Recently developed nonequilibrium statistical physics relationships, including Jarzynski’s equality and the Crooks fluctuation theorem, have been used to calculate equilibrium thermodynamic properties using data from both laboratory and computational experiments. Although Jarzynski’s derivation does not include an explicit time dependency, prior work utilizing the relationship to reconstruct free-energy surfaces has combined data from experiments performed under identical conditions. Here, a formalism is developed for combining data from a variety of biasing protocols, as in dynamic force spectroscopy experiments. The method is then demonstrated on data from simulations conducted under a wide range of pulling velocities and with a random biasing protocol.

This paper reports a theoretical study of the electrostatic potential within a so-called pen-heterojunction made up of two semi-infinite, doped semiconductor media separated by an electrolyte region. An external potential is then applied across the entire system. Both the electrostatic potentials and double layer surface forces are studied as functions of the usual double layer system properties, semiconductor properties such as doping concentrations of acceptor and donator atoms, as well as applied potential. We find that both attractive and repulsive forces are possible depending on the surface charges on the electrolyte-semiconductor interfaces, and that these forces can be significantly modified by the applied potential and by the doping levels in the semiconductors.

A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng [Phys. Rev. E 58, 7475 (1998)] equations for the evolution of the velocity and tensor order-parameter fields. The resulting algorithm is able to include five independent Leslie viscosities, a Landau-deGennes free energy which introduces three or more elastic constants, a temperature dependent order parameter, surface anchoring and viscosity coefficients, flexoelectric and order electricity, and chirality. When combined with a solver for the Maxwell equations associated with the electric field, the algorithm is able to provide a full “device solver” for a liquid crystal display. Coupled lattice Boltzmann schemes are used to capture the evolution of the fast momentum and slow director motions in a computationally efficient way. The method is shown to give results in close agreement with analytical results for a number of validating examples. The use of the method is illustrated through the simulation of the motion of defects in a zenithal bistable liquid crystal device.

With experimental investigations and current theories, molecular modeling became an inevitable technique to study the perplexing phenomenon of glass transition. Among polymers, small variations in atomic interactions yield different values of the glass transition temperature, $T_g$. To reveal the influence of differences in the atomic functionality on the value of $T_g$, and thus to probe the molecular mechanisms responsible for this transition, atomistic simulations have to be undertaken. However, such simulations are argued not to accurately represent physically the glass transition due to the long relaxation times involved. Here we show the universality of the well-known Williams-Landel-Ferry equation for the experimental thermal dependence of polymer viscosities as demonstrated with atomistic simulations. Consequently, atomic aspects could be explicitly revealed. The contribution of atomistic simulation to the study of glass transition is thus confirmed. However, it has to be used complementarily with experiments and coarse-grained simulation to reveal the atomic aspects of current theories.

We derive general kinetic equations for reacting and subdiffusing entities based on a nonlinear continuous time random walk formalism proposed by Vlad and Ross [Phys. Rev. E 66, 061908 (2002)]. Reaction and diffusion processes are separable in a typical reaction-diffusion system, and their combined influence on the evolution of the density of a species is a simple sum. Our derivation shows that this is no longer true for subdiffusive entities undergoing reactions. The strong memory effects in the transport process, i.e., the non-Markovian nature of subdiffusion, results in a nontrivial combination of reactions and spatial dispersal, which we discuss in detail. We carry out a linear stability analysis of the derived reaction-subdiffusion system to understand the effects of memory on pattern formation. We find that the Turing instability persists in the subdiffusive system. However, the memory modifies the Turing threshold and the characteristics of the band of unstable modes close to this threshold.

We calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor of a ballistic chaotic cavity using periodic orbit theory. For the case of broken time-reversal symmetry, when the quantum correction to the form factor involves two small-angle encounters of classical trajectories, our result differs from that previously obtained using field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. While we believe that the existing field-theoretic calculation is technically flawed, the question whether the field theoretic and periodic-orbit approaches agree when more than one small-angle encounter of classical orbits is involved remains unanswered.

A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota’s method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.

Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous papers. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety of practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc.

Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field (SCF) iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problems. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before.

We explore the role of an intermediate state (phase) in homogeneous nucleation by examining the decay process through a double-humped potential barrier. We analyze the one-dimensional Fokker-Planck (FP) equations with the fourth- and sixth-order Landau potentials. In the low-temperature case, we apply the WKB method to the FP equation and obtain an analytic expression for the decay rate which is accurate for a wide range of depth and curvature of the middle well. In the case of a deep middle well, it reduces to an extended Kramers formula, in which the barrier height in the original formula is replaced by the arithmetic mean height of the higher (outer) and lower (inner) barriers, and the curvature of the initial well in the original one is replaced by the geometric mean curvature of the initial and intermediate wells. In the case of a shallow middle well, the Kramers escape rate is evaluated also within the standard framework of the mean-first-passage-time problem, whose result is consistent with our WKB analysis. Criteria for enhancement of the decay rate are revealed.

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena et al., Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter $\lambda$ and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime.

We describe the behavior of a rod bouncing upon a horizontal surface which is undergoing sinusoidal vertical vibration. The predictions of computer simulations are compared with experiments in which a stainless-steel rod bounces upon a metal-coated glass surface. We find that, as the dimensionless acceleration parameter $\Gamma$ is increased appreciably above unity, the motion of a long rod passes from periodic or near-periodic motion into stochastic dynamics. Within this stochastic regime the statistics of the times between impacts follow distributions with tails of approximately Gaussian form while the probability distributions of the angles at impact have tails that are close to exponential. We determine the dependence of each distribution upon the length of the rod, upon frequency, and on $\Gamma$. The statistics of the total energy and of the translational and rotational components each approximately follow a Boltzmann distribution in their tails, the translational and rotational energy components being strongly correlated. The time-averaged mean vertical translational energy is significantly larger than the mean rotational energy, and both are considerably larger than the energy associated with horizontal motion.

Granular materials are predominantly plastic, incrementally nonlinear, preparation-dependent, and anisotropic under shear. Nevertheless, their static stress distribution is well accounted for, in the whole range up to the point of failure, by a judiciously tailored isotropic nonanalytic elasticity theory termed granular elasticity. The first purpose of this paper is to carefully expound this view. Then granular elasticity is employed to consider the stress distribution in two-dimensional sand piles (or sand wedges). Starting from a uniform density, the pressure at the bottom of the pile is found to show a single central peak. It turns into a pressure dip, if some density inhomogeneity, with the center being less compact, is assumed. These two pressure distributions are remarkably similar to recent measurements, made in piles obtained, respectively, by rainlike pouring and funneling. In an accompanying paper, the stress distributions in silos and under point loads, calculated using the same method, are also found to agree with experiments.

An elastic-strain–stress relation, the result of granular elasticity as introduced in the preceding paper, is employed here to calculate the stress distribution (a) in cylindrical silos and (b) under point loads assuming uniform density. In silos, the ratio $k_J$ between the horizontal and vertical stress is found to be constant (as conjectured by Janssen) and given as $k_J=1-\sin \phi$ (with $\phi$ the Coulomb yield angle), in agreement with a construction industry standard usually referred to as the Jaky formula. Next, the stress distribution at the bottom of a granular layer exposed to a point force at its top is calculated. The results include both vertical and oblique point forces, which agree well with simulations and experiments using rainlike preparation. Moreover, the stress distribution of a sheared granular layer exposed to the same point force is calculated and again found in agreement with given data.

We developed an efficient computation scheme for the phase-field simulation of grain growth, which allows unlimited number of the orientation variables and high computational efficiency independent of them. Large-scale phase-field simulations of the ideal grain growth in two-dimensions (2D) and three-dimensions (3D) were carried out with holding the coalescence-free condition, where a few tens of thousands grains evolved into a few thousand grains. By checking the validity of the von Neumann-Mullins law for individual grains, it could be shown that the present simulations were correctly carried out under the conditions of the ideal grain growth. The steady-state grain size distribution in 2D appeared as a symmetrical shape with a plateau slightly inclined to the small grain side, which was quite different from the Hillert 2D distribution. The existence of the plateau stems from the wide separation of the peaks in the size distributions of the grains with five, six, and seven sides. The steady-state grain size distribution in 3D simulation of the ideal grain growth appeared to be very close to the Hillert 3D distribution, independent of the initial average grain size and size distribution. The mean-field assumption, the Lifshitz-Slyozov stability condition, and all resulting predictions in the Hillert 3D theory were in excellent agreement with the present 3D simulation. Thus the Hillert theory can be regarded as an accurate description for the 3D ideal grain growth. The dependence of the growth rate in 3D simulations on the grain topology were discussed. The large-scale phase-field simulation confirms the 3D growth law obtained from the Surface Evolver simulations in smaller scales.

We present an investigation of the phase diagram of cholesteric liquid crystals within the framework of Landau–de Gennes theory. The free energy is modified to incorporate all three Frank elastic constants and to allow for a temperature dependent pitch in the cholesteric phase. It is found that the region of stability of the cubic blue phases depends significantly on the value of the elastic constants, being reduced when the bend elastic constant is larger than splay and when twist is smaller than the other two. Most dramatically we find a large increase in the region of stability of blue phase I, and a qualitative change in the phase diagram, in a system where the cholesteric phase displays helix inversion.

We have studied the effect of an anisotropic polymer network on the coupling of molecular tilt to applied electric field in the chiral $S_A$ phase. The polymer network is formed from a photoreactive achiral monomer in a thin planar $S_C^{*}$ cell. Experimental data, obtained from electro-optical measurements near to the $S_A-S_c^{*}$ transition temperature, $T_c$, of the induced molecular tilt, switching time, as well as induced polarization as a function of temperature and electric field strength are presented. The results clearly show that, close to $T_c$, the electroclinic effect is largely controlled by the polymer network. The experimental results are discussed in the framework of a simple phenomenological model, extended from the Landau model, which includes the bulk free energy arising from the anisotropic interaction between the polymer network and the liquid crystal director, and the elastic free energy resulting from the anchoring (supposed rigid) of the liquid crystal molecules at the polymer boundaries.

A long-time fluctuation correlation function with a power-law form has been observed in recent single-molecule experiments by the Xie group. By analyzing the dynamics of an elastic network model (ENM) under white noise, we show that the observed long-time memory kernel can be explained by the discrepancy between the experimentally measured coordinate (or the coordinate directly coupled to protein function) and the minimum energy path of the system. Consequently, the dynamics of the measured collective coordinate has contributions from degrees of freedoms with a broad distribution of time scales. Our study also implies that the widely used ENM Hamiltonian should be viewed as a coarse-grained model of a protein over a rugged energy landscape. Large effective drag coefficients are needed to describe protein dynamics with the ENM’s.

We present experimental and numerical evidence of synchronization of burst events in two different modulated ${\mathrm{CO}}_2$ lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.

Exploring conformational spaces is still a challenging task for simulations of complex systems. One way to enhance such a task is weighted sampling, e.g., by assigning high weights to regions that are rarely sampled. It is, however, difficult to estimate adequate weights beforehand, and therefore adaptive methods are desired. Here we present a method for adaptive weighted sampling based on Bayesian inference. Within the framework of Bayesian inference, we develop an update scheme in which the information from previous data is stored in a prior distribution which is then updated to a posterior distribution according to new data. The method proposed here is particularly well suited for distributed computing, in which one must deal with rapid influxes of large amounts of data.