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At least 1,513 records · Page 84Linked to original sources
PubMed2003

Nonequilibrium critical dynamics of the triangular antiferromagnetic Ising model.

We investigate the nonequilibrium critical dynamics of antiferromagnetic Ising model on a two-dimensional triangular lattice via dynamic Monte Carlo simulation employing spin-flip kinetics. Macroscopic degeneracy of the ground state originating from geometric frustration fundamentally affects the nonequilibrium dynamics of the system. In particular, the defects and the loose spins (whose flip costs no energy) play key roles in the dynamics. The long-time evolution is characterized by a critical dynamic scaling with a growing length scale xi(t). With random initial configurations, xi(t) exhibits a subdiffusive growth in time, xi(t) approximately t(1/z) with 1/z approximately 0.43, while xi(t) shows a diffusive growth with z=2 for the relaxation within the dominant sector of the ground-state manifold. The nonequilibrium critical dynamics therefore exhibits an interesting initial-state dependence. Persistence and the two-time temporal properties are also discussed.

Journal Article↗
PubMed2004

Viscoelastic model for the dynamic structure factors of binary systems.

This paper presents the viscoelastic model for the Ashcroft-Langreth dynamic structure factors of liquid binary mixtures. We also provide expressions for the Bhatia-Thornton dynamic structure factors and, within these expressions, show how the model reproduces both the dynamic and the self-dynamic structure factors corresponding to a one-component system in the appropriate limits (pseudobinary system or zero concentration of one component). In particular we analyze the behavior of the concentration-concentration dynamic structure factor and longitudinal current, and their corresponding counterparts in the one-component limit, namely, the self-dynamic structure factor and self-longitudinal current. The results for several lithium alloys with different ordering tendencies are compared with computer simulation data, leading to a good qualitative agreement, and showing the natural appearance in the model of the fast sound phenomenon.

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PubMed2005

Effective dynamics in Hamiltonian systems with mixed phase space.

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by effective dynamical invariants, which are significantly different from the dynamical invariants that describe the asymptotic Hamiltonian dynamics. The effective invariants depend both on the scale of resolution and the region of the phase space under consideration, and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the Hamiltonian system is modeled as a chain of hyperbolic systems.

Journal Article↗
PubMed2005

Coarsening dynamics of the one-dimensional Cahn-Hilliard model.

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We characterize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system. A set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations. We also compare these dynamics with the bubble dynamics deduced from the classical kink interaction computation where our model seems to be more appropriated. In the case of two bubbles, we deduce analytical expressions for the bubble's position and the bubble's width. Besides, a simple description of the ulterior dynamics is presented.

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PubMed2005

Pressure-enhanced dynamic heterogeneity in block copolymers of poly(methyl vinyl ether) and poly(isobutyl vinyl ether).

The static structure factor and associated dynamics have been investigated in a series of block copolymers of poly(methyl vinyl ether) (PMVE) and poly(isobutyl vinyl ether) (PiBVE) using x-ray scattering and dielectric spectroscopy (DS). The origin of the dynamic arrest at the glass temperature (T(g)) of PiBVE has been explored by temperature- and pressure-dependent DS and pressure-volume-temperature measurements. Both temperature and volume are responsible for the segmental dynamics but temperature has a stronger effect. The copolymers display a minimal dynamic asymmetry (Delta T(g) approximately 7 K), nevertheless, are spatially and dynamically heterogeneous. Increasing pressure, unlike temperature, enhances the dynamic heterogeneity. This effect originates from the distinctly different pressure sensitivities of the homopolymers and can be traced back to differences in local packing.

Journal Article↗
PubMed2005

Discriminating additive from dynamical noise for chaotic time series.

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only for one variable of the system, while the noise corrupting the second variable is still Gaussian distributed independent of distribution of dynamical noise. Based on these results and using scaling properties of the correlation entropy, we propose a simple method of discriminating additive from dynamical noise. This approach is also useful for estimation of noise level for chaotic time series. We show that the proposed method works well in a wide range of noise levels, providing that one kind of noise predominates and we analyze the variable of the system for which the contamination follows Cauchy-like distribution in the presence of dynamical noise.

Journal Article↗
PubMed2006

Dynamical behavior of hydrodynamic Lyapunov modes in coupled map lattices.

In our previous study of hydrodynamic Lyapunov modes (HLMs) in coupled map lattices, we found that there are two classes of systems with different lambda-k dispersion relations. For coupled circle maps we found the quadratic dispersion relations lambda approximately k2 and lambda approximately k for coupled standard maps. Here, we carry out further numerical experiments to investigate the dynamic Lyapunov vector (LV) structure factor which can provide additional information on the Lyapunov vector dynamics. The dynamic LV structure factor of coupled circle maps is found to have a single peak at omega=0 and can be well approximated by a single Lorentzian curve. This implies that the hydrodynamic Lyapunov modes in coupled circle maps are nonpropagating and show only diffusive motion. In contrast, the dynamic LV structure factor of coupled standard maps possesses two visible sharp peaks located symmetrically at +/- omega. The spectrum can be well approximated by the superposition of three Lorentzian curves centered at omega=0 and +/-omegau, respectively. In addition, the omega-k dispersion relation takes the form omegau=cuk for k --> 2pi/L. These facts suggest that the hydrodynamic Lyapunov modes in coupled standard maps are propagating. The HLMs in the two classes of systems are shown to have different dynamical behavior besides their difference in spatial structure. Moreover, our simulations demonstrate that adding damping to coupled standard maps turns the propagating modes into diffusive ones alongside a change of the lambda-k dispersion relation from lambda approximately k to lambda approximately k2. In cases of weak damping, there is a crossover in the dynamic LV structure factors; i.e., the spectra with smaller k are akin to those of coupled circle maps while the spectra with larger k are similar to those of coupled standard maps.

Journal Article↗
PubMed2006

Surface and interfacial dynamics of polymeric bilayer films.

The theory for surface dynamics of the thermally excited fluctuations on a homogenous single-layer film of arbitrary depth is generalized to describe surface and interfacial dynamics of polymeric liquid bilayer films in terms of susceptibilities, power spectra, and characteristic relaxation time constants. The effects on surface dynamics originating from viscosity inhomogeneities close to the surface and interfacial regions are investigated by the bilayer theory and compared with the surface dynamics of homogeneous single-layer films under nonslip and slip boundary conditions. Our bilayer theory can also be extended to study interfacial dynamics of more generalized multilayer systems. The effects of viscoelasticity and van der Waals interactions on surface and interfacial dynamics are also briefly discussed.

Journal Article↗
PubMed2006

Anomalous dynamic arrest in a mixture of large and small particles.

We present molecular dynamics simulations of the slow dynamics of a mixture of large and small soft spheres with a large size disparity. The dynamics are investigated in a broad range of temperature and mixture composition. As a consequence of the large size disparity, large and small particles exhibit very different relaxation times. As previously reported for simple models of short-ranged attractive colloids and polymer blends, several anomalous dynamic features are observed: (i) sublinear behavior for mean-squared displacements, (ii) concave-to-convex crossover for density-density correlators, by varying the temperature or wave vector, and (iii) logarithmic decay for specific wave vectors of density-density correlators. These anomalous features are observed over time intervals extending up to four decades and strongly resemble predictions of the mode coupling theory (MCT) for state points close to higher-order MCT transitions, which originate from the competition between different mechanisms for dynamic arrest. For the large particles we suggest competition between soft-sphere repulsion and depletion effects induced by neighboring small particles. For the small particles we suggest competition between bulklike dynamics and confinement, respectively induced by neighboring small particles and by the slow matrix of large particles.

Journal Article↗
PubMed2006

Large-time dynamics and aging of a polymer chain in a random potential.

We study the out-of-equilibrium large-time dynamics of a Gaussian polymer chain in a quenched random potential. The dynamics studied is a simple Langevin dynamics commonly referred to as the Rouse model. The equations for the two-time correlation and response functions are derived within the Gaussian variational approximation. In order to implement this approximation faithfully, we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical action. For a short-ranged correlated random potential the equations are solved analytically in the limit of large times using certain assumptions concerning the asymptotic behavior. Two possible dynamical behaviors are identified depending upon the time separation: a stationary regime and an aging regime. In the stationary regime time translation invariance holds and so does the fluctuation dissipation theorem. The aging regime which occurs for large time separations of the two-time correlation functions is characterized by a history dependence and the breakdown of certain equilibrium relations. The large-time limit of the equations yields equations among the order parameters that are similar to the equations obtained in statics using replicas. In particular the aging solution corresponds to the broken replica solution. But there is a difference in one equation that leads to important consequences for the solution. The stationary regime corresponds to the motion of the polymer inside a local minimum of the random potential, whereas in the aging regime the polymer hops between different minima. As a by-product we also solve exactly the dynamics of a chain in a random potential with quadratic correlations.

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PubMed2000

Estimation of noise levels for models of chaotic dynamical systems

We investigate how far it is possible to identify and separate dynamical noise from measurement noise in observed nonlinear time series. Using Bayesian methods, we derive estimates for the two noise levels, and find that, given a good model of the dynamics, these can give accurate results even if the dynamical noise level is orders of magnitude smaller than the measurement noise level, whereas a simple calculation of root mean square error badly understates the dynamical noise. We argue that this allows better estimates of the underlying dynamical time series, and so better predictions of its future and of its fundamental dynamical properties.

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PubMed2003

Using distributed nonlinear dynamics for public key encryption.

We introduce a new method for asymmetric (public key/private key) encryption exploiting properties of nonlinear dynamical systems. A high-dimensional dissipative nonlinear dynamical system is distributed between transmitter and receiver, so we call the method distributed dynamics encryption (DDE). The transmitter dynamics is public, and the receiver dynamics is hidden. A message is encoded by modulation of parameters of the transmitter, and this results in a shift of the overall system attractor. An unauthorized receiver does not know the hidden dynamics in the receiver and cannot decode the message. We present an example of DDE using a coupled map lattice.

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PubMed2003

Structural relaxation and dynamic heterogeneity in a polymer melt at attractive surfaces.

Molecular dynamics simulations of polymer melts at flat and structured surfaces reveal that, for the former, slow dynamics and increased dynamic heterogeneity for an adsorbed polymer is due to densification of the polymer in a surface layer, while, for the latter, the energy topography of the surface plays the dominant role in determining dynamics of interfacial polymer. The dramatic increase in structural relaxation time for polymer melts at the attractive structured surface is largely the result of dynamic heterogeneity induced by the surface and does not resemble dynamics of a bulk melt approaching T(g).

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PubMed2004

Dynamic criticality in glass-forming liquids.

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero-temperature dynamical critical point. To support our proposal, we derive a dynamic field theory for a generic kinetically constrained model, which we expect to describe the dynamics of a supercooled liquid. We study this field theory using the renormalization group (RG). Its long time behavior is dominated by a zero-temperature critical point, which for d>2 belongs to the directed percolation universality class. Molecular dynamics simulations seem to confirm the existence of dynamic scaling behavior consistent with the RG predictions.

Journal Article↗
PubMed2005

Lattice mesoscopic model of dynamically heterogeneous fluids.

We introduce a mesoscopic three-dimensional lattice Boltzmann model which attempts to mimic the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard lattice Boltzmann dynamics with self-consistent constraints based on the nonlocal density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic heterogeneous fluids, such as non-Gaussian density distributions and long-time relaxation. Because of its intrinsically parallel dynamics, and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo, and lattice glass models.

Journal Article↗
PubMed2006

Adiabatic shear failure and dynamic stored energy of cold work.

Dynamic testing of statically predeformed specimens of magnesium (AM50) shows that the failure strain increases with the level of prestrain. Interrupted and other dynamic tests show that the temperature rise prior to localization has only a minor influence on adiabatic shear band (ASB) formation. For all the tests, the dynamic deformation energy until ASB formation is found to be relatively constant, indicating that ASB is dependent almost solely on dynamic deformation processes, with quasistatic and thermal effects prior to localization being very marginal. We suggest the concept of a constant dynamic mechanical energy (toughness) as a quantitative criterion for ASB formation--this concept being related physically to the dynamic stored energy of cold work. All in all, the tests indicate that ASB failure is more dependent on energy considerations that on strain criteria, as has been considered until now.

Journal Article↗
PubMed2005

Robot-enhanced motor learning: accelerating internal model formation during locomotion by transient dynamic amplification.

When adapting to novel dynamic environments the nervous system learns to anticipate the imposed forces by forming an internal model of the environmental dynamics in a process driven by movement error reduction. Here, we tested the hypothesis that motor learning could be accelerated by transiently amplifying the environmental dynamics. A novel dynamic environment was created during treadmill stepping by applying a perpendicular viscous force field to the leg through a robotic device. The environmental dynamics were amplified by an amount determined by a computational learning model fit on a per-subject basis. On average, subjects significantly reduced the time required to predict the applied force field by approximately 26% when the field was transiently amplified. However, this reduction was not as great as that predicted by the model, likely due to nonstationarities in the learning parameters. We conclude that motor learning of a novel dynamic environment can be accelerated by exploiting the error-based learning mechanism of internal model formation, but that nonlinearities in adaptive response may limit the feasible acceleration. These results support an approach to movement training devices that amplify rather than reduce movement errors, and provide a computational framework for both implementing the approach and understanding its limitations.

Adaptation, Physiological↗
PubMed2006

Improved gait recognition by gait dynamics normalization.

Potential sources for gait biometrics can be seen to derive from two aspects: gait shape and gait dynamics. We show that improved gait recognition can be achieved after normalization of dynamics and focusing on the shape information. We normalize for gait dynamics using a generic walking model, as captured by a population Hidden Markov Model (pHMM) defined for a set of individuals. The states of this pHMM represent gait stances over one gait cycle and the observations are the silhouettes of the corresponding gait stances. For each sequence, we first use Viterbi decoding of the gait dynamics to arrive at one dynamics-normalized, averaged, gait cycle of fixed length. The distance between two sequences is the distance between the two corresponding dynamics-normalized gait cycles, which we quantify by the sum of the distances between the corresponding gait stances. Distances between two silhouettes from the same generic gait stance are computed in the linear discriminant analysis space so as to maximize the discrimination between persons, while minimizing the variations of the same subject under different conditions. The distance computation is constructed so that it is invariant to dilations and erosions of the silhouettes. This helps us handle variations in silhouette shape that can occur with changing imaging conditions. We present results on three different, publicly available, data sets. First, we consider the HumanlD Gait Challenge data set, which is the largest gait benchmarking data set that is available (122 subjects), exercising five different factors, i.e., viewpoint, shoe, surface, carrying condition, and time. We significantly improve the performance across the hard experiments involving surface change and briefcase carrying conditions. Second, we also show improved performance on the UMD gait data set that exercises time variations for 55 subjects. Third, on the CMU Mobo data set, we show results for matching across different walking speeds. It is worth noting that there was no separate training for the UMD and CMU data sets.

Algorithms↗