We study the applicability of the parallel tempering (PT) method in the investigation of first-order phase transitions. In this method, replicas of the same system are simulated simultaneously at different temperatures, and the configurations of two randomly chosen replicas can occasionally be interchanged. We apply the PT method for the Blume-Emery-Griffiths model, which displays strong first-order transitions at low temperatures. A precise estimate of coexistence lines is obtained, revealing that the PT method may be a successful tool for the characterization of discontinuous transitions.

The origin of anomalous or non-Fickian transport in disordered media is the broad spectrum of transition rates intrinsic to these systems. A system that contains within it heterogeneities over multiple length scales is geological formations. The continuous time random walk (CTRW) framework, which has been demonstrated to be an effective means to model non-Fickian transport features in these systems and to have predictive capacities, has at its core this full spectrum represented as a joint probability density $\psi (\mathbf{s},t)$ of random space time displacements $(\mathbf{s},t)$. Transport in a random fracture network (RFN) has been calculated with a coupled $\psi (\mathbf{s},t)$ and has subsequently been shown to be approximated well by a decoupled form $\psi (\mathbf{s},t)=F\left(\mathbf{s}\right)\psi \left(t\right)$. The latter form has been used extensively to model non-Fickian transport in conjunction with a velocity distribution $\Phi \left(\xi \right),\xi \equiv 1∕v$, where $v$ is the velocity magnitude. The power-law behavior of $\psi \left(t\right)\propto t^{-1-\beta }$, which determines non-Fickian transport, derives from the large $\xi$ dependence of $\Phi \left(\xi \right)$. In this study we use numerical CTRW simulations to explore the expanded transport phenomena derived from a coupled $\psi (\mathbf{s},t)$. Specifically, we introduce the features of a power-law dependence in the $\mathbf{s}$ distribution with different $\Phi \left(\xi \right)$ distributions (including a constant $v$) coupled by $t=s\xi$. Unlike Lévy flights in this coupled scenario the spatial moments of the plumes are well defined. The shapes of the plumes depend on the entire $\Phi \left(\xi \right)$ distribution, i.e., both small and large $\xi$ dependence; there is a competition between long displacements (which depend on the small $\xi$ dependence) and large time events (which depend on a power law for large $\xi$). These features give rise to an enhanced range of transport behavior with a broader scope of applications, e.g., to correlated migrations in a RFN and in heterogeneous permeability fields. The approximation to the decoupled case is investigated as a function of the nature of the $\mathbf{s}$ distribution.

Mechanical rejuvenation and overaging of glasses is investigated through stochastic simulations of the soft glassy rheology (SGR) model. Strain- and stress-controlled deformation cycles for a wide range of loading conditions are analyzed and compared to molecular dynamics simulations of a model polymer glass. Results indicate that deformation causes predominantly rejuvenation, whereas overaging occurs only at very low temperatures, small strains, and for high initial energy states. Although the creep compliance in the SGR model exhibits full aging independent of applied load, large stresses in the nonlinear creep regime cause configurational changes leading to rejuvenation of the relaxation time spectrum probed after a stress cycle. During recovery, however, the rejuvenated state rapidly returns to the original aging trajectory due to collective relaxations of the internal strain.

Various experimental settings that involve drying solutions or suspensions of nanoparticles—often called nanofluids—have recently been used to produce structured nanoparticle layers. In addition to the formation of polygonal networks and spinodal-like patterns, the occurrence of branched structures has been reported. After reviewing the experimental results we use a modified version of the Monte Carlo model first introduced by Rabani et al. [Nature 426, 271 (2003)] to study structure formation in evaporating films of nanoparticle solutions for the case that all structuring is driven by the interplay of evaporating solvent and diffusing nanoparticles. After introducing the model and its general behavior we focus on receding dewetting fronts which are initially straight but develop a transverse fingering instability. We analyze the dependence of the characteristics of the resulting branching patterns on the driving effective chemical potential, the mobility and concentration of the nanoparticles, and the interaction strength between liquid and nanoparticles. This allows us to understand the underlying instability mechanism.

We consider a relaxed semisoft elastomer with its director oriented along the $z$ axis that is first subjected to a large stretch in the $x$ direction then to a slight $x\text{−}z$ shear. We give a general argument that in any theory including director rotation, at the onset and end of the director rotation induced by these large stretches, there will be kinks in the stress-large strain curve (forming a stress-strain plateau) and zeros in the $x\text{−}z$ shear modulus $\left(C_5\right)$ associated with small shears imposed on top of the stretches. We then find the analytical forms of the $C_5$-strain curves for a particular model of semisoftness (arising from compositional fluctuations) and show that it, together with the known stress-strain curve, provides the basis for a strong test of this theory. Finally, we consider the scope for other semisoft models and show that the compositional fluctuations model in fact yielded a generic form, that is, it is the most general quadratic free energy that does not explicitly include a final state direction other than the director. By introducing such additional directions, a large range of alternative models could be developed.

Feedback connections and noise are ubiquitous features of neuronal networks and affect in a determinant way the patterns of neural activity. Here we study how the subthreshold dynamics of a neuron interacts with time-delayed feedback and noise. We use a Hodgkin-Huxley-type model of a thermoreceptor neuron and assume the feedback to be linear, corresponding effectively to a recurrent electrical connection via gap junctions. This type of feedback can model electrical autapses, which connect the terminal fibers of a neuron’s axon with dendrites from the same neuron. Thus the delay in the feedback loop is due basically to the axonal propagation time. We chose model parameters for which the neuron displays, in the absence of feedback and noise, only subthreshold oscillations. These oscillations, however, take the neuron close to the firing threshold, such that small perturbations can drive it above the level for generation of action potentials. The resulting interplay between weak delayed feedback, noise, and the subthreshold intrinsic activity is nontrivial. For negative feedback, depending on the delay, the firing rate can be lower than in the noise-free situation. This is due to the fact that noise inhibits feedback-induced spikes by driving the neuronal oscillations away from the firing threshold. For positive feedback, there are regions of delay values where the noise-induced spikes are inhibited by the feedback; in this case, it is the feedback that drives the neuronal oscillations away from the threshold. Our study contributes to a better understanding of the role of electrical self-connections in the presence of noise and subthreshold activity.

We introduce an alternative way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the $1∕N$ accuracy, where $N$ is the genome length. For a smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics and discontinuous dynamics. The latter phase arises naturally with no explicite singular fitness function, counterintuitively. The Hamilton-Jacobi method yields straightforward analytical results for the models that utilize fitness as a function of Hamming distance from a reference genome sequence. We also show the way in which this method gives dynamical phase structure for multipeak fitness.

We discuss effects of the stepping kinetics of molecular motors on their traffic behavior on crowded filaments using a simple two-state chemomechanical cycle. While the general traffic behavior is quite robust with respect to the detailed kinetics of the step, a few observable parameters exhibit a strong dependence on these parameters. Most strikingly, the effective unbinding rate of the motors may both increase and decrease with increasing traffic density, depending on the details of the motor step. Likewise the run length either exhibits a strong decrease or almost no dependence on the traffic density. We compare our theoretical results with recent experimental observations on motor traffic.

Using the phase-field method, effects of the surface-tension anisotropy on sidebranching are investigated during solutal dendritic growth. The results show that without external perturbations the surface tension anisotropy has decisive effects on sidebranching and the nonmonotonic behavior of the solute profile along the interface characterizes the evolution of sidebranches. The scaled dendritic profiles indicate that the dendrites have the self-affine primary trunks but with different sidebranches for different anisotropy at the same evolution time. The dynamic evolution process of dendritic growth with low surface tension anisotropy reveals the same generating place of sidebranch in the scaled dendritic profile during the dendritic growth.

We propose an experimental setup based on diffusive wave spectroscopy for studying deformations of a solid material. The scattered waves are measured during the deformation of the solid material at different locations of its surface. The correlations of the scattered intensities are measured. The loss of correlation can be related to the invariants of the strain tensor of the solid, giving us a spatially resolved determination of the deformation near the surface. Experiments dealing with a point stress on plate for two kinds of elastic materials are presented and compared with the theoretical predictions.

A lattice Boltzmann model for incompressible axisymmetric flow is proposed in this paper. Unlike previous axisymmetric lattice Boltzmann models, which were based on “primitive-variables” Navier-Stokes equations, the target macroscopic equations of the present model are vorticity-stream-function formulations. Due to the intrinsic features of vorticity-stream-function formulations, the present model is more efficient, more stable, and much simpler than the existing models. The advantages of the present model are validated by numerical experiments.

We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.

Langmuir monolayers of chiral liquid crystals on the surface of water exhibit orientational waves with complex spatiotemporal patterns. These patterns arise from a collective precession of the mesogenic molecules, driven by the evaporation of water through the monolayer. We investigate the behavior of these orientational waves around topological defects in the molecular orientation. Through Brewster angle microscopy, we find that the waves form a reversing spiral pattern, which rotates about the central vortex. With increasing relative humidity, the rotation slows and then stops. We model the system theoretically, and show that predicted patterns are in good agreement with the experiments.

Conformational fluctuations of a molecule are important to its function since such intrinsic fluctuations enable the molecule to respond to the external environmental perturbations. For extracting large conformational fluctuations, which predict the primary conformational change by the perturbation, principal component analysis (PCA) has been used in molecular dynamics simulations. However, several versions of PCA, such as Cartesian coordinate PCA and dihedral angle PCA (dPCA), are limited to use with molecules with a single dominant state or proteins where the dihedral angle represents an important internal coordinate. Other PCAs with general applicability, such as the PCA using pairwise atomic distances, do not represent the physical meaning clearly. Therefore, a formulation that provides general applicability and clearly represents the physical meaning is yet to be developed. For developing such a formulation, we consider the conformational distribution change by the perturbation with arbitrary linearly independent perturbation functions. Within the second order approximation of the Kullback-Leibler divergence by the perturbation, the PCA can be naturally interpreted as a method for (1) decomposing a given perturbation into perturbations that independently contribute to the conformational distribution change or (2) successively finding the perturbation that induces the largest conformational distribution change. In this perturbational formulation of PCA, (i) the eigenvalue measures the Kullback-Leibler divergence from the unperturbed to perturbed distributions, (ii) the eigenvector identifies the combination of the perturbation functions, and (iii) the principal component determines the probability change induced by the perturbation. Based on this formulation, we propose a PCA using potential energy terms, and we designate it as potential energy PCA (PEPCA). The PEPCA provides both general applicability and clear physical meaning. For demonstrating its power, we apply the PEPCA to an alanine dipeptide molecule in vacuum as a minimal model of a nonsingle dominant conformational biomolecule. The first and second principal components clearly characterize two stable states and the transition state between them. Positive and negative components with larger absolute values of the first and second eigenvectors identify the electrostatic interactions, which stabilize or destabilize each stable state and the transition state. Our result therefore indicates that PCA can be applied, by carefully selecting the perturbation functions, not only to identify the molecular conformational fluctuation but also to predict the conformational distribution change by the perturbation beyond the limitation of the previous methods.

We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian mean field model as a simple example. These systems generically undergo a violent relaxation to a quasistationary state (QSS) before relaxing towards Boltzmann equilibrium. In the collisional regime, the out-of-equilibrium one-particle distribution function (DF) is a quasistationary solution of the Vlasov equation, slowly evolving in time due to finite-$N$ effects. For subcritical energy densities, we exhibit cases where the DF is well fitted by a Tsallis $q$ distribution with an index $q\left(t\right)$ slowly decreasing in time from $q\simeq 3$ (semiellipse) to $q=1$ (Boltzmann). When the index $q\left(t\right)$ reaches an energy-dependent critical value $q_{\mathit{crit}}$, the nonmagnetized (homogeneous) phase becomes Vlasov unstable and a dynamical phase transition is triggered, leading to a magnetized (inhomogeneous) state. While Tsallis distributions play an important role in our study, we explain this dynamical phase transition by using only conventional statistical mechanics. For supercritical energy densities, we report the existence of a magnetized QSS with a very long lifetime.

We analyze the molecular dynamics heterogeneity of the liquid crystal 4-$n$-octyl-$4^{\prime }$-cyanobiphenyl nanoconfined in porous silicon. We show that the temperature dependence of the dynamic correlation length ${\xi }_{\mathit{\text{wall}}}$, which measures the distance over which a memory of the interfacial slowing down of the molecular dynamics persists, is closely related to the growth of the short-range static order arising from quenched random fields. More generally, this result may also shed some light on the connection between static and dynamic heterogeneities in a wide class of condensed and soft matter systems.

The Monte Carlo wave function method or the quantum-trajectory–jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. We extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method is also discussed.

We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided that some constraints on the microscopic reaction rates of this system are fulfilled. Under these constraints the steady state of the system can be written as a linear superposition of such shock measures. We show that the coefficients of this expansion can be calculated using the finite-dimensional representation of the quadratic algebra of the system obtained from a matrix-product approach.

This Brief Report corrects and extends the results of Zhuang and Ogata [Phys. Rev. E 73, 046134 (2006)] on the asymptotic behavior of the largest event in the epidemic-type aftershock-sequence model for earthquake occurrence. We show that, in the special case that the underlying branching process is critical, there exists a previously unnoticed mode of behavior, which occurs when the expected family size grows relatively slowly.

Both the energy differences between metastable and stable phases and the energy barriers separating these phases decrease with decreasing particle number. Then, for small enough systems, random heterophasic fluctuations of the entire system become an observable form of thermal motion. We discuss mechanisms and observation conditions for these random transitions between phases.