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1.
Chaos ; 34(5)2024 May 01.
Artículo en Inglés | MEDLINE | ID: mdl-38717405

RESUMEN

A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, and materials science is the representative sampling of the phase space over long time scales of interest; this task is not, however, without challenges. For example, the long term behavior of a system with many degrees of freedom often cannot be efficiently computationally explored by direct dynamical simulation; such systems can often become trapped in local free energy minima. In the study of physics-based multi-time-scale dynamical systems, techniques have been developed for enhancing sampling in order to accelerate exploration beyond free energy barriers. On the other hand, in the field of machine learning (ML), a generic goal of generative models is to sample from a target density, after training on empirical samples from this density. Score-based generative models (SGMs) have demonstrated state-of-the-art capabilities in generating plausible data from target training distributions. Conditional implementations of such generative models have been shown to exhibit significant parallels with long-established-and physics-based-solutions to enhanced sampling. These physics-based methods can then be enhanced through coupling with the ML generative models, complementing the strengths and mitigating the weaknesses of each technique. In this work, we show that SGMs can be used in such a coupling framework to improve sampling in multiscale dynamical systems.

2.
Phys Rev E ; 104(4-1): 044202, 2021 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-34781528

RESUMEN

The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g., within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrödinger equation and systematically derive a normal form for the emergence of radially symmetric blowup solutions from stationary ones. While this is an extensively studied problem, such a normal form, based on the methodology of asymptotics beyond all algebraic orders, applies to both the dimension-dependent and power-law-dependent bifurcations previously studied. It yields excellent agreement with numerics in both leading and higher-order effects, it is applicable to both infinite and finite domains, and it is valid in both critical and supercritical regimes.

3.
Langmuir ; 32(19): 4736-45, 2016 05 17.
Artículo en Inglés | MEDLINE | ID: mdl-27077328

RESUMEN

We investigate the dynamics of a droplet on a planar substrate as the droplet volume changes dynamically due to liquid being pumped in or out through a pore. We adopt a diffuse-interface formulation which is appropriately modified to account for a localized inflow-outflow boundary condition (the pore) at the bottom of the droplet, hence allowing to dynamically control its volume, as the droplet moves on a flat substrate with a periodic chemical pattern. We find that the droplet undergoes a stick-slip motion as the volume is increased (fattening droplet) which can be monitored by tracking the droplet contact points. If we then switch over to outflow conditions (thinning droplet), the droplet follows a different path (i.e., the distance of the droplet midpoint from the pore location evolves differently), giving rise to a hysteretic behavior. By means of geometrical arguments, we are able to theoretically construct the full bifurcation diagram of the droplet equilibria (positions and droplet shapes) as the droplet volume is changed, finding excellent agreement with time-dependent computations of our diffuse-interface model.

4.
Artículo en Inglés | MEDLINE | ID: mdl-26764846

RESUMEN

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force ("antiresonances") between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) "nonlinear spectrum" in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). We rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.

5.
Artículo en Inglés | MEDLINE | ID: mdl-24730930

RESUMEN

By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. We demonstrate a remarkable control over the number of breathers within the multibreather pattern that can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (or amplitude) where the transition between different multibreather states occurs are predicted accurately by the proposed theoretical model, which is numerically shown to support exact dark breather and multibreather solutions. Moreover, we visualize detailed temporal and spatial profiles of breathers and, especially, of multibreathers using a full-field probing technology and enable a systematic favorable comparison among theory, computation, and experiments. A detailed bifurcation analysis reveals that the dark and multibreather families are connected in a "snaking" pattern, providing a roadmap for the identification of such fundamental states and their bistability in the laboratory.


Asunto(s)
Coloides/química , Modelos Químicos , Simulación por Computador , Transferencia de Energía , Fricción , Viscosidad
6.
J Theor Biol ; 264(3): 893-913, 2010 Jun 07.
Artículo en Inglés | MEDLINE | ID: mdl-20178805

RESUMEN

We propose a (time) multiscale method for the coarse-grained analysis of collective motion and decision-making in self-propelled particle models of swarms comprising a mixture of 'naïve' and 'informed' individuals. The method is based on projecting the particle configuration onto a single 'meta-particle' that consists of the elongation of the flock together with the mean group velocity and position. We find that the collective states can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a continuous time random walk (CTRW). These properties can be accurately predicted at the macroscopic level by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model.


Asunto(s)
Algoritmos , Toma de Decisiones/fisiología , Memoria/fisiología , Modelos Psicológicos , Animales , Simulación por Computador , Movimiento/fisiología , Factores de Tiempo
7.
Phys Rev E Stat Nonlin Soft Matter Phys ; 80(6 Pt 2): 066601, 2009 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-20365288

RESUMEN

We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem's linear limit, we identify the system's eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations.


Asunto(s)
Biofisica/métodos , Oscilometría/métodos , Algoritmos , Cristalización , Modelos Lineales , Modelos Estadísticos , Factores de Tiempo
8.
Phys Rev E Stat Nonlin Soft Matter Phys ; 78(5 Pt 2): 055203, 2008 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-19113178

RESUMEN

It is shown that the pulses which develop in the NO+H2 reaction on an alkali promoted Rh(110) surface reaction can transport alkali metal. This leads to the accumulation of a substantial alkali-metal concentration in the collision area of pulse trains. Realistic simulations revealed that the effect is due to the strong energetic interactions of the alkali metal with coadsorbates, i.e., the attractive interaction with coadsorbed oxygen and the effectively repulsive interaction with coadsorbed nitrogen.

9.
Phys Rev E Stat Nonlin Soft Matter Phys ; 77(3 Pt 2): 036214, 2008 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-18517492

RESUMEN

We explore the effect of spatiotemporally varying substrate temperature profiles on the dynamics and the resulting reaction rate enhancement of the catalytic oxidation of CO on Pt(110). The catalytic surface is "addressed" by a focused laser beam whose motion is computer controlled. The averaged reaction rate is observed to undergo a characteristic maximum as a function of the speed of this moving laser spot. Experiments as well as modeling are used to explore and rationalize the existence of such an optimal laser speed.

10.
Phys Rev E Stat Nonlin Soft Matter Phys ; 75(5 Pt 1): 051309, 2007 May.
Artículo en Inglés | MEDLINE | ID: mdl-17677056

RESUMEN

We use an "equation-free," coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the coarse-grained dynamics of these phenomena in gently fluidized beds of solid mixtures of different densities, typically a slow process for which reasonable continuum models are currently unavailable.

11.
J Theor Biol ; 246(1): 100-12, 2007 May 07.
Artículo en Inglés | MEDLINE | ID: mdl-17258774

RESUMEN

We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for heterogeneous populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each individual is characterized by an angle, whose dynamics are nonlinearly coupled with those of all the other individuals, with an explicit dependence on the difference between the individual's orientation and the instantaneous average direction. Choosing convenient coarse-grained variables (suggested by uncertainty quantification methods) that account for rapidly developing correlations during initial transients, we perform efficient computations of coarse-grained steady states and their bifurcation analysis. We circumvent the derivation of coarse-grained governing equations, following an equation-free computational approach.


Asunto(s)
Modelos Psicológicos , Movimiento/fisiología , Conducta Social , Animales , Biología Computacional , Dominación-Subordinación , Dinámicas no Lineales
12.
Phys Rev E Stat Nonlin Soft Matter Phys ; 74(1 Pt 2): 016702, 2006 Jul.
Artículo en Inglés | MEDLINE | ID: mdl-16907211

RESUMEN

Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.

13.
Phys Rev Lett ; 96(14): 144101, 2006 Apr 14.
Artículo en Inglés | MEDLINE | ID: mdl-16712078

RESUMEN

We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.

14.
Phys Rev E Stat Nonlin Soft Matter Phys ; 73(3 Pt 2): 036217, 2006 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-16605641

RESUMEN

We explore the effect of boundary curvature on the instability of reactive pulses in the catalytic oxidation of on microdesigned Pt catalysts. Using ring-shaped domains of various radii, we find that the pulses disappear (decollate from the inert boundary) at a turning point bifurcation, and we trace this boundary in both physical and geometrical parameter space. These computations corroborate experimental observations of pulse decollation.

15.
Phys Rev E Stat Nonlin Soft Matter Phys ; 73(3 Pt 2): 036219, 2006 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-16605643

RESUMEN

We study computationally and experimentally the propagation of chemical pulses in complex geometries. The reaction of interest, CO oxidation, takes place on single crystal Pt(110) surfaces that are microlithographically patterned; they are also addressable through a focused laser beam, manipulated through galvanometer mirrors, capable of locally altering the crystal temperature and thus affecting pulse propagation. We focus on sudden changes in the domain shape (corners in a Y-junction geometry) that can affect the pulse dynamics; we also show how brief, localized temperature perturbations can be used to control reactive pulse propagation. The computational results are corroborated through experimental studies in which the pulses are visualized using reflection anisotropy microscopy.

16.
Phys Rev E Stat Nonlin Soft Matter Phys ; 67(4 Pt 2): 047602, 2003 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-12786538

RESUMEN

We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space's metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric's evolution is governed by a partial differential equation). Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.

17.
Phys Rev Lett ; 90(14): 148301, 2003 Apr 11.
Artículo en Inglés | MEDLINE | ID: mdl-12731950

RESUMEN

We study the initiation of pulses and fronts in a two-dimensional catalytic reaction-diffusion system: CO oxidation on Pt(110). Using a computer-controlled mobile focused laser beam, we impart various patterns (in space and time) of localized temperature "kicks" to the surface. We explore, and also rationalize through modeling, the cooperativity of such individually subcritical perturbations in both the excitable and the bistable regime.

18.
Phys Rev Lett ; 90(1): 018302, 2003 Jan 10.
Artículo en Inglés | MEDLINE | ID: mdl-12570653

RESUMEN

Using a recently realized "addressable catalyst surface" [Science 294, 134 (2001)]] we study the interaction of chemical reaction waves with prescribed spatiotemporal fields. In particular, we study how a traveling chemical pulse is "dragged" by a localized, moving temperature heterogeneity as a function of its intensity and speed. The acceleration and eventual "detachment" of the wave from the heterogeneity is also explored through simulation and stability analysis.

19.
Phys Rev E Stat Nonlin Soft Matter Phys ; 65(4 Pt 2B): 046613, 2002 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-12006053

RESUMEN

We study analytically and numerically continuum models derived on the basis of Padé approximations and their effectiveness in modeling spatially discrete systems. We not only analyze features of the temporal dynamics that can be captured through these continuum approaches (e.g., shape oscillations, radiation effects, and trapping) but also point out ones that cannot be captured (such as Peierls-Nabarro barriers and Bloch oscillations). We analyze the role of such methods in providing an effective "homogenization" of spatially discrete, as well as of heterogeneous continuum equations. Finally, we develop numerical methods for solving such equations and use them to establish the range of validity of these continuum approximations, as well as to compare them with other semicontinuum approximations.

20.
Phys Rev E Stat Nonlin Soft Matter Phys ; 64(5 Pt 2): 056624, 2001 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-11736133

RESUMEN

We propose a method for mapping a spatially discrete problem, stemming from the spatial discretization of a parabolic or hyperbolic partial differential equation of gradient type, to a heterogeneous one with certain comparable dynamical features pertaining, in particular, to coherent structures. We focus the analysis on a (1+1)-dimensional phi(4) model and confirm the theoretical predictions numerically. We also discuss possible generalizations of the method and the ensuing qualitative analogies between heterogeneous and discrete systems and their dynamics.

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