Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Stability analysis”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 739 records · Page 41Linked to original sources
PubMed1999

Nonhyperbolic behavior in the thermostated Lorentz gas.

We show that nonhyperbolic behavior in the length-2 periodic orbits of the thermostated random Lorentz gas occurs only at field strengths greater than unity. For the thermostatted periodic Lorentz gas the range of fields is reduced further due to pruning. Stability analysis shows that there are three classes of period-2 orbits: elliptic orbits and two different hyperbolic orbits. Within the nonergodic elliptic region, trajectories manifest complex behavior that resembles that of perturbed resonant tori in Hamiltonian systems. We present a detailed dynamical study of the nonhyperbolic region.

Journal Article↗
PubMed1999

Effects of time-delayed interactions on dynamic patterns in a coupled phase oscillator system.

We investigate the effects of time delayed interactions in the network of neural oscillators. We perform the stability analysis in the vicinity of a synchronized state at vanishing time delay and present a related phase diagram. In the simulations it is shown that time delay induces various phenomena such as clustering where the system is spontaneously split into two phase locked groups, synchronization, and multistability. Time delay effects should be considered both in the natural and artificial neural systems whose information processing is based on the spatiotemporal dynamic patterns.

Journal Article↗
PubMed1999

Instability of the Kolmogorov flow in a soap film.

We examine the instability of a soap film flow driven by a time-independent force that is spatially periodic in the direction perpendicular to the forcing (Kolmogorov flow). Linear stability analysis of an idealized model of this flow predicts a critical Reynolds number R(c) is approximately equal to the square root of 2. In our soap film experiment, we find a critical value R(c) is approximately equal to 70. This discrepancy can be ascribed to frictional effects from viscous coupling of gas to the film, which is neglected in the idealized model. The kinematic viscosity of the surrounding gas and the thickness of gas layers on each side of the soap film are varied in the experiments to better understand these frictional effects. Our observations indicate that flow in the soap film cannot be decoupled from flow in the surrounding gas.

Journal Article↗
PubMed1999

Intrinsic localized modes and chaos in damped driven rotator lattices.

It is shown that intrinsic localized rotational modes (ILRMs) in parametrically driven damped lattices of coupled classical dipole rotators can become chaotic without losing their localized character. Insight into this behavior is obtained by means of a nonlinear stability analysis. Moreover, we discuss a robust scheme for exploiting a spatially extended chaotic state to generate stationary randomly spaced arrays of driven ILRMs, and show that the associated absorption exhibits unusual signatures.

Journal Article↗
PubMed1999

Suppression of transverse instabilities for vector solitons.

We analyze the transverse instability of two-component spatial solitons in a saturable nonlinear medium, in relation to recent experimental observations of spatial vector solitons in photorefractive media. We present the stability analysis for all three realizations: dark-bright, bright-bright, and dark-dark soliton pairs, and demonstrate that both the nonlinearity saturation and incoherent mode interaction can lead to a strong suppression of the soliton transverse instabilities.

Journal Article↗
PubMed1999

Instabilities of cavity solitons in optical parametric oscillators.

Using an example of cavity solitons in optical parametric oscillators it is demonstrated that Hopf instability of these dissipative structures can be directly associated with internal modes of their conservative counterparts. The latter ones are free propagating quadratic solitons in this case. Linear stability analysis and numerical simulation also reveal multistability and complex instability induced spatiotemporal dynamics of single and multihump cavity solitons.

Journal Article↗
PubMed2000

Electro-osmotically induced convection at a permselective membrane

The paper is concerned with convection at an ion exchange electrodialysis membrane induced by nonequilibrium electro-osmosis in the course of concentration polarization under the passage of electric current through the membrane. Derivation of nonequilibrium electro-osmotic slip condition is recapitulated along with the linear stability analysis of quiescent electrodiffusion through a flat ion exchange membrane. Results of numerical calculation for nonlinear steady state convection, developing from the respective instability, are reported along with those for a slightly wavy membrane. Besides these results, we report those of time dependent calculations for periodic and chaotic oscillations, resulting from instability of the respective steady state flows, and also the results of recent experiments with modified membranes. These latter rule in favor of electro-osmotic versus bulk electroconvective origin of overlimiting conductance through ion exchange membranes.

Journal Article↗
PubMed2000

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which self-similarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N-1 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features.

Journal Article↗
PubMed2000

Instability of symmetric couette flow in a granular gas: hydrodynamic field profiles and transport

We investigated the inelastic hard-disk gas sheared by two parallel bumpy walls (Couette flow). In our molecular dynamic simulations we found a sensitivity to the asymmetries of the initial particle positions and velocities and an asymmetric stationary state, where the deviation from (anti)symmetric hydrodynamic fields is stronger as the normal restitution coefficient decreases. For better understanding of this sensitivity we carried out a linear stability analysis of the former kinetic theoretical solution [J. T. Jenkins and M. W. Richman, J. Fluid. Mech. 171, 53 (1986)] and found it to be unstable. The effect of this asymmetry on the self-diffusion coefficient is also discussed.

Journal Article↗
PubMed2000

Bobylev's instability

In 1982 Bobylev [A.V. Bobylev, Sov. Phys. Dokl. 27, 29 (1982)] made a linear stability analysis of the Burnett equations and showed that beyond a certain critical reduced wave number there exist normal modes that grow exponentially, concluding that the Burnett equations are linearly unstable. We have partially extended his analysis, originally made for Maxwellian molecules, for any interaction potential and argue that his results can be reinterpreted as to give a bound for the Knudsen number above which the Burnett equations are not valid.

Journal Article↗
PubMed2000

Variational studies and replica symmetry breaking in the generalization problem of the binary perceptron

We analyze the average performance of a general class of learning algorithms for the nondeterministic polynomial time complete problem of rule extraction by a binary perceptron. The examples are generated by a rule implemented by a teacher network of similar architecture. A variational approach is used in trying to identify the potential energy that leads to the largest generalization in the thermodynamic limit. We restrict our search to algorithms that always satisfy the binary constraints. A replica symmetric ansatz leads to a learning algorithm which presents a phase transition in violation of an information theoretical bound. Stability analysis shows that this is due to a failure of the replica symmetric ansatz and the first step of replica symmetry breaking (RSB) is studied. The variational method does not determine a unique potential but it allows construction of a class with a unique minimum within each first order valley. Members of this class improve on the performance of Gibbs algorithm but fail to reach the Bayesian limit in the low generalization phase. They even fail to reach the performance of the best binary, an optimal clipping of the barycenter of version space. We find a trade-off between a good low performance and early onset of perfect generalization. Although the RSB may be locally stable we discuss the possibility that it fails to be the correct saddle point globally.

Journal Article↗
PubMed2000

Rayleigh-taylor instability with magnetic fluids: experiment and theory

We present experiments showing the Rayleigh-Taylor instability at the interface between a dense magnetic liquid and an immiscible less dense liquid. The liquids are confined in a Hele-Shaw cell and a magnetic field is applied perpendicular to the cell. We measure the wavelength and the growth rate at the onset of the instability as a function of the external magnetic field. The wavelength decreases as the field increases. The amplitude of the interface deformation grows exponentially with time in the early stage, and the growth rate is an increasing function of the field. These results are compared to theoretical predictions given in the framework of linear stability analysis.

Journal Article↗
PubMed2000

Fingering in a driven hele-shaw cell

A modified Hele-Shaw cell in which the plate gap can be modulated in time was constructed. Highly nonlinear fingers on the interface between air and water in the cell were observed as the plate gap was driven at a variety of frequencies, but typically near 60 Hz. Modified equations to describe the flow in a periodically driven cell were derived and the linear stability analysis of waves on a circular fluid-fluid interface was performed.

Journal Article↗
PubMed2000

Logistic map with a delayed feedback: Stability of a discrete time-delay control of chaos.

The logistic map with a delayed feedback is studied as a generic model. The stability of the model and its bifurcation scheme is analyzed as a function of the feedback amplitude and of the delay. Stability analysis is performed semianalytically. A relation between the delay and the periodicity of the orbit, which explains why some terms used in chaos control are ineffective, was found. The consequences for chaos control are discussed. The structure of bifurcations is found to depend strongly on the parity and on the length of the delay. Boundary crisis, the tangent, the Neimark, as well as the period-doubling bifurcations occur in this system. The effective dimension of the model is also discussed.

Journal Article↗
PubMed2000

Gravity-driven instability in a spherical Hele-Shaw cell.

A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.

Journal Article↗
PubMed2001

Bunching transition in a time-headway model of a bus route.

A time-headway model is presented to mimic bus behavior on the bus route. The motion of a bus is described in terms of the time headway between its bus and the bus in front. We study the bunching behavior of buses induced by interacting with other buses and passengers. It is shown that the dynamical phase transitions among the inhomogeneous bunching phase, the homogeneous free phase, the coexisting phase, and the homogeneous congested phase occur with varying the initial time headway. We study the effect of not stopping at bus stops on the time-headway profile. It is found that the bunching transition lines are consistent with the neutral stability curves obtained by the linear stability analysis.

Journal Article↗
PubMed2001

Formulation of subgrid stresses for large-scale fluid equations.

A formulation is presented based on a previously derived self-consistent procedure for obtaining subgrid scale models for complex system of equations. Using linear stability analysis and numerical simulations of the one-dimensional Burgers equation the formulation is shown to be very stable numerically and to reproduce accurately the large-scale flow of a high-resolution, direct simulation. Moreover, the resulting equation has a structure very similar to the viscous Camassa-Holm equation recently introduced in the modeling of turbulent flows.

Journal Article↗
PubMed2001

Bifurcation diagram for compartmentalized granular gases.

The bifurcation diagram for a vibrofluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution (in which the gas is equi-partitioned over the compartments) is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N=2, this transition takes place via a pitchfork bifurcation but for all N>2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multipeaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.

Journal Article↗