Three-dimensional Rayleigh-Taylor incompressible turbulence is numerically studied with the Boussinesq approximation. Our focus is on scaling properties of the moments of the density and the velocity differences (structure functions), which are directly measured from the numerical data. A comparison with the phenomenology proposed by Chertkov [Phys. Rev. Lett. 91, 115001 (2003)] is made. It is found that deviation from the phenomenology (anomalous scaling or intermittency effect) of the density observed for high-order structure functions is quite close to that of the passive scalar with a uniform mean scalar gradient advected by the barotropic homogeneous isotropic turbulence.

The dynamics of a spring-mass system under repeated impact with a vibrating wall is investigated using the static wall approximation. The evolution of the harmonic oscillator is described by two coupled difference equations. These equations are solved numerically, and in some cases exact analytical expressions have also been found. For a periodically vibrating wall, Fermi acceleration is only found at resonance. There, the average rebounding velocity increases linearly with the number of collisions. Near resonance, the average rebounding velocity grows initially with the number of collisions and eventually reaches a plateau. In the vicinity of resonance, the motion of the oscillator exhibits scaling properties over a range of frequency ratios. The presence of dissipation at resonance destroys the Fermi-acceleration process and induces scaling behavior similar to that at near resonance. For a moving wall with a random amplitude at collisions, Fermi acceleration is observed independently of the ratio between the wall and oscillator frequencies. In this case the average rebounding velocity grows with the square root of the number of collisions with the wall. Also, in this latter case, dissipation suppresses the Fermi-acceleration mechanism and induces a scaling behavior with the same universality class as that of the dissipative bouncing ball model with random external perturbations.

We studied a modified reaction-diffusion model theoretically by coupling two ideal excitable media systems. In the simulated homogeneous system, we observed the propagation of reaction-diffusion wave trains that required no external force after the initial stimulation. We investigated the dependence of the system’s oscillation patterns on model parameters, and we discussed the influence of the different dynamic constants of the individual coupled systems on the dynamics of the coupled systems. Some complex two-dimensional patterns generated by our model are shown. We also found similar phenomena in the models for catalytic CO oxidation on Pt(110), and for cardiac tissue.

We present a model for the rate of temperature relaxation between electrons and ions in plasmas. The model includes self-consistently the effects of particle screening, electron degeneracy, and correlations between electrons and ions. We successfully validate the model over a wide range of plasma coupling against molecular-dynamics simulations of classical plasmas of like-charged electrons and ions. We present calculations of the relaxation rates in dense hydrogen and show that, while electron-ion correlation effects are indispensable in classical, like-charged plasmas at any density and temperature, quantum diffraction effects prevail over electron-ion correlation effects in dense hydrogen plasmas.

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

The paper discusses the relation between streamer velocity and diameter that follows from an analytical approach to description of the streamer head structure. It is shown that using measured data for streamer velocity and diameter one can evaluate the electric field in the streamer head. The analytical approach predicts that for positive streamers a minimum diameter exists, inversely proportional to the gas density.

Two weak-coupling continuous time quantum Monte Carlo (CTQMC) methods are shown to be equivalent for Hubbard-type interactions. A relation between these CTQMC methods and the Hirsch-Fye quantum Monte Carlo (HFQMC) method is established, identifying the latter as an approximation within CTQMC and providing a diagrammatic interpretation. Both HFQMC and CTQMC are shown to be equivalent when the number of time slices in HFQMC becomes infinite, implying the same degree of fermion sign problem in this limit.

A phenomenological description of transition from an unstable to a (meta)stable phase state, including microscopic and mesoscopic scales, is presented. It is based on the introduction of specific memory functions which take into account contributions to the driving force of transformation from the past. A region of applicability for phase-field crystals and Swift-Hohenberg-type models is extended by inclusion of inertia effects into the equations of motion through a memory function of an exponential form. The inertia allows us to predict fast degrees of freedom in the form of damping perturbations with finite relaxation time in the instability of homogeneous and periodic model solutions.

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two-dimensional colloidal disks in confined geometries. We calculate the velocity autocorrelation functions and observe the predicted $t^{-1}$ long-time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the $t^{-1}$ tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system. The Langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times.

We present a neutron-scattering investigation of the crystal structure formed by $p\text{H}$-sensitive poly(2-vinylpyridine) microgel particles with $5\text{wt}\%$ of cross-linker. We focus on highly swollen particles and explore concentrations ranging from below close packing to well above close packing, where the particles are forced to shrink and/or interpenetrate. The crystal structure is found to be random hexagonal close packed, similar to the structure typically found in hard-sphere systems.

“Leaping” methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the “partitioned leaping algorithm” (PLA) [L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly used “exact” stochastic methods. We also illustrate bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice.

We study the kinetics of growing cell populations by means of a kinetic Monte Carlo method. By applying the same growth mechanism to a two-dimensional (2D) and a three-dimensional (3D) model, and making direct comparison with experimental studies, we show that both models exhibit similar behavior. Based on this we propose a method for establishment of a mapping between the 2D and 3D results. Additionally, we present an analytic approach to obtain the time evolution, and show in case of the 3D model how synchronization effects can influence the growth kinetics. Finally, we compare the results of our models to experimental data of the growth kinetics of 2D monolayers and 3D NIH3T3 xenografts in mice.

We develop and validate an algorithm for integrating stochastic differential equations under green noise. Utilizing it and the standard methods for computing dynamical systems under red and white noise, we address the problem of synchronization among chaotic oscillators in the presence of common colored noise. We find that colored noise can induce synchronization, but the onset of synchronization, as characterized by the value of the critical noise amplitude above which synchronization occurs, can be different for noise of different colors. A formula relating the critical noise amplitudes among red, green, and white noise is uncovered, which holds for both complete and phase synchronization. The formula suggests practical strategies for controlling the degree of synchronization by noise, e.g., utilizing noise filters to suppress synchronization.

We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schrödinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). Nonlinear terms in the equations of motion destroy the Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single-site, single-mode, and general finite-size excitations and study the statistics of detrapping times. We investigate the properties of mode-mode resonances, which are responsible for the incoherent delocalization process.

In this paper we demonstrate an unusual behavior in the shear-banded flow of a viscoelastic fluid. We report large and patterned fluctuations in the shear stress in an apparently fluid material undergoing steady shear, which we interpret as an intermittent and microscopic fracture and self-healing process. The statistical pattern of the fluctuations is indicative of self-organized criticality, and their magnitude can be directly related to the constitutive instability that underlies the shear banding.

We study theoretically the chirality of a generic rigid object’s sedimentation in a fluid under gravity in the low Reynolds number regime. We represent the object as a collection of small Stokes spheres or stokeslets and the gravitational force as a constant point force applied at an arbitrary point of the object. For a generic configuration of stokeslets and forcing point, the motion takes a simple form in the nearly free draining limit where the stokeslet radius is arbitrarily small. In this case, the internal hydrodynamic interactions between stokeslets are weak, and the object follows a helical path while rotating at a constant angular velocity $\omega$ about a fixed axis. This $\omega$ is independent of initial orientation and thus constitutes a chiral response for the object. Even though there can be no such chiral response in the absence of hydrodynamic interactions between the stokeslets, the angular velocity obtains a fixed nonzero limit as the stokeslet radius approaches zero. We characterize empirically how $\omega$ depends on the placement of the stokeslets, concentrating on three-stokeslet objects with the external force applied far from the stokeslets. Objects with the largest $\omega$ are aligned along the forcing direction. In this case, the limiting $\omega$ varies as the inverse square of the minimum distance between stokeslets. We illustrate the prevalence of this robust chiral motion with experiments on small macroscopic objects of arbitrary shape.

We study numerically the interplay of surface topography and kinetics in the relaxation of crystal surface corrugations below roughening in two independent space dimensions. The kinetic processes are isotropic diffusion of adatoms across terraces and attachment-detachment of atoms at steps. We simulate the corresponding anisotropic partial differential equation for the surface height via the finite element method. The numerical results show a sharp transition from initially biperiodic surface profiles to one-dimensional surface morphologies. This transition is found to be enhanced by an applied electric field. Our predictions demonstrate the dramatic influence on morphological relaxation of geometry-induced asymmetries in the adatom fluxes transverse and parallel to step edges.

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the two-dimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

A simple monatomic system in two dimensions with a double-well interaction potential is investigated in a wide range of temperatures by molecular-dynamics simulation. The system is melted and equilibrated well above the melting temperature, and then it is quenched to a temperature 88% below the melting temperature at several cooling rates to produce an amorphous state. Various thermodynamic quantities are measured as functions of temperature while the system is heated at a constant rate. The glass transition is observed with a sudden increase in the energy and the glass transition temperature is shown to be an increasing function of the cooling rate in the preparation process of the amorphous state. In a relatively high-temperature region, the system gradually transforms into crystals, and the time-temperature-transformation curve shows a typical nose shape. It is found that the transformation time to a crystalline state is the shortest at a temperature $14–15\%$ below the melting temperature and that at sufficiently low temperatures the system does not transform into a crystalline state within an observation time in our simulation. This indicates that a long-lived glassy state is realized.

We examine the anisotropy of a four-point correlation function $G_4\left(\vec{k},\vec{r};t\right)$ and its associated structure factor $S_4\left(\vec{k},\vec{q};t\right)$ calculated using Brownian dynamics computer simulations of a model glass forming system. These correlation functions measure the spatial correlations of the relaxation of different particles. We examine the time and temperature dependences of the anisotropy in both functions. We find that the anisotropy is strongest at nearest-neighbor distances at time scales corresponding to the peak of the non-Gaussian parameter ${\alpha }_2\left(t\right)=3⟨\delta r^4\left(t\right)⟩/\left[5{⟨\delta r^2\left(t\right)⟩}^2\right]-1$ but is still pronounced around the $\alpha$ relaxation time. We find that the structure factor $S_4\left(\vec{k},\vec{q};t\right)$ is anisotropic even for the lowest wave vector accessible in our simulation, suggesting that our system (and other systems commonly used in computer simulations) may be too small to extract the $\vec{q}\to 0$ limit of the structure factor. We find that the determination of a dynamic correlation length from $S_4\left(\vec{k},\vec{q};t\right)$ is influenced by the anisotropy. We extract an effective anisotropic dynamic correlation length from the small $q$ behavior of $S_4\left(\vec{k},\vec{q};t\right)$.