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Results for “Nonlinear Dynamics”

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At least 271 records · Page 15Linked to original sources

PubMed2006

Nonlinear dynamics of semiflexible magnetic filaments in an ac magnetic field.

Flexible spontaneously magnetized filaments exist in the living world (magnetotactic bacteria) and arise in magnetic colloids with large magnetodipolar interaction parameter. We demonstrate that these filaments possess variety of novel nonlinear phenomena in an ac magnetic field: orientation of the filament in the direction perpendicular to the field and the development of the oscillating U-like shapes, which presumably can lead to the formation of rings of magnetic filaments. It is found that these phenomena are determined by the development of the localized boundary modes of the filament deformation. We have illustrated by qualitative estimates that the phenomena found may be useful for insight into the complex pattern formation phenomena in ensembles of magnetic particles under the action of an ac magnetic field.

Journal Article↗

PubMed2002

Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables.

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.

Journal Article↗

PubMedDate not supplied

[Chaotic nonlinear dynamics of prestimulus EEG and the structure of auditory evoked potentials ].

The dynamic pattern of a prestimulus EEG was studied by the fractal analysis technique. The character of this pattern was shown to affect the structure of cortical auditory evoked potentials (EP). A monoperiodic pattern in the control frequency band was accompanied by a formation of several new attractors with low dimensionality attributed to simultaneous functioning of several weakly connected dynamic systems with an indefinite trend of a leading process. During development of multiperiodic processes in EEG segments, the fractal analysis revealed a tendency for a formation of a single complex dynamic system with high dimensionality of the attractor. Characteristic changes in parameters of the primary and middle-latency EP components, their correlation, and factor models are related with the character of nonlinear patterns. Analysis of variance revealed the most effective role of pattern changes in the EEG alpha control band. The structure of combination of parameters of the EP primary components into connected complexes depends on the nonlinear prestimulus EEG patterns. The above predictors determine differently directed and differently pronounced changes in parameters of the middle-latency positive waves.

Adult↗

PubMed2003

Length scale coupling for nonlinear dynamical problems in magnetism.

The dynamics of real magnets is often governed by several interacting processes taking place simultaneously at different length scales. For dynamical simulations, the relevant length scales should be coupled, and the energy transfer accurately described. We show that in this case the micromagnetic theory is not always reliable. We present a coarse-graining approach applicable to nonlinear problems, which provides a unified description of all relevant length scales, allowing a smooth, seamless coupling. The simulations performed on model systems show that the coarse-graining approach achieves nearly the precision of all-atom simulations.

Journal Article↗

PubMed2003

[Analysis of nonlinear dynamics of aging (experimental study)].

The research is devoted to the analysis of individual dependencies of weight of a body, rectal temperature and functional motor asymmetry of behavior of mice female CBA from age received in longitudinal research. Both individual, and the average age dependencies of the above named parameters have an extreme (nonlinear) kind. It is revealed, that by the age of achievement of the maximal weight (Tm) and greatest asymmetry of behavior (Tn) are connected with each other (r = 0.6, p < 0.001). The difference (Tm-Tn) is linearly connected to life expectancy (r = 0.62, p < 0.001), that is this parameter can be used for the forecast of individual life expectancy.

Aging↗

PubMedDate not supplied

Participation of nonlinear dynamic processes in the formation of the high-frequency EEG of the rabbit.

The informativeness of the high-frequency EEG for the assessment of the functional state of the brain has been proven by means of a new method of analysis of the EEG which is suitable, by contrast with the traditional spectral correlation analysis, for the description of nonlinear processes. Evidence has been obtained in favor of the hypothesis that a deterministic chaotic component, the parameters of which depend on the region of recording of the EEG and which changes conjointly with change in the functional state of the brain, is present in the EEG of the neocortex and hippocampus of the rabbit.

Animals↗

PubMed1997

Nonlinear Dynamics of Lipid Films under Electric Forces

We study the dynamics and rupture of lipid films perturbed in the symmetric mode squeezing through an electrohydrodynamical approach. The lipid phase and the two surrounding aqueous phases are considered as incompressible Newtonian viscous fluids submitted to van der Waals, steric, and electric body forces. A nonlinear evolution equation for the film thickness, at the long-wavelength limit, is obtained for two symmetric cases: a film with equally charged surfaces with no potential drop and a neutral film submitted to an external electric field. At the long-wavelength limit, the electric term only influences the film evolution when the electric field inside the film is nonvanishing. We solve numerically, as an initial value problem with periodic boundary conditions, the nonlinear evolution equation. The rupture time is obtained and compared with analytical estimates. Sufficiently strong steric forces prevent the film from narrowing beyond a minimum thickness leading the film to a steady state different from the planar one consistently with the nonlinear analytical approach. The presence of a transmembrane electric potential destabilizes the perturbed film as predicted by the linear and nonlinear approaches; however, as expected, destabilization is not relevant at physiological values of the potential drop.

Journal Article↗

PubMed1997

What should be the focus of emotion regulation in children? A nonlinear dynamic mathematical model of children's peer interaction in groups.

This paper questions the assumption that children's social and emotional competence be placed within the developing child, rather than in the interaction of the child with the range of peer social ecologies in which the children might function. This paper presents a new nonstatistical mathematical approach to modeling children's peer social interaction in small groups using nonlinear difference equations in which both an uninfluenced and an influenced regulatory set point of positive minus negative interaction can be separately estimated. Using this model and the estimation procedure, it is possible to estimate what a focal child and the group initially brings to the group interaction and also how these regulatory set points are influenced by the interaction to determine two influenced regulatory set points. Six-person mainstreamed and specialized groups were established involving three types of unacquainted preschool boys: children with and without developmental delays and a language disordered but intellectually normally functioning group, using a methodology that ensured appropriate matching of child and family characteristics. For each 2-week play group, the social interactions of each child were observed during a designated free play period. Handicapped children were observed in either a specialized or mainstreamed setting. The application made of this modeling process in this paper is generating theory to attempt to understand influence processes. Parameters are introduced that reflect uninfluenced target child and group set points, emotional inertia, and influence functions.

Child, Preschool↗

PubMed1998

Stochastic resonance in coupled nonlinear dynamic elements.

We investigate the response of a linear chain of diffusively coupled diode resonators under the influence of thermal noise. We also examine the connection between spatiotemporal stochastic resonance and the presence of kink-antikink pairs in the array. The interplay of nucleation rates and kink speeds is briefly addressed. The experimental results are supplemented with simulations on a coupled map lattice. We furthermore present analytical results for the synchronization and signal processing properties of a Phi(4) field theory and explore the effects of various forms of nonlinear coupling. (c) 1998 American Institute of Physics.

Journal Article↗

PubMed1997

Nonlinear dynamics of intracellular methylene blue during light activation of cell cultures.

Methylene blue (MB+) is a well-known dye in medicine and has been discussed as an easily applicable drug for topical treatment in photodynamic therapy (PDT). Methylene blue can potentially be used as a redox indicator to detect the important redox reactions that are induced during PDT. The kinetics of this process was analyzed on a subcellular level with confocal laser scanning microscopy. BKEz-7 endothelial cells were incubated 4 h with 1 microM MB+. The fluorescence dynamics of MB+ during irradiation with 633 nm light was observed with subcellular resolution. Images were acquired at 0.5 s intervals (frame rate 1 image/0.5 s). Fluorescence was observed in the red channel of the laser scanning microscope. Synchronously, the phase-contrast image was visualized with the green channel. Morphological changes could therefore be correlated with the dynamics of MB+. In addition, the light-dose-dependent phototoxicity at 633 nm irradiation was determined by viable cell counting. After an induction period (phase I), fast fluorescent spikes could be observed in the whole cytoplasm, which decayed with a time constant of about 20 s (phase II), followed by a period of nearly constant fluorescence intensity (phase III) and exponential photobleaching (phase IV). Phase II exhibits highly nonlinear kinetics, which is hypothesized to correlate probably with a nonlinear quantal production of reactive oxygen species (ROS). Morphological cell changes were not observed during phase II. During phase III, a pycnotic cell nucleus developed. From the determination of viable cells we can conclude that a light dose applied within phase II was only sublethal in correlation with morphological observations. Overproduction of ROS leading finally to cell killing during phases III and IV is discussed.

Animals↗

PubMed1998

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.

Journal Article↗

PubMed2004

Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives.

We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of a omega/(2 pi), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a nonzero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.

Journal Article↗

PubMed2005

Nonlinear dynamical model and response of avian cranial kinesis.

All modern birds have kinetic skulls in which the upper bill can move relative to the braincase, but the biomechanics and motion dynamics of cranial kinesis in birds are poorly understood. In this paper, we model the dynamics of avian cranial kinesis, such as prokinesis and proximal rhynchokinesis in which the upper jaw pivots around the nasal-frontal (N-F) hinge. The purpose of this paper is to present to the biological community an approach that demonstrates the application of sophisticated predictive mathematical modeling tools to avian kinesis. The generality of the method, however, is applicable to the advanced study of the biomechanics of other skeletal systems. The paper begins with a review of the relevant biological literature as well as the essential morphology of avian kinesis, especially the mechanical coupling of the upper and lower jaw by the postorbital ligament. A planar model of the described bird jaw morphology is then developed that maintains the closed kinematic topology of the avian jaw mechanism. We then develop the full nonlinear equations of motion with the assumption that the M. protractor pterygoideus and M. depressor mandibulae act on the quadrate as a pure torque, and the nasal frontal hinge is elastic with damping. The mechanism is shown to be a single degree of freedom device due to the holonomic constraints present in the quadrate-jugal bar-upper jaw-braincase-quadrate kinematic chain as well as the quadrate-lower jaw-postorbital ligament-braincase-quadrate kinematic chain. The full equations are verified via simulation and animation using the parameters of a Grey Heron (Ardea cinerea). Next we develop a simplified analytical model of the equations by power series expansion. We demonstrate that this model reproduces the dynamics of the full model to a high degree of fidelity. We proceed to use the harmonic balance technique to develop the frequency response characteristics of the jaw mechanism. It is shown that this avian cranial kinesis model exhibits the characteristics of a hardening Duffing oscillator. Beyond the identification of the characteristics of the underlying dynamics, which provides insight into the behavior of the system, the model and methodology presented here provides other potential benefits. A framework has been developed that could be utilized to study the biomechanics of feeding and bite force as well the effects of cranial kinesis on the frequency and modulation of bird songs.

Animals↗

PubMed1991