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At least 595 records · Page 33Linked to original sources
PubMed2003

Fractional dynamics and nonlinear harmonic responses in dielectric relaxation of disordered liquids.

The problem of the nonlinear dielectric response due to the application of a strong electric field is reconsidered in the context of fractional kinetic equations. To accomplish that, we start from a fractional noninertial Fokker-Planck equation and restrict ourselves to the case of anomalous subdiffusive processes characterized by the critical exponent alpha ranging from 0 to 1, the limit of normal diffusion. In particular, we evaluate the first- and third-order nonlinear harmonic components of the electric polarization in the case of either a pure ac field or a strong dc bias field superimposed on a weak ac field. The stationary regime is therefore calculated from an infinite set of differential recurrence relations by using a perturbation method. The results so obtained are illustrated by three-dimensional dispersion and absorption plots in order to show the influence of alpha. Cole-Cole diagrams are also presented, allowing one to see that the arcs become more and more flattened as alpha-->0, and corresponding to a broadening of the absorption peaks as effectively observed in complex liquids. The theoretical model is supported by comparison with experimental data of the third-order nonlinear dielectric permittivity of a ferroelectric liquid crystal.

Journal Article↗
PubMed2001

Spin-wave instabilities in large-scale nonlinear magnetization dynamics.

The stability of large magnetization motions in systems with uniaxial symmetry subject to a circularly polarized radio-frequency field is analytically studied. Instability conditions valid for arbitrary values of the amplitude and frequency of the driving field are derived. In the limit of small motions, these conditions yield Suhl's theory of spin-wave instabilities for the case of ferromagnetic resonance. It is shown that the input powers capable of inducing spin-wave instabilities are bounded from both below and above, so that large enough motions are always stable. In addition, it is demonstrated that stability of uniform motions depends on their preparation history.

Journal Article↗
PubMed2002

New relativistic effects in the dynamics of nonlinear hydrodynamical waves.

In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a relativistic Riemann problem when velocities tangential to the initial discontinuity are present. A smooth transition from one wave pattern to another can be produced by varying the initial tangential velocities while maintaining the initial states unmodified. These special relativistic effects are produced by the Lorentz factors and do not have a Newtonian counterpart.

Journal Article↗
PubMed2006

Synthesis of "cactus" top-decorated aligned carbon nanotubes and their third-order nonlinear optical properties.

We report a new morphology of "cactus" top-decorated aligned carbon nanotubes grown by the PECVD method using pure C2H2 gas. Unlike most previous reports, no additional carrier gas is used for pretreatment. Carbon nanotubes can still grow and maintain the tubular structure underneath the "cactus" tops. It is proposed that the H atoms produced by the dissociation of C2H2 activate the catalyst nanoparticles. Scanning electron microscopy (SEM) shows that the top "cactus" morphology is composed of a large quantity of small nanosheets. Transmission electron microscopy (TEM) reveals the amorphous carbon nature of these "cactus" structures. The formation of these "cactus" structures is possibly due to covalent absorption and reconstruction of carbon atoms on the broken graphite layers of nanotubes produced by the strong ion bombardment under plasma. The third-order optical nonlinearities and nonlinear dynamics are also investigated. The third-order nonlinear susceptibility magnitude /chi(3)/ is found to be 2.2 x 10(-11) esu, and the relaxation process takes place in about 1.8 ps.

Cactaceae↗
PubMedDate not supplied

An adaptive strategy for controlling chaotic system.

This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rössler chaos.

Computer Simulation↗
PubMed1995

Aminoglycoside pharmacokinetics and -dynamics: a nonlinear approach.

A model which correctly describes the pharmacokinetic-pharmacodynamic relationship is necessary to perform a rational pharmacotherapy. This model could predict the effects under variable conditions. The prediction will provide a basis for adapting therapy to individuals. A nonlinear model should be most appropriate for describing drug effects. A new model, containing nonlinear pharmacokinetics and pharmacodynamics, is presented to describe effects of aminoglycosides on bacterial growth and accumulation in kidney tissue.

Amikacin↗
PubMed1991

Dissection of a nonlinear cascade model for sensory encoding.

Action potential encoding in the cockroach tactile spine neuron may be treated as a single-input, single-output dynamic nonlinear process, where the input is the electric current flowing across the neuronal membrane and the output is the resultant train of action potentials. The nonlinear behavior of the system may be characterized by a functional expansion method which efficiently and accurately yields similar kernels to the Wiener method. A simple nonlinear cascade consisting of sequential dynamic linear, static nonlinear, and dynamic linear components was identified and gives a good approximation to the response of the neuron to random stimulation. Next, we attempted to study the components of the cascade by the use of a drug, phentolamine, which selectively modifies the dynamic behavior of the encoder. Application of phentolamine to the neuron caused a significant change in the first dynamic linear component of the cascade without affecting the other components. The change was much larger than the variability between results obtained from individual animals. This finding has implications for the biophysical processes which are involved in the components of the cascade.

Action Potentials↗
PubMed1999

Quantitative measure of complexity of EEG signal dynamics.

Since electroencephalographic (EEG) signal may be considered chaotic, Nonlinear Dynamics and Deterministic Chaos Theory may supply effective quantitative descriptors of EEG dynamics and of underlying chaos in the brain. We have used Karhunen-Loeve decomposition of the covariance matrix of the EEG signal to analyse EEG signals of 4 healthy subjects, under drug-free condition and under the influence of Diazepam. We found that what we call KL-complexity of the signal differs profoundly for the signals registered in different EEG channels, from about 5-8 for signals in frontal channels up to 40 and more in occipital ones. But no consistency in the influence of Diazepam administration on KL-complexity is observed. We also estimated the embedding dimension of the EEG signals of the same subjects, which turned to be between 7 and 11, so endorsing the presumption about existence of low-dimensional chaotic attractor. We are sure that nonlinear time series analysis can be used to investigate the dynamics underlying the generation of EEG signal. This approach does not seem practical yet, but deserves further study.

Adult↗
PubMed2000

Effects of noise on different disease states of recurrent affective disorders.

BACKGROUND: Nonlinear dynamics are currently proposed to explain the course of recurrent affective disorders. Such a nonlinear disease model predicts complex interactions with stochastic influences, in particular, because both disease dynamics and stochastic influences, such as psychosocial stressors, will vary during the course of the disease. We approach this problem by investigating general effects of noise intensity on different disease states of a nonlinear model for recurrent affective disorders. METHODS: A recently developed neurodynamic model is studied numerically. RESULTS: Noise can cause unstructured randomness or can maximize periodic order. The frequency of episode occurrence can increase with noise but it can also remain unaffected or even can decrease. The observed effects, thereby, depend critically on both the noise intensity and the internal nonlinear dynamics of the disease model. CONCLUSIONS: Our findings indicate that altered stochastic influences can significantly affect the outcome of a dynamic disease. To evaluate the effects of noise, it is essential to know about the underlying dynamics of respective disease states. Therefore, characterization of low-dimensional dynamics might become valuable for disease prediction and control.

Acoustic Stimulation↗
PubMed2005

An efficient parameterization of dynamic neural networks for nonlinear system identification.

Dynamic neural networks (DNNs), which are also known as recurrent neural networks, are often used for nonlinear system identification. The main contribution of this letter is the introduction of an efficient parameterization of a class of DNNs. Having to adjust less parameters simplifies the training problem and leads to more parsimonious models. The parameterization is based on approximation theory dealing with the ability of a class of DNNs to approximate finite trajectories of nonautonomous systems. The use of the proposed parameterization is illustrated through a numerical example, using data from a nonlinear model of a magnetic levitation system.

Algorithms↗
PubMed1996

Low-frequency dynamics of lasers.

An approach to nonlinear dynamics of multimode lasers is developed. It is based on the concept of two systems of eigenoscillations: optical modes and relaxation oscillations. The importance of a correct (not arbitrary) choice of a model is underlined. Characteristic features of two different rate equation models are formulated and compared. A method of selective perturbation on the system is described which makes it possible to study interrelations between optical modes and relaxation oscillations, and to control dynamical behavior of a laser. The possibility of using dynamical regularities for solving both applied and basic problems is illustrated in several examples. (c) 1996 American Institute of Physics.

Journal Article↗
PubMed2000

Modeling the dynamics of cardiac action potentials.

The nonlinear dynamics of cardiac action potentials is explained via simple model equations describing the membrane potential and the inward and outward currents through the membrane. The equations approximate ionic models, yet are expressed as polynomial functions, and robustly capture the phase-space dynamics of action potentials.

Action Potentials↗