct metastable atmospheric regimes despite nearly Gaussian statistics: a paradigm model.

A controversial topic in the recent climate modeling literature is the fashion in which metastable low-frequency regimes in the atmosphere occur despite nearly Gaussian statistics for these planetary waves. Here a simple 57-mode paradigm model for such metastable atmospheric regime behavior is introduced and analyzed through hidden Markov model (HMM) analysis of the time series of suitable low-frequency planetary waves. The analysis of this paradigm model elucidates how statistically significant metastable regime transitions between blocked and zonal statistical states occur despite nearly Gaussian behavior in the associated probability distribution function and without a significant role for the low-order truncated nonlinear dynamics alone; turbulent backscatter onto the three-dimensional subspace of low-frequency modes is responsible for these effects. It also is demonstrated that suitable stochastic mode reduction strategies, which include both augmented cubic nonlinearity and multiplicative noise, are also capable of capturing the metastable low-frequency regime behavior through a single stochastic differential equation compared with the full turbulent chaotic 57-mode model. This feature is attractive for issues such as long-term weather predictability. Although there have been many applications of HMM in other sciences, this work presents a previously undescribed application of HMM analysis to atmospheric low-frequency variability and points the way for further applications including their use in extended range predictability.

Journal Article↗

PubMed2006

Synchronization of coupled nonidentical genetic oscillators.

The study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using a control theory approach, we provide a theoretical method for analysing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.

Biological Clocks↗

PubMed2004

Dynamic stability of gait cycles as a function of speed and system constraints.

The purpose of this study was to examine the dynamic stability of two groups of children with different dynamic resources in changing contexts. The stability of the lower extremity segments of preadolescent children (8-10 years old) with and without Down syndrome (DS) was evaluated as children walked on a motorized treadmill at varying speeds. Tools from nonlinear dynamics, maximum Lyapunov exponent, and approximate entropy were used to assess the behavioral stability of segmental angular displacements of the thigh, shank, and foot. Our results suggest that children with DS show decreased dynamic stability during walking in all segments and that this might be a consequence of inherently different subsystem constraints between these groups. Differences between groups also varied, though not uniformly, with speed, suggesting that inherent differences could further constrain the behavioral response to changing task demands.

Anthropometry↗

PubMed1999

HCP<=>CPH isomerization: caught in the act.

In this overview we discuss the vibrational spectrum of phosphaethyne, HCP, in its electronic ground state, as revealed by complementary experimental and theoretical examinations. The main focus is the evolution of specific spectral patterns from the bottom of the potential well up to excitation energies of approximately 25,000 cm(-1), where large-amplitude, isomerization-type motion from H-CP to CP-H is prominent. Distinct structural and dynamical changes, caused by an abrupt transformation from essentially HC bonding to mainly PH bonding, set in around 13,000 cm(-1). They reflect saddle-node bifurcations in the classical phase space--a phenomenon well known in the nonlinear dynamics literature--and result in characteristic patterns in the spectrum and the quantum-number dependence of the vibrational fine-structure constants. Two polar opposites are employed to elucidate the spectral patterns: the exact solution of the Schrödinger equation, using an accurate potential energy surface and an effective or resonance Hamiltonian (expressed in a harmonic oscillator basis set and block diagonalized into polyads), which is defined by parameters adjusted to fit either the measured or the calculated vibrational energies. The combination of both approaches--together with classical mechanics and semiclassical analyses--provides a detailed spectroscopic picture of the breaking of one bond and the formation of a new one.

Journal Article↗

PubMed2001

Fronts, Waves, and Stationary Patterns in Electrochemical Systems In the appendix we list the minimal equations (prototype equations) that describe the phenomena of self-organization discussed in the individual sections.

Oscillatory behavior has been observed for almost all electrochemical reactions in a certain, although sometimes small, range of external parameters. Only in the past ten years has it been possible, however, to find a common explanation for the occurrence of these temporal self-organization phenomena of chemically completely different electrochemical reactions. The breakthrough was achieved because new methods and concepts, which had been developed in nonlinear dynamics to describe the spontaneous formation of order in various disciplines, could be applied. This development in turn was only possible because the underlying laws are universal at a certain abstract level. Oscillations are only one possible manifestation of nonlinear behavior. Examples of other features that are often closely associated with temporal instabilities are spatial structures and waves. Initiated by the theoretical progress and the development of new experimental techniques, spatial pattern formation in electrochemical systems has been targeted for investigations in the past few years. Based on these investigations, it can be predicted under which conditions temporal or spatial pattern formation can be expected. Furthermore, the possibility of predicting the occurrence of instabilities indicates that it might be feasible to exploit nonlinear effects to increase, for example, the yield of electrocatalytic reactions. Here we discuss physicochemical mechanisms that lead to pattern formation in electrochemical systems. At the same time, we stress the generic principles that are responsible for self-structuring processes in many chemical and biological systems.

Journal Article↗

PubMed1996

Impact of vaccination on the spatial correlation and persistence of measles dynamics.

The onset of measles vaccination in England and Wales in 1968 coincided with a marked drop in the temporal correlation of epidemic patterns between major cities. We analyze a variety of hypotheses for the mechanisms driving this change. Straightforward stochastic models suggest that the interaction between a lowered susceptible population (and hence increased demographic noise) and nonlinear dynamics is sufficient to cause the observed drop in correlation. The decorrelation of epidemics could potentially lessen the chance of global extinction and so inhibit attempts at measles eradication.

Child↗

PubMed2006

Transient bifurcations in neural error correction.

This paper presents an investigation into the responses of neurons to errors in presynaptic spike trains. Errors are viewed, in nonlinear dynamical terms, as brief-duration changes in stationary presynaptic spike trains which induce transient responses in the postsynaptic cell. As these are generally large-magnitude transients, linearized neural models are not helpful. Instead, the responses of a full, nonlinear physiological model of a neuron that includes the recognized living prototype of an inhibitory synapse are analyzed. More specifically, the transients are examined in the context of the stationary behaviors that precede and succeed each error. It is shown that one and two dimensional bifurcation diagrams can be constructed from the transient responses--that there are marked changes in the transient responses at points that correspond to bifurcations in the stationary responses, qualitative changes in transients on either side of bifurcations, and only quantitative changes in transients between bifurcations.

Action Potentials↗

PubMed2006

Glassy behavior of light.

We study the nonlinear dynamics of a multimode random laser using the methods of statistical physics of disordered systems. A replica-symmetry breaking phase transition is predicted as a function of the pump intensity. We thus show that light propagating in a random nonlinear medium displays glassy behavior; i.e., the photon gas has a multitude of metastable states and a nonvanishing complexity, corresponding to mode-locking processes in random lasers. The present work reveals the existence of new physical phenomena, and demonstrates how nonlinear optics and random lasers can be a benchmark for the modern theory of complex systems and glasses.

Journal Article↗

PubMed1990

Creative dynamics approach to neural intelligence.

The thrust of this paper is to introduce and discuss a substantially new type of dynamical system for modelling biological behavior. The approach was motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks-their rigid behavior compared with even simplest biological systems. This approach exploits a novel paradigm in nonlinear dynamics based upon the concept of terminal attractors and repellers. It was demonstrated that non-Lipschitzian dynamics based upon the failure of Lipschitz condition exhibits a new qualitative effect--a multi-choice response to periodic external excitations. Based upon this property, a substantially new class of dynamical systems--the unpredictable systems--was introduced and analyzed. These systems are represented in the form of coupled activation and learning dynamical equations whose ability to be spontaneously activated is based upon two pathological characteristics. Firstly, such systems have zero Jacobian. As a result of that, they have an infinite number of equilibrium points which occupy curves, surfaces or hypersurfaces. Secondly, at all these equilibrium points, the Lipschitz conditions fails, so the equilibrium points become terminal attractors or repellers depending upon the sign of the periodic excitation. Both of these pathological characteristics result in multi-choice response of unpredictable dynamical systems. It has been shown that the unpredictable systems can be controlled by sign strings which uniquely define the system behaviors by specifying the direction of the motions in the critical points. By changing the combinations of signs in the code strings the system can reproduce any prescribed behavior to a prescribed accuracy.(ABSTRACT TRUNCATED AT 250 WORDS)

Artificial Intelligence↗

PubMed2002

Current-sheet formation in incompressible electron magnetohydrodynamics.

The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia.

Journal Article↗