Dynamics and stability of volume-scavenging drop arrays: Coarsening by capillarity

N drops, pinned by circular contact lines, are arranged in an array and coupled by a network of conduits. Inertialess exchange of volume among drops is driven by capillarity through the minimization of total surface energy. Drops scavenge volume from one another based on pressure differences, proportional to the surface tension, and arising from curvature differences. The system coarsens in the sense that, with time, volume is increasingly localized and ends up in a single ‘winner’ drop. Numerical simulations show that the identity of the winner can depend discontinuously on the initial condition and connectivity network. This motivates a study of the corresponding N-dimensional nonlinear dynamical system. All fixed points and their linear stabilities, obtained analytically, are found to be independent of connectivity. To determine which of the stable fixed points will be the winner, manifolds separating the attracting regions are found using a method which combines local information (eigenvectors at fixed points) with global information (invariant manifolds due to symmetry). This method is demonstrated for three N=3 systems with various connectivity networks, and is used to explain the numerical observations.     

Kaluza-Klein Dilatonic Matter: a Simplified Toy Model

International Journal of Theoretical Physics - We construct a field theoretical toy model for dilatonic matter using the five-dimensional Kaluza-Klein theory in the compactified approach....     

Friction in a Model of Hamiltonian Dynamics

We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle’s trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest.

“A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion.”—— Aristotle     

Entanglement Dynamics of a Generic-Spin Model

We investigate the entanglement dynamics of a generic-spin model with weak external field. We first derive the time-dependent solutions of angular momentum operators with short-time approximation and then numerically calculate the entangled witness. It’s shown that one can dynamically generate quantum entanglement by adjusting coupling strength.     

Coarsening in granular systems

We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called “granular gases”, are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g., shear patterns, vortices, and clusters. In fluidized experiments, liquid–gas or solid–gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which is relevant in many practical situations, is usually described in terms of coarsening dynamics: there, bubbles of misaligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of the total occupied volume.     

Coarsening in inhomogeneous systems

This article is a brief review of coarsening phenomena occurring in systems where quenched features—such as random field, varying coupling constants or lattice vacancies—spoil homogeneity. We discuss the current understanding of the problem in ferromagnetic systems with a non-conserved scalar order parameter by focusing primarily on the form of the growth law of the ordered domains and on the scaling properties.     

Entanglement Dynamics in a Model Tripartite Quantum System

A Λ-type atom interacting with two radiation fields exhibits electromagnetically induced transparency and other nonclassical effects that appear in the entanglement dynamics of the atomic subsystem and in appropriate field observables. Both EIT and field-atom entanglement are important for quantum information processing. We investigate the roles played by specific initial field states, detuning parameters, field nonlinearities and intensity-dependent field-atom couplings on EIT and the entanglement between subsystems. Departure from coherence of the initial field states produces significant effects. We investigate these aspects in a model that exhibits the salient features of entangled tripartite systems. For initial photon-added coherent states, collapses and revivals of the atomic subsystem von Neumann entropy appear as the intensity parameter varies over a narrow range of values. These features could be useful in enabling entanglement.     

Coarsening of cracks in a uniaxially strained solid

We discuss the stress relaxation in a uniaxially strained solid due to the coarsening of a system of parallel cracks. We emphasize similarities and differences of this process to Ostwald ripening in a first order phase transition. A conventional mean-field approximation breaks down and several independent length scales have to be taken into account. Strong elastic interactions between the cracks determine the growth behavior. We derive scaling laws for the coarsening of the different length scales involved and the time evolution of stress relaxation, finally leading to the equilibrium state of a fractured body. The characteristic size of the cracks grows linearly in time which is much faster than in usual Ostwald ripening.     

Interlaced solitons and vortices in coupled DNLS lattices

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.     

Coarsening in a driven Ising chain with conserved dynamics

We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping, except for the shortest domains-dimers-which undergo long-range hopping. This system exhibits anomalous ordering dynamics due to the existence of two characteristic length scales: the average domain length L(t) approximately t(1/2) and the average dimer hopping distance l(t) approximately square root[L(t)] approximately t(1/4). As a consequence of these two scales, the density of short domains decays as t(-5/4), instead of the t(-3/2) decay that would arise from pure domain diffusion.     

平均键能方法在应变层异质结带阶计算中的简化模型

将平均键能方法推广应用于应变层异质结的价带和导带阶研究。通过平均带阶参数形变热amv来研究带阶参数Emv随应变状态的变化关系,发现平均带阶参数Emv.av=Em-Ev.av在不同应变状态下基本上保持不变。因此,在应变层带阶参数Emv的计算中,只需计算其发生应变前体材料的带阶参数Emv.o值并引用形变b和SO裂距△0的实验值,通过简便的代数运算即可得到应变层的Emv值,从而方便地预言不同应变层异质结的价带带阶。本文引入带隙形变势aGap来描述带隙改变量△Eg随应变状态的变化。由导带带阶和价带带阶的关系△Ec=△Eg △Ev可以求出不同应变情况下的导带带阶。     

Coarsening in fluid phase transitions

We review the understanding of the kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected domains, based on overall composition in a binary liquid or on density in a vapor–liquid system, are discussed. Depending upon the morphology, various possible mechanisms for domain growth are pointed out and discussions of corresponding theoretical predictions are provided. On the computational front, useful models and simulation methodologies are presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor–liquid transitions. In the case of a disconnected structure, the mechanism has been confirmed directly.     

Observation Constraints on the Simplified GCG Model

A simplified version of generalized Chaplygin gas （GCG） as a dark energy model is studied. By using the latest 162 ESSENCE type Ia supernovae （She Ia） data, 30 high redshift She Ia data, the baryonic acoustic oscillation peak from SDSS and the CMB data from WMAP3, a strong constraint on this simplified GCG model is obtained. At the 95.4% confidence level we obtain 0.21 ≤ Ωm ≤ 0.31 and 0.994 〈 α 〈 1.0 with the best fit Ωm = 0.25 and a = 1. This best fit scenario corresponds to an accelerating universe with qo ≈-0.65 and z ≈ 0.81 （a redshiR of cosmic phase transition from deceleration to acceleration）.     

Chaotic Dynamics in an Electronic Model of a Genetic Network

We consider dynamics in a class of piecewise-linear ordinary differential equations and in an electronic circuit that model genetic networks. In these models, gene activity varies continuously in time. However, as in Boolean or discrete-time switching networks, gene activity is driven high or low based only on whether the activities of the regulating genes are high or low (i.e., above or below certain thresholds). Depending on the “regulatory logic”, these models can exhibit simple dynamics, like stable fixed points or oscillation, or chaotic dynamics. The observed qualitative and quantitative differences between the dynamics in the idealized equations and the dynamics in the electronic circuit lead us to focus attention on the analysis of the dynamics as a function of parameter values. We propose new techniques for solving the inverse problem – the problem of inferring the regulatory logic and parameters from time series data. We also give new symbolic and statistical methods for characterizing dynamics in these networks.     

The LSW Model for Domain Coarsening: Asymptotic Behavior for Conserved Total Mass

In the classical theory of domain coarsening the particles of the coarsening phase evolve by diffusional mass transfer with a mean field. We study the long-time behavior of measure-valued solutions with compact support to this model coupled with the constraint of conserved total mass, including mean-field mass. Unlike the case of conserved volume fraction, this system has no precisely self-similar solutions, and sufficiently low supersaturation can lead to the finite-time extinction of all particles. We find a new explicit family of asymptotically self-similar solutions, and in case that the largest particle size is unbounded we establish results similar to the volume-conserved case. These include necessary criteria for asymptotic self-similarity, and sensitive dependence of long-time behavior on the distribution of largest particles in the system.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001