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At least 1,405 records · Page 78Linked to original sources
PubMed2005

Modifications of the equation for gas bubble dynamics in a soft elastic medium.

A model equation for the oscillation of a pressurized gas bubble in a nonlinear incompressible elastic medium [Emelianov et al., J. Acoust. Soc. Am. 115, 581 (2004)] is extended to include effects of surface tension, viscosity, weak compressibility, and confinement by an elastic shell. The significance of this work is that starting from first principles, the full nonlinearity of the incompressible elastic medium surrounding the bubble and forming its shell is taken into account. Measurements of equilibrium radius as a function of external pressure for a gas bubble in a tissue-like gel are also presented. A general approach to including hysteresis is also discussed.

Elasticity↗
PubMed2005

Hierarchical organization in smooth dynamical systems.

This article is concerned with defining and characterizing hierarchical structures in smooth dynamical systems. We define transitions between levels in a dynamical hierarchy by smooth projective maps from a phase space on a lower level, with high dimensionality, to a phase space on a higher level, with lower dimensionality. It is required that each level describe a self-contained deterministic dynamical system. We show that a necessary and sufficient condition for a projective map to be a transition between levels in the hierarchy is that the kernel of the differential of the map is tangent to an invariant manifold with respect to the flow. The implications of this condition are discussed in detail. We demonstrate two different causal dependences between degrees of freedom, and how these relations are revealed when the dynamical system is transformed into global Jordan form. Finally these results are used to define functional components on different levels, interaction networks, and dynamical hierarchies.

Linear Models↗
PubMed2006

Fifth-order two-dimensional Raman spectroscopy of liquid water, crystalline ice Ih and amorphous ices: sensitivity to anharmonic dynamics and local hydrogen bond network structure.

The theoretical study of off-resonant fifth-order two-dimensional (2D)-Raman spectroscopy is made to analyze the intermolecular dynamics of liquid and solid water. The 2D-Raman spectroscopy is susceptible to the nonlinear anharmonic dynamics and local hydrogen bond structure in water. It is found that the distinct 2D-Raman response appears as the negative signal near the t(2) axis. The origin of this negative signal for t(2)<15 fs is from the nonlinear polarizability in the librational motions, whereas that for 30 fs<t(2)<150 fs is attributed to the anharmonic translational motions. It is found that the mechanical anharmonicity and nonlinear polarizability couplings among modes clearly can be observed as the sum- and difference-frequency peaks in the 2D-Raman spectrum (i.e., Fourier transforms of the response). The 2D-Raman spectroscopies of ice Ih and amorphous ices, i.e., low density, high density, and very high density amorphous ices, are also investigated. It is found that the 2D-Raman spectroscopy is very sensitive to the anisotropy of the structure of ice Ih. The strong hydrogen bond stretching band is seen in the 2D-Raman spectroscopy of the polarization directions parallel to the c axis, whereas the contributions of the librational motion can be also seen in the spectrum with the polarization directions parallel to the a axis. The 2D-Raman spectroscopy is also found to be also very sensitive to the differences in local hydrogen bond network structures in various amorphous phases.

Journal Article↗
PubMed2005

Modeling a multivariable reactor and on-line model predictive control.

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.

Algorithms↗
PubMed2001

Robust chaos in a model of the electroencephalogram: Implications for brain dynamics.

Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2002

Statistical theory for incoherent light propagation in nonlinear media.

A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrödinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave fields are shown to exist for a wide class of nonlinear media.

Journal Article↗
PubMed2005

Linear-Nonlinear-Poisson models of primate choice dynamics.

The equilibrium phenomenon of matching behavior traditionally has been studied in stationary environments. Here we attempt to uncover the local mechanism of choice that gives rise to matching by studying behavior in a highly dynamic foraging environment. In our experiments, 2 rhesus monkeys (Macacca mulatta) foraged for juice rewards by making eye movements to one of two colored icons presented on a computer monitor, each rewarded on dynamic variable-interval schedules. Using a generalization of Wiener kernel analysis, we recover a compact mechanistic description of the impact of past reward on future choice in the form of a Linear-Nonlinear-Poisson model. We validate this model through rigorous predictive and generative testing. Compared to our earlier work with this same data set, this model proves to be a better description of choice behavior and is more tightly correlated with putative neural value signals. Refinements over previous models include hyperbolic (as opposed to exponential) temporal discounting of past rewards, and differential (as opposed to fractional) comparisons of option value. Through numerical simulation we find that within this class of strategies, the model parameters employed by animals are very close to those that maximize reward harvesting efficiency.

Animals↗
PubMed2000

Evaluation of the growth dynamics of Trichophyton rubrum cultures by morphometry and non-linear curve fitting analysis.

To determine the size of dermatophyte thalli, a point-counting procedure with a square lattice grid is proposed instead of using the one-dimensional diameter as the size parameter. For an analysis of the growth dynamics of such colonies, the area values might be subjected to a non-linear curve-fitting procedure. To demonstrate the method, samples of 15 Trichophyton rubrum strains, isolated from human skin and cultured concomitantly on Sabouraud and Selective agar during a period of 8 weeks, were used. The morphometric assessment of the area of the thalli, subjected to non-linear curve fitting, disclosed only a slight difference in the growth dynamics.

Dermatomycoses↗
PubMed2003

Theoretical and experimental aspects of chaos control by time-delayed feedback.

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential-difference systems which are hard to tackle. The essential ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments. Our results show that the control performance can be understood on the basis of experimentally accessible quantities without resort to any model for the internal dynamics.

Fourier Analysis↗
PubMed2005

A new scheme to generalized (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems.

In this paper, a generalized (lag, anticipated, and complete) synchronization of a class of continuous-time systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated, and complete) synchronization between the drive system and response system based on the active control idea. The hyperchaotic Rössler system, transformed Rössler and Chen system as well as two coupled nonidentical Rössler oscillators are chosen to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme can be also extended to research generalized (lag, anticipated, and complete) synchronization between other dynamical systems.

Algorithms↗
PubMed1996

Optimized sampling and parameter estimation for quantification in whole body PET.

Whole-body positron emission tomography (PET) has recently emerged as an important imaging tool for cancer detection and staging. Initial applications of the technique have been primarily qualitative. One of the major reasons is the limits imposed by kinetically undersampled data over the whole body, as opposed to the standard method of continuous dynamic sampling in one body location. In this paper, a new estimation method using weighted nonlinear least squares (WNLS) for the first bed position and Bayesian regression (BR) for subsequent positions is proposed. A general criterion for designing optimal sampling schedules which maximizes the measurement information with multiple bed positions is developed. The overall approach is illustrated with the problem of estimating the metabolic rate of glucose (MRGLu) in tumors at different axial positions (image bed positions) in the body by using computer simulations and patient data. The results show that estimates of MRGLu using sparse data and the optimized Bayesian approach are comparable with those obtained by standard methods and fully sampled data. This study demonstrates the potential of the technique described for quantification where several bed positions have to be used to image all the regions of interest (ROI).

Abdominal Muscles↗
PubMed1967

A nonlinear model for transient responses from light-adapted wolf spider eyes.

A quantitative model is proposed to test the hypothesis that the dynamics of nonlinearities in retinal action potentials from light-adapted wolf spider eyes may be due to delayed asymmetries in responses of the visual cells. For purposes of calculation, these delayed asymmetries are generated in an analogue by a time-variant resistance. It is first shown that for small incremental stimuli, the linear behavior of such a resistance describes peaking and low frequency phase lead in frequency responses of the eye to sinusoidal modulations of background illumination. It also describes the overshoots in linear step responses. It is next shown that the analogue accounts for nonlinear transient and short term DC responses to large positive and negative step stimuli and for the variations in these responses with changes in degree of light adaptation. Finally, a physiological model is proposed in which the delayed asymmetries in response are attributed to delayed rectification by the visual cell membrane. In this model, cascaded chemical reactions may serve to transduce visual stimuli into membrane resistance changes.

Action Potentials↗
PubMed2006

Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity.

The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow.

Journal Article↗