Identifying stochastic basin hopping by partitioning with graph modularity

It has been known that noise in a stochastically perturbed dynamical system can destroy what was the original zero-noise case barriers in the phase space (pseudobarrier). Noise can cause the basin hopping. We use the Frobenius-Perron operator and its finite rank approximation by the Ulam-Galerkin method to study transport mechanism of a noisy map. In order to identify the regions of high transport activity in the phase space and to determine flux across the pseudobarriers, we adapt a new graph theoretical method which was developed to detect active pseudobarriers in the original phase space of the stochastic dynamic. Previous methods to identify basins and basin barriers require a priori knowledge of a mathematical model of the system, and hence cannot be applied to observed time series data of which a mathematical model is not known. Here we describe a novel graph method based on optimization of the modularity measure of a network and introduce its application for determining pseudobarriers in the phase space of a multi-stable system only known through observed data.     

Phase control algorithms for focusing light through turbid media

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.     

How efficiently Do three pointlike particles sample phase space?

We show that the continuous phase space of a hard particle system can be mapped onto a discrete but infinite phase space. For three pointlike particles confined to a ring, the evolution of the system maps onto a chaotic walk on a hexagonal lattice. This facilitates direct measurement of the departure of the system from its original configuration. In special cases of mass ratios the phase space becomes closed and finite (nonergodic). There are qualitative differences between this chaotic walk and a random walk, in particular a more rapid sampling of phase space.     

Noise- and inertia-induced inhomogeneity in the distribution of small particles in fluid flows

The dynamics of small spherical neutrally buoyant particulate impurities immersed in a two-dimensional fluid flow are known to lead to particle accumulation in the regions of the flow in which vorticity dominates over strain, provided that the Stokes number of the particles is sufficiently small. If the flow is viewed as a Hamiltonian dynamical system, it can be seen that the accumulations occur in the nonchaotic parts of the phase space: the Kolmogorov-Arnold-Moser tori. This has suggested a generalization of these dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use a bailout embedding of the standard map to mimic the dynamics of neutrally buoyant impurities subject not only to drag but also to fluctuating forces modeled as white noise. We find that the generation of inhomogeneities associated with the separation of particle from fluid trajectories is enhanced by the presence of noise, so that they appear in much broader ranges of the Stokes number than those allowing spontaneous separation. (c) 2002 American Institute of Physics.     

On the Asymmetric Simple Exclusion Process with Multiple Species

In previous work the authors, using the Bethe Ansatz, found for the N-particle asymmetric simple exclusion process on the integers a formula—a sum of multiple integrals—for the probability that a system is in a particular configuration at time t given an initial configuration. The present work extends this to the case where particles are of different species, with particles of a higher species having priority over those of a lower species. Here the integrands in the multiple integrals are defined by a system of relations whose consistency requires verifying that the Yang-Baxter equations hold.     

Particle surface treatment for nanocomposites containing ceramic particles

Polymer matrix composites containing dispersed ceramic nanoparticles were formed by UV activated photopolymerization from the reactive liquid monomer hexanediol-diacrylate (HDODA). The polymer forming reaction proceeds by a free-radical mechanism. In forming polymer composites that contain nanoparticles, dispersing the particles as discrete entities is critical for developing optimum properties. In the as-received condition, ceramic particles are aggregated. They must be dispersed in the monomer but if the particles are not surface treated and stabilized, they rapidly settle out of the suspension. Surface modification of the ceramic allows the particles to be suspended in the organic monomer and stabilizes the dispersion so that the particles will not reagglomerate. In this study silanes were employed as surface modifiers to disperse two nano-particulate ceramics in the HDODA monomer. The ceramic particles used are silicon carbide (SiC) and barium titanate (BaTiO₃). The shapes and sizes of the ceramic particles were established using transmission electron microscopy (TEM). A method for dispersing nanoparticles was developed in which silane-treated particles were stabilized so that they did not settle out of the liquid monomer. An analytical method based on atomic force microscopy (AFM) was used to characterize the particle distribution in the cured composites. Focusing on work with SiC nanoparticles in HDODA as a model system, the process for silane application was advanced so that it successfully yielded composites having no aggregates with particle sizes closely matching those of the neat ceramic particles.     

Exploring the origins of the power-law properties of energy landscapes: An egg-box model

Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a power-law. To explore how both these features can simultaneously be true, we introduce an “egg-box” model. In these model landscapes, the Gaussian energy distribution is used as a starting point and we examine whether a power-law basin area distribution can arise as a natural consequence through the swallowing up of higher-energy minima by larger low-energy basins when the variance of this Gaussian is increased sufficiently. Although the basin area distribution is substantially broadened by this process, it is insufficient to generate power-laws, highlighting the role played by the inhomogeneous distribution of basins in configuration space for actual PELs.     

表面微观形貌测量中数字图象处理的应用

应用相移干涉术测量物体表面微观形貌时,由于各种因素的影响,表面形貌的测量会产生失真的现象.本文采用数字信号滤波与平滑技术消除了测量过程中系统误差引起的波纹度及系统噪音,去除了在图象的数字化和传输过程中产生的高频噪音和假轮廓,使得测量结果更接近于实际值.     

Deterministic and stochastic effects near the convective onset

The pure conduction state of a horizontal layer of fluid heated from below becomes unstable with respect to a convecting state when the temperature difference exceeds a critical value. We examine the question of how real, physical systems evolve from conduction to convection. Most experimental cells contain geometric or thermal inhomogeneities which render the bifurcation to convection imperfect. In that case the pure conduction state never exists and the convecting state evolves continuously and smoothly as the temperature difference is raised. When a sufficiently perfect experimental cell is constructed to eliminate this route to convection, then dynamic imperfections will usually prevail. When the temperature difference across the cell is raised, the vertical gradients in the sidewalls evolve at a rate which differs from that in the fluid. The resultingtransient horizontal thermal gradients initiate the convective flow. This phenomenon can be eliminated by providing sidewalls which have the same thermal diffusivity as that of the fluid. When that is done, the convective flow is started by random noise which exists in any experimental system. Analysis of experiments shows that the noise source is considerably stronger than thermal noise, but its origin is unclear at this time.     

Collective motion of active particles in environmental noise

We study the collective motion of active particles in environmental noise, where the environmental noise is caused by noise particles randomly diffusing in two-dimensional space. We show that active particles in a noisy environment can self organize into three typical phases: polar liquid, band, and disordered gas states. In our model, the transition between band and disordered gas states is discontinuous. Giant number fluctuation is observed in the polar liquid phase. We also compare our results with the Vicsek model and show that the interaction with noise particles can stabilize the band state to very low noise condition. This band structure could recruit most of the active particles in the system, which greatly enhances the coherence of the system. Our findings of complex collective behaviors in environmental noise help us to understand how individuals modify their self-organization by environmental factors, which may further contribute to improving the design of collective migration and navigation strategies.     

Semi-infinite TASEP with a Complex Boundary Mechanism

We consider a totally asymmetric exclusion process on the positive half-line. When particles enter the system according to a Poisson source, Liggett has computed all the limit distributions when the initial distribution has an asymptotic density. In this paper we consider systems for which particles enter according to a complex mechanism depending on the current configuration in a finite neighborhood of the origin. For this kind of models, we prove a strong law of large numbers for the number of particles which have entered the system at a given time. Our main tool is a new representation of the model as a multi-type particle system with infinitely many particle types.     

Complexification of gauge theories

For the case of a first-class constrained system with equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations G is equivalent to the single process of dividing out the initial phase space by the complexification G_C of G. For the particular case of a phase space action that is the lift of a configuration space action, conditions are found under which, in finite dimensions, the physical phase space of a gauge system with first-class constraints is diffeomorphic to a manifold imbedded in the physical configuration space of the complexified gauge system. Similar conditions are shown to hold for the infinite-dimensional example of Yang-Mills theories. As a physical application we discuss the adequateness of using holomorphic Wilson loop variables as (generalized) global coordinates on the physical phase space of Yang-Mills theory.     

Effective potential method for active particles

ABSTRACT

We investigate the steady-state properties of an active fluid modelled as an assembly of soft repulsive spheres subjected to Gaussian coloured noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified coloured noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of coloured noise and interactions enhances the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.     

A physical perspective on classical cloning

The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach to the classical cloning process showing how cloning can be realised using Hamiltonians. After writing down a canonical transformation that clones classical states, we show how this can be implemented by Hamiltonian evolution. We then propose an experiment using the tools of nonlinear optics to realise the ideas presented here. Finally, to understand the cloning process in a more realistic context, we introduce statistical mechanical noise to the system and study how this affects the cloning process. While most of our work deals with linear systems and harmonic oscillators, we give some examples of cloning maps on manifolds and show that any system whose configuration space is a group manifold admits a cloning canonical transformation.     

Can non-propagating hydrodynamic solitons be forced to move?

Development of technologies based on localized states depends on our ability to manipulate and control these nonlinear structures. In order to achieve this, the interactions between localized states and control tools should be well modelled and understood. We present a theoretical and experimental study for handling non-propagating hydrodynamic solitons in a vertically driven rectangular water basin, based on the inclination of the system. Experiments show that tilting the basin induces non-propagating solitons to drift towards an equilibrium position through a relaxation process. Our theoretical approach is derived from the parametrically driven damped nonlinear Schr?dinger equationwhich models the system. The basin tilting effect is modelled by promoting the parameters that characterize the system, e.g. dissipation, forcing and frequency detuning, as space dependent functions. A motion law for these hydrodynamic solitons can be deduced from these assumptions. The model equation, which includes a constant speed and a linear relaxation term, nicely reproduces the motion observed experimentally.     

Noncolliding Squared Bessel Processes

We consider a particle system of the squared Bessel processes with index ν>−1 conditioned never to collide with each other, in which if −1<ν<0 the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function J _ν is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.     

粒子-转子模型和推转壳模型中的能谱统计分析

用粒子–转子模型和推转壳模型研究了6个粒子分别填充在单j壳和双j壳上的混沌行为.分析了单j壳和双j壳情况下能谱的最近邻能级间距分布和谱刚度随自旋及推转频率的变化,结果表明,当组态空间大小不变时,系统在双j壳(g_7/2+d_5/2)情况下比在单j壳(i_13/2)情况下更规则,而当组态空间从单j壳(i_13/2)扩大到双j壳(i_13/2+g_9/2)时,系统的混沌程度变化不大.同时比较了将6个粒子的两体相互作用分别取为δ力和对力时的系统的混沌行为     

The Role of Noise and Initial Conditions in the Asymptotic Solution of a Bounded Confidence, Continuous-Opinion Model

We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.     

Diffusion in crystals with traps: A simple phenomenological model

We present a phenomenological model describing the trapping and release of mobile defects at random inhomogeneities. The traps are characterized by two parameters, the capture radiusR _t, describing the range of the interaction and the binding energyE _b describing the escape. We give an integral representation of the correlation function of the mobile particles in the presence of traps. For large distances the correlation function can be described by a simple diffusional process with an effective diffusion constant. Finally we discuss the neutron scattering by mobile defects resulting from this trapping model.     

Dynamical realization of l-conformal Galilei algebra and oscillators

The method of nonlinear realizations is applied to the l-conformal Galilei algebra to construct a dynamical system without higher derivative terms in the equations of motion. A configuration space of the model involves coordinates, which parametrize particles in d spatial dimensions, and a conformal mode, which gives rise to an effective external field. It is shown that trajectories of the system can be mapped into those of a set of decoupled oscillators in d dimensions.