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PubMed2006

Evaluation of nonlinear quantum time correlation functions within the centroid dynamics formulation.

A method to evaluate nonlinear centroid correlation functions is presented that is amenable to simple numerical computation. It can be implemented with the centroid molecular dynamics method for approximate quantum dynamics with no additional assumptions. Two nonlinear correlation functions are evaluated for a model potential using this scheme and compared with results from exact quantum calculations.

Models, Molecular↗
PubMed1998

[From Chronos to Chaos: from the determinism of circadian rhythm of arterial pressure to the undeterminism of hypertensive crises].

This paper delineates the scientific though about the disorder (chaos) in dynamic phenomena. The discussion shows how the periodic functions, which are intrinsically deterministic, can break down into chaotic patterns, either global or catastrophic, because of their "dependence on the limits in the oscillatory modulation" (cycle stress limits). The argumentations demonstrate that order and disorder, chronos and chaos, are intrinsic aspects of dynamic phenomena. The text presents the fractal mathematics for analysing nonlinear events. The fractal interpolation is proposed for predicting the potential risk of hypertensive crisis using the noninvasive ambulatory blood pressure monitoring.

Blood Pressure↗
PubMed2005

Structural dynamics and resonance in plants with nonlinear stiffness.

Although most biomaterials are characterized by strong stiffness nonlinearities, the majority of studies of plant biomechanics and structural dynamics focus on the linear elastic range of their behavior. In this paper, the effects of hardening (elastic modulus increases with strain) and softening (elastic modulus decreases with strain) nonlinearities on the structural dynamics of plant stems are investigated. A number of recent studies suggest that trees, crops, and other plants often uproot or snap when they are forced by gusting winds or waves at their natural frequency. This can be attributed to the fact that the deflections of the plant, and hence mechanical stresses along the stem and root system, are greatest during resonance. To better understand the effect of nonlinear stiffness on the resonant behavior of plants, plant stems have been modeled here as forced Duffing oscillators with softening or hardening nonlinearities. The results of this study suggest that the resonant behavior of plants with nonlinear stiffness is substantially different from that predicted by linear models of plant structural dynamics. Parameter values were considered over a range relevant to most plants. The maximum amplitudes of deflection of the plant stem were calculated numerically for forcing frequencies ranging from zero to twice the natural frequency. For hardening nonlinearities, the resonant behavior was 'pushed' to higher frequencies, and the maximum deflection amplitudes were lower than for the linear case. For softening nonlinearities, the resonant behavior was pushed to lower frequencies, and the maximum deflection amplitudes were higher than for the linear case. These nonlinearities could be beneficial or detrimental to the stability of the plant, depending on the environment. Damping had the effect of drastically decreasing deflection amplitudes and reducing the effect of the nonlinearities.

Elasticity↗
PubMed2005

Complex light: dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium.

The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and nonlocal random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a dynamic phase transition. A connection with the random matrices approach for explaining the vibrational spectra of an ensemble of solitons is pointed out. General arguments based on a Brownian dynamics model are validated by the numerical simulation of a stochastic partial differential equation system. The results are also relevant for Bose condensed gases and plasma physics.

Journal Article↗
PubMed2004

Video-rate nonlinear microscopy of neuronal membrane dynamics with genetically encoded probes.

Biological membranes decorated with suitable contrast agents give rise to nonlinear optical signals such as two-photon fluorescence and harmonic up-conversion when illuminated with ultra-short, high-intensity pulses of infrared laser light. Microscopic images based on these nonlinear contrasts were acquired at video or higher frame rates by scanning a focused illuminating spot rapidly across neural tissues. The scan engine relied on an acousto-optic deflector (AOD) to produce a fast horizontal raster and on corrective prisms to offset the AOD-induced dispersion of the ultra-short excitation light pulses in space and time. Two membrane-bound derivatives of the green fluorescent protein (GFP) were tested as nonlinear contrast agents. Synapto-pHluorin, a pH-sensitive GFP variant fused to a synaptic vesicle membrane protein, provided a time-resolved fluorescent read-out of neurotransmitter release at genetically specified synaptic terminals in the intact brain. Arrays of dually lipidated GFP molecules at the plasma membrane generated intense two-photon fluorescence but no detectable second-harmonic power. Comparison with second-harmonic generation by membranes stained with a synthetic styryl dye suggested that the genetically encoded chromophore arrangement lacked the orientational anisotropy and/or dipole density required for efficient coherent scattering of the incident optical field.

Animals↗
PubMed2000

Time series and the dynamics of demand pacing.

Motivated by a common practice in cardiology, we analyze the dynamics of a demand paced system where one seeks to create a stable periodic response. By using techniques originally developed for controlling chaotic systems, one can enhance the information contained in time series regarding hidden, unstable periodic orbits. This makes it possible, for example, to track drifts in a system's dynamics.

Electrocardiography↗
PubMed2003

Observability in strategic models of viability selection.

Strategic models of frequency-dependent viability selection, in terms of mathematical systems theory, are considered as a dynamic observation system. Using a general sufficient condition for observability of nonlinear systems with invariant manifold, it is studied whether, observing certain phenotypic characteristics of the population, the development of its genetic state can be recovered, at least near equilibrium.

Biological Evolution↗
PubMed2000

Observation of harmonic generation and nonlinear coupling in the collective dynamics of a bose-einstein condensate

We report the observation of harmonic generation and strong nonlinear coupling of two collective modes of a condensed gas of rubidium atoms. Using a modified time averaged orbiting potential trap we changed the trap anisotropy to a value where the frequency of the m = 0 high-lying mode corresponds to twice the frequency of the m = 0 low-lying mode, thus leading to strong nonlinear coupling between these modes. By changing the anisotropy of the trap and exciting the low-lying mode we observed significant frequency shifts of this fundamental mode and also the generation of its second harmonic.

Journal Article↗
PubMed1994

Chaos in one-predator, two-prey models: general results from bifurcation theory.

We show that chaos is the expected outcome of the dynamics of a class of one-predator, two-prey models. This generalizes results of previous studies of Lotka-Volterra models. We examine dynamics near a state in which a high codimension bifurcation occurs, considering all possible nearby dynamics in both parameter and state space by doing an unfolding analysis of the model's normal form. In this way, we argue that realistic predator-prey systems that can be closely modeled by the general models discussed here must exhibit chaotic dynamics.

Animals↗
PubMed2006

The effect of the Holling type II functional response on apparent competition.

This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics.

Biological Evolution↗
PubMed2005

Flexible control of mutual inhibition: a neural model of two-interval discrimination.

Networks adapt to environmental demands by switching between distinct dynamical behaviors. The activity of frontal-lobe neurons during two-interval discrimination tasks is an example of these adaptable dynamics. Subjects first perceive a stimulus, then hold it in working memory, and finally make a decision by comparing it with a second stimulus. We present a simple mutual-inhibition network model that captures all three task phases within a single framework. The model integrates both working memory and decision making because its dynamical properties are easily controlled without changing its connectivity. Mutual inhibition between nonlinear units is a useful design motif for networks that must display multiple behaviors.

Algorithms↗
PubMed2000

[Neural network based on modified simplex method and its application in studying forest self-thinning].

The mechanism of forest self-thinning is generally nonlinear and dynamic, and the artificial neural network has the characteristic of expressing arbitrary nonlinear mapping. In this paper, the feasibility and limitation of artificial neural network used to simulating forest self-thinning was expounded, and the principle and algorithms of the neural network model based on modified simplex method (BP-MSM mixed algorithms) for modeling forest self-thinning were described. Its applications in self-thinning of Populus tremula natural forest Cunninghamia lanceolata plantation were illustrated. The results of forest self-thinning examples show the BP-MSM mixed algorithms were satisfactory in simulating forest self-thinning, and its precision was higher, which develops the method and theory of artificial neural network, and enriches the simulating method of forest self-thinning.

Algorithms↗
PubMedDate not supplied

Compact and accurate linear and nonlinear autoregressive moving average model parameter estimation using laguerre functions.

A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre function remain with our algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation and makes the physiological interpretation of higher order kernels easier. Furthermore, simulation results show better performance of the proposed approach in estimating the system dynamics than LEK in certain cases, and it remains effective in the presence of significant additive measurement noise.

Algorithms↗
PubMed2005

Molecular dynamics integration and molecular vibrational theory. II. Simulation of nonlinear molecules.

A series of molecular dynamics (MD) simulations of nonlinear molecules has been performed to test the efficiency of newly introduced semianalytical second-order symplectic time-reversible MD integrators that combine MD and the standard theory of molecular vibrations. The simulation results indicate that for the same level of accuracy, the new algorithms allow significantly longer integration time steps than the standard second-order symplectic leap-frog Verlet method. Since the computation cost per integration step using new MD integrators with longer time steps is approximately the same as for the standard method, a significant speed-up in MD simulation is achieved.

Journal Article↗
PubMed2000

Effects of collagenase and elastase on the mechanical properties of lung tissue strips.

The dynamic stiffness (H), damping coefficient (G), and harmonic distortion (k(d)) characterizing tissue nonlinearity of lung parenchymal strips from guinea pigs were assessed before and after treatment with elastase or collagenase between 0.1 and 3.74 Hz. After digestion, data were obtained both at the same mean length and at the same mean force of the strip as before digestion. At the same mean length, G and H decreased by approximately 33% after elastase and by approximately 47% after collagenase treatment. At the same mean force, G and H increased by approximately 7% after elastase and by approximately 25% after collagenase treatment. The k(d) increased more after collagenase (40%) than after elastase (20%) treatment. These findings suggest that, after digestion, the fraction of intact fibers decreases, which, at the same mean length, leads to a decrease in moduli. At the same mean force, collagen fibers operate at a higher portion of their stress-strain curve, which results in an increase in moduli. Also, G and H were coupled so that hysteresivity (G/H) did not change after treatments. However, k(d) was decoupled from elasticity and was sensitive to stretching of collagen, which may be of value in detecting structural alterations in the connective tissue of the lung.

Airway Resistance↗
PubMed2004

Ray chaos and ray clustering in an ocean waveguide.

We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a randomlike sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincare maps, plots of variations of the action per ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a randomlike multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves.

Acoustics↗