We present a simple, transferable, efficient, and effective algorithmic enhancement designed to improve the accuracy of all multicomponent lattice Boltzmann methods when applied to the simulation in the continuum approximation of fluid mechanics. By applying a collision parameter (kinematic viscosity) perturbation to reduce velocity gradients in the interfacial region, a kinematic condition is effectively enforced. Matters relating to a variation in the collision parameter are briefly discussed.

The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter $Q$ is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic “bias” field, $H_b$, for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, ${\delta }_{\mathrm{d}}$, of $H_b$ at the critical period of the DPT is equal to the exponent for the critical isotherm, ${\delta }_{\mathrm{e}}$, in the equilibrium Ising model. This implies that $H_b$ is a significant component of the field conjugate to $Q$. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of $H_b$ in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature $T_{\mathrm{eff}}(T,P,H_0)$ depending on the period, and possibly the temperature and field amplitude, holds for the variables $Q$ and $H_b$. This FDR justifies the use of the scaled variance of $Q$ as a proxy for the nonequilibrium susceptibility, $\partial ⟨Q⟩∕\partial H_b$, in the critical region.

We propose generalization of the escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate-to-large damping limit and investigate the effect of degree of correlation on the resulting rate. Comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength.

We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In particular, we define two overlap order parameters, which quantify the correlation between particle configurations at different times, based on a Voronoi construction and the persistence in the resulting cells and nearest neighbors. Temporal fluctuations in the decay of the persistent area and bond order parameters define two alternative dynamic four-point susceptibilities ${\chi }_A\left(\tau \right)$ and ${\chi }_B\left(\tau \right)$, well suited for characterizing spatially heterogeneous dynamics. These are analogous to the standard four-point dynamic susceptibility ${\chi }_4(l,\tau )$, but where the space dependence is fixed uniquely by topology rather than by discretionary choice of cutoff function. While these three susceptibilities yield characteristic time scales that are somewhat different, they give domain sizes for the dynamical heterogeneities that are in good agreement and that diverge on approach to jamming.

Pectin is an important structural polysaccharide found in the cell walls of all land plants. While in detail its composition and its organization in muro are complex, it is predominantly a copolymer of galacturonic acid and its methylesterified counterpart. Previous single-molecule stretching studies carried out on a sparsely methylesterified pectin sample indicated the importance of force-induced conformational transitions of the pyranose ring during extension, and the possible biological role of such transitions was discussed. More heavily methylesterified samples are better biomimetic models of the polymeric components as found in the plant cell wall, in particular being less restricted by the shackles of the significant intermolecular interactions expected to constrain the behavior of bare galacturonic acid sequences. Density functional theory calculations revealed that upon extending galacturonic acid monomers, whether methylesterified or not, the initial $\left({}^{4}C_1\right)$ chair structure is transformed to a $\left({}^{3}S_5\right)$ skew boat and that subsequently upon further elongation, via an intermediate inverted skew boat $\left({}^{5}S_3\right)$, the inverted chair $\left({}^{1}C_4\right)$ is reached. Experimentally, the force-extension curve of highly methylesterified pectin was found to be solvent dependent in the same manner as the un-esterified sample, indicating that minimal changes in the strength of interring hydrogen bonding result from such a substitution, and finally, as only subtle changes in the force-extension behavior of pectin resulted from changes in the degree of methylesterification, previous speculations about the role of force-induced transformations in vivo are supported.

The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the leading unstable directions by translating the problem to the language of scale-invariant growing surfaces. We find that the so-called characteristic LVs exhibit spatial localization, strong clustering around given spatiotemporal loci, and remarkable dynamic scaling properties of the corresponding surfaces. In contrast, the commonly used backward LVs (obtained through Gram-Schmidt orthogonalization) spread all over the system and do not exhibit dynamic scaling due to artifacts in the dynamical correlations by construction.

We demonstrate experimental generation of two-dimensional (2D) chaotic vector fields from a surface-emitting microcavity laser with precisely control of the operating temperature and the operating current. The 2D optical vector field is found to be formed by frequency locking of two linearly polarized laser modes with different chaotic spatial structures. The eigenfunction expansion method is used to reconstruct the experimental wave function for analyzing the properties of the vector singularities. It is shown that the distribution of vector singularities obeys the sign rule of nearest-neighbor singularities in the phase space of the vector field.

The ninth-order weighted essentially nonoscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air (acetone)/$\mathrm{S}{\mathrm{F}}_6$ shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of linear and nonlinear amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock by Latini, Schilling, and Don [Phys. Fluids 19, 024104 (2007)]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe the reshock process. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney-Zabusky model and with linear instability theory. The time evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the magnitudes of the circulations are equal before as well as after reshock, until the interaction of the reflected rarefaction with the layer induces flow symmetry breaking and different evolutions of the magnitude of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in generally good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating enstrophy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops nontrivial spectral content from its inception. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra may be consistent with many of these scalings over wave number ranges less than a decade. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles, and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction exhibits an approach toward unity across the layer at the latest time, signifying nearly complete mixing of the gases. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is demonstrated that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.

We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent $\nu$. Our results are compared to previous results for this system using a wide variety of other approaches.

The relaxation dynamics of a model fluid of platelike colloidal particles is investigated by means of a phenomenological dynamic density functional theory. The model fluid approximates the particles within the Zwanzig model of restricted orientations. The driving force for time dependence is expressed completely by gradients of the local chemical potential, which in turn is derived from a density functional—hydrodynamic interactions are not taken into account. These approximations are expected to lead to qualitatively reliable results for low densities like those within the isotropic-nematic two-phase region. The formalism is applied to model an initially spatially homogeneous stable or metastable isotropic fluid which is perturbed by switching a two-dimensional array of Gaussian laser beams. Switching on the laser beams leads to an accumulation of colloidal particles in the beam centers. If the initial chemical potential and the laser power are large enough, a preferred orientation of particles occurs, breaking the symmetry of the laser potential. After switching off the laser beams again, the system can follow different relaxation paths: It either relaxes back to the homogeneous isotropic state or it forms an approximately elliptical high-density core which is elongated perpendicular to the dominating orientation in order to minimize the surface free energy. For large supersaturations of the initial isotropic fluid, the high-density cores of neighboring laser beams of the two-dimensional array merge into complex superstructures.

When an electric field is applied to microspheres which are dispersed in a ferroelectric smectic liquid crystal, particle translation along the smectic layer plane, i.e., in a direction nearly perpendicular to that of the director, can be observed. Under certain electric field conditions the translation is shown to be linear in time. We have determined the stability regime of linear particle displacement in the parameter space of amplitude and frequency for various applied wave forms. This regime enlarges for increasing electric field amplitude and frequency, with a threshold behavior observed for small parameters. The upper stability boundary is related to the reciprocal ferroelectric switching time. The microspheres translational velocity is independent of the applied electric field amplitude, but increases linearly with applied frequency. The microsphere velocity also increases with increasing temperature, which is indicative of the respective decrease in liquid crystal viscosity. Possible mechanisms of electric-field-induced particle motion are discussed.

When a flexible polymer is sucked into a localized small hole, the chain can initially respond only locally and the sequential nonequilibrium processes follow in line with the propagation of the tensile force along the chain backbone. We analyze this dynamical process by taking the nonuniform stretching of the polymer into account both with and without hydrodynamics interactions. Earlier conjectures on the absorption time are criticized and formulas are proposed together with time evolutions of relevant dynamical variables.

In micromechanical studies of DNA, plectonemically supercoiled domains are often used as sources of constant torque. These torques are not easily measured and are instead usually estimated. Here, coexisting extended and supercoiled DNA domains are analyzed, and closed-form expressions for the dependence of extension and torque on force and linking number are presented. When there are coexisting domains of plectonemic and extended DNA, the torque depends only on force, with no dependence on linking number. However, torque depends on force in a manner more complex than a simple power law, involving the free energy of the extended and plectonemic DNA. A simple strategy is described for measurement of the free energies of both extended and plectonemic DNA without reference to specific microscopic polymer models. Applications of the theory to analysis of relaxation of supercoiling by enzymes which permit friction-controlled rotational relaxation of linking number is also presented. Such enzymes must display a breaking of symmetry between relaxations driven by equal magnitude but opposite direction torques.

Is it possible to solve Boltzmann-type kinetic equations using only a small number of particle velocities? We introduce a technique of solving kinetic equations with a (arbitrarily) large number of particle velocities using only a lattice Boltzmann method on standard, low-symmetry lattices. The renormalized kinetic equation is validated with an exact solution of the planar Couette flow at moderate Knudsen numbers.

We introduce an exponential random graph model for networks with a fixed degree distribution and a tunable degree-degree correlation. We then investigate the nature of the percolation transition in a correlated network with a Poisson degree distribution. It is found that negative correlation is irrelevant in that the percolation transition in the disassortative network belongs to the same universality class as in the uncorrelated network. Positive correlation turns out to be relevant. The percolation transition in the assortative network is characterized by the nondiverging mean size of finite clusters and power-law scalings of the density of the largest cluster and the cluster size distribution in the nonpercolating phase as well as at the critical point. Our results suggest that the unusual type of percolation transition in the growing network models reported recently may be inherited from the assortative degree-degree correlation.

We have numerically investigated statistical properties of the so-called interoccurrence time or the waiting time, i.e., the time interval between successive earthquakes, based on the two-dimensional (2D) spring-block (Burridge-Knopoff) model, selecting the velocity-weakening property as the constitutive friction law. The statistical properties of frequency distribution and the cumulative distribution of the interoccurrence time are discussed by tuning the dynamical parameters, namely, a stiffness and frictional property of a fault. We optimize these model parameters to reproduce the interoccurrence time statistics in nature; the frequency and cumulative distribution can be described by the power law and Zipf-Mandelbrot type power law, respectively. In an optimal case, the $b$ value of the Gutenberg-Richter law and the ratio of wave propagation velocity are in agreement with those derived from real earthquakes. As the threshold of magnitude is increased, the interoccurrence time distribution tends to follow an exponential distribution. Hence it is suggested that a temporal sequence of earthquakes, aside from small-magnitude events, is a Poisson process, which is observed in nature. We found that the interoccurrence time statistics derived from the 2D BK (original) model can efficiently reproduce that of real earthquakes, so that the model can be recognized as a realistic one in view of interoccurrence time statistics.

The dependences of the macroscopic detonation properties of a two-dimensional (2D) diatomic (AB) molecular system on the fundamental molecular properties were investigated. This includes examining the detonation velocity, reaction zone thickness, and critical width as functions of the exothermicity $\left(Q\right)$ of the gas-phase reaction $[\mathrm{AB}\to (1∕2)({\mathrm{A}}_2+{\mathrm{B}}_2)]$ and the gas-phase dissociation energy $\left(D_e^{\mathrm{AB}}\right)$ for $\mathrm{AB}\to \mathrm{A}+\mathrm{B}$. Following previous work, molecular dynamics (MD) simulations with a reactive empirical bond-order potential were used to characterize the shock-induced response of a diatomic AB molecular solid, which exothermically reacts to produce ${\mathrm{A}}_2$ and ${\mathrm{B}}_2$ gaseous products. Nonequilibrium MD simulations reveal that there is a linear dependence between the square of the detonation velocity and both of these molecular parameters. The detonation velocities were shown to be consistent with the Chapman–Jouguet (CJ) model, demonstrating that these dependences arise from how the equation of state of the products and reactants are affected. Equilibrium MD simulations of microcanonical ensembles were used to determine the CJ states for varying $Q$’s, and radial distribution functions characterize the atomic structure. The character of this material near the CJ conditions was found to be somewhat unusual, consisting of polyatomic clusters rather than discrete molecular species. It was also found that there was a minimum value of $Q$ and a maximum value of $D_e^{\mathrm{AB}}$ for which a pseudo-one-dimensional detonation could not be sustained. The reaction zone of this material was characterized under both equilibrium (CJ) and transient (underdriven) conditions. The basic structure is consistent with the Zeldovich–von Neumann-Döring model, with a sharp shock rise and a reaction zone that extends to $200–300\mathrm{\AA }$. The underdriven systems show a buildup process which requires an extensive time to approach equilibrium conditions. The rate stick failure diameter (critical width in 2D) was also found to depend on $Q$ and $D_e^{\mathrm{AB}}$. The dependence on $Q$ could be explained in terms of the reaction zone properties.

We demonstrate analytically and experimentally the existence and behavior of two types of modes in finite size one-dimensional coaxial photonic crystals made of $N$ cells with vanishing magnetic field on both sides. We highlight the existence of $N-1$ confined modes in each band and one mode by gap associated to either one or the other of the two surfaces surrounding the structure. The latter modes are independent of $N$. These results generalize our previous findings on the existence of surface modes in two semi-infinite superlattices obtained from the cleavage of an infinite superlattice between two cells. The analytical results are obtained by means of the Green’s function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime.

We present a method for performing sampling from a Boltzmann distribution of an ill-conditioned quadratic action. This method is based on heat-bath thermalization along a set of conjugate directions, generated via a conjugate-gradient procedure. The resulting scheme outperforms local updates for matrices with very high condition number, since it avoids the slowing down of modes with lower eigenvalue, and has some advantages over the global heat-bath approach, compared to which it is more stable and allows for more freedom in devising case-specific optimizations.

We propose an observer-based approach for chaos synchronization and parameter estimation from a scalar output signal. To begin with, we use geometric control to transform the master system into a standard form with zero dynamics. Then we construct a slaver to synchronize with the master using a combination of slide mode control and linear feedback control. Within a finite time, partial synchronization is realized, which further results in complete synchronization as time tends to infinity. Even if there exists model uncertainty in the slaver, we can also estimate the unknown model parameter by a simple adaptive rule.