Generalized Bose-Einstein and Fermi-Dirac distributions in nonextensive quantum statistics have been discussed by the maximum-entropy method (MEM) with the optimum Lagrange multiplier based on the exact integral representation [A. K. Rajagopal, R. S. Mendes, and E. K. Lenzi, Phys. Rev. Lett. 80, 3907 (1998)]. It has been shown that the $\left(q-1\right)$ expansion in the exact approach agrees with the result obtained by the asymptotic approach valid for $O\left(q-1\right)$. Model calculations have been made with a uniform density of states for electrons and with the Debye model for phonons. Based on the result of the exact approach, we have proposed the interpolation approximation to the generalized distributions, which yields results in agreement with the exact approach within $O\left(q-1\right)$ and in high- and low-temperature limits. By using the four methods of the exact, interpolation, factorization, and superstatistical approaches, we have calculated coefficients in the generalized Sommerfeld expansion and electronic and phonon specific heats at low temperatures. A comparison among the four methods has shown that the interpolation approximation is potentially useful in the nonextensive quantum statistics. Supplementary discussions have been made on the $\left(q-1\right)$ expansion of the generalized distributions based on the exact approach with the use of the un-normalized MEM, whose results also agree with those of the asymptotic approach.

Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa [Prog. Theor. Phys. 121, 647 (2009)]]. We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a mean field theory and the simulation.

We report on video-microscopy measurements of the translational and rotational Brownian motions of isolated ellipsoidal particles in quasi-two-dimensional sample cells of increasing thickness. The long-time diffusion coefficients were measured along the long $\left(D_a\right)$ and short $\left(D_b\right)$ ellipsoid axes, respectively, and the ratio, $D_a/D_b$, was determined as a function of wall confinement and particle aspect ratio. In three dimensions (3D), this ratio $\left(D_a/D_b\right)$ cannot be larger than 2, but in quasi-two dimensions, wall confinement was found to substantially alter diffusion anisotropy and substantially slow particle diffusion along the short axis compared to 3D.

We theoretically study the kinetics of photoinduced ordering in azo-dye photoaligning layers and present the results of modeling performed using two different phenomenological approaches. A phenomenological two-state model is deduced from the master equation for the one-particle distribution functions of an ensemble of two-level molecular systems by specifying the angular redistribution probabilities and by expressing the order parameter correlation functions in terms of the order parameter tensor. Using an alternative approach that describes light-induced reorientation of azo-dye molecules in terms of a rotational Brownian motion, we formulate the two-dimensional diffusion model as the free energy Fokker-Planck equation simplified for the limiting regime of purely in-plane reorientation. The models are employed to interpret the irradiation time dependence of the absorption order parameters defined in terms of the principal extinction (absorption) coefficients. Using the exact solution to the light transmission problem for a biaxially anisotropic absorbing layer, these coefficients are extracted from the absorbance-vs-incidence angle curves measured at different irradiation doses for the probe light linearly polarized parallel and perpendicular to the plane of incidence. It is found that, in the azo-dye films, the transient photoinduced structures are biaxially anisotropic whereas the photosteady and the initial states are uniaxial.

We present a history-dependent Monte Carlo scheme for the efficient calculation of the free energy of quantum systems inspired by Wang-Landau and metadynamics. In the two-dimensional quantum Ising model, chosen here for illustration, the accuracy of free energy, critical temperature, and specific heat is demonstrated as a function of simulation time and successfully compared with the best available approaches. The approach is based on a path integral formulation of the quantum problem and can be applied without modifications to quantum Hamiltonians of any level of complexity. The combination of high accuracy and performance with a much broader applicability is a major advance with respect to other available methods.

We consider the classical and quantum properties of the “Chirikov typical map,” proposed by Boris Chirikov in 1969. This map is obtained from the well-known Chirikov standard map by introducing a finite-number $T$ of random phase-shift angles. These angles induce a random behavior for small time-scales $\left(t<T\right)$ and a $T$-periodic iterated map which is relevant for larger time-scales $\left(t>T\right)$. We identify the classical chaos border $k_c\sim T^{-3/2}⪡1$ for the kick parameter $k$ and two regimes with diffusive behavior on short and long time scales. The quantum dynamics is characterized by the effect of Chirikov localization (or dynamical localization). We find that the localization length depends in a subtle way on the two classical diffusion constants in the two time-scale regime.

The use of hyperasymptotics (H) and the Weniger transformation (WT) has been proposed, in a joint fashion, for decoding the divergent asymptotic series generated by the steepest descent on a wide class of saddle-point integrals evaluated across Stokes sets [R. Borghi, Phys. Rev. E 78, 026703 (2008)]. In the present sequel, the full development of the hyperasymptotic-Weniger transformation (H-WT) up to the second order in H is derived. Numerical experiments, carried out on several classes of saddle-point integrals, including the swallowtail diffraction catastrophe, show the effectiveness of the second-level H-WT, in particular when the integrals are evaluated beyond the asymptotic realm.

We study numerically a Ginzburg-Landau-type equation for micelles in two dimensions. The domain size and the interface length of a cellular structure are controlled by two feedback terms. The deformation and the successive splitting of the cellular structure are observed when the controlled interface length is increased. The splitting instability is further investigated using coupled mode equations to understand the bifurcation structure.

Following the nonequilibrium thermodynamics approach, we develop a dynamic model to emulate thermo-diffusion process and propose expressions for estimating the thermal diffusion factor in binary nonassociating liquid mixtures. Here, we correlate the net heat of transport in thermodiffusion with parameters, such as the mixture temperature and pressure, the size and shape of the molecules, and mobility of the components, because the molecules have to become activated before they can move. Based on this interpretation, the net heat of transport of each component can be somehow related to the viscosity and the activation energy of viscous flow of the same component defined in Eyring’s reaction-rate theory [S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion and Electrochemical Phenomena (McGraw-Hill, New York, 1941)]. This modeling approach is different from that of Haase and Kempers, in which thermodiffusion is considered as a function of the thermostatic properties of the mixture such as enthalpy. In simulating thermodiffusion, by correlating the net heat of transport with the activation energy of viscous flow, effects of the above mentioned parameters are accounted for, to some extent of course. The model developed here along with Haase-Kempers and Drickamer-Firoozabadi models linked with the Peng-Robinson equation of sate are evaluated against the experimental data for several recent nonassociating binary mixtures at various temperatures, pressures, and concentrations. Although the model prediction is still not perfect, the model is simple and easy to use, physically justified, and predicts the experimental data very good and much better than the existing models.

We present salient results of the analysis of the geometrical structure of a large fully equilibrated ensemble of nearly jammed packings of linear freely jointed chains of tangent hard spheres generated via extensive Monte Carlo simulations. In spite the expected differences due to chain connectivity, both the pair-correlation function and the contact network for chain packings are found to strongly resemble those in packings of monomeric hard spheres at the maximally random jammed (MRJ) state. A remarkable finding of the present work is the tendency of chains to form closed loops at the MRJ state as a consequence of chain collapse. Our simulations on disordered nearly jammed chain packings yield an average coordination number of 6, which fulfills the isostaticity condition and is in excellent agreement with the corresponding simulation [A. Donev, S. Torquato, and F. H. Stillinger, Phys. Rev. E 71, 011105 (2005)] and experimental [T. Aste, M. Saadatfar, and T. J. Senden, Phys. Rev. E 71, 061302 (2005)] findings for jammed packings of monatomic hard spheres. An exact correspondence between the statistical-mechanical ensembles of monomeric spheres and of hard-sphere chains offers insights regarding the structure and topology of the contact network of hard-sphere systems at the MRJ state.

Simultaneous measurements of rheological and dielectric properties are made to investigate shear-induced structural change in the smectic-$A$ phase of 8CB $\left(4\text{−}n\text{-octyl-}{4}^{\prime }\text{-cyanobiphenyl}\right)$. With increasing the shear rate, the fluidity changes from non-Newtonian to Newtonian flow via an unstable flow region, accompanied by a characteristic change in the dielectric permittivity. In the non-Newtonian flow region, a dielectric dispersion, which can be ascribed to an undulation motion of smectic layer, is recognized. On the basis of these results, it is suggested that with increasing the shear rate the undulation changes to a chaotic structure, which is followed by a more simple structure with the layer normal along the neutral axis, and that these structural changes are responsible for the fluidity change.

The quasiharmonic approximation is the most widely used estimate for the configurational entropy of macromolecules from configurational ensembles generated from atomistic simulations. This method, however, rests on two assumptions that severely limit its applicability, (i) that a principal component analysis yields sufficiently uncorrelated modes and (ii) that configurational densities can be well approximated by Gaussian functions. In this paper we introduce a nonparametric density estimation method which rests on adaptive anisotropic kernels. It is shown that this method provides accurate configurational entropies for up to 45 dimensions thus improving on the quasiharmonic approximation. When embedded in the minimally coupled subspace framework, large macromolecules of biological interest become accessible, as demonstrated for the 67-residue coldshock protein.

This work shows the relationship of the state variable rock-friction law proposed by Dieterich to the Carlson and Langer friction law commonly used in the Burridge-Knopoff (BK) model of earthquakes. Further to this, the Dieterich law is modified to allow slip rates of zero magnitude yielding a three parameter friction law that is included in the BK system. Dynamic phases of small scale and large scale events are found with a transition surface in the parameter space. Near this transition surface the event size distribution follows a power law with an exponent that varies as the transition is approached contrasting with the invariant exponent observed using the Carlson and Langer friction. This variability of the power-law exponent is consistent with the range of exponents measured in real earthquake systems and is more selective than the range observed in the Olami-Feder-Christensen model.

Driven transport of noninteracting Brownian particles in two-dimensional asymmetric channels is investigated by fully accounting for longitudinal and transverse diffusions. Bona fide two-dimensional rectification effects are reported, which cannot be explained by an approximate Fick-Jacobs kinetics, such as the characteristic curve of the current pumped by a transverse ac bias and the selective gating exerted by a transverse ac bias on a driven longitudinal current. Possible experimental demonstrations of these effects in superconducting devices are also discussed.

We investigate the relation between an applied potential and the corresponding stationary-state occupation for nonequilibrium and overdamped diffusion processes. This relation typically becomes long ranged resulting in global changes for the relative density when the potential is locally perturbed, and inversely, we find that the potential needs to be wholly rearranged for the purpose of creating a locally changed density. The direct question, determining the density as a function of the potential, comes under the response theory out of equilibrium. The inverse problem of determining the potential that produces a given stationary distribution naturally arises in the study of dynamical fluctuations. This link to the fluctuation theory results in a variational characterization of the stationary density upon a given potential and vice versa.

Recent laboratory experiments on solute migration in composite porous columns have shown an asymmetry in the solute arrival time upon reversal of the flow direction, which is not explained by current paradigms of transport. In this work, we propose a definition for the solute flux across sharp interfaces and explore the underlying microscopic particle dynamics by applying Monte Carlo simulation. Our results are consistent with previous experimental findings and explain the observed transport asymmetry. An interpretation of the proposed physical mechanism in terms of a flux rectification is also provided. The approach is quite general and can be extended to other situations involving transport across sharp interfaces.

We propose a method for determining the ground states of lattice-gas (or Ising) models. The method makes possible to find all types of ground states, including chaotic and ordered-but-aperiodic ones, and to identify the first-order phase transitions between them. Using this method, we prove the existence of an infinite series of ground states (the so-called “devil’s step”) in the lattice-gas model on the triangular lattice with up to third nearest-neighbor interactions and we study the effect of the interactions up to 19th neighbors on this series. To our best knowledge, this is only the second example of the devil’s step at zero temperature in the lattice-gas models with one kind of particles.

We use an effective Markovian description to study the long-time behavior of a nonlinear second-order Langevin equation with a Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power law with an anomalous scaling exponent that depends both on the confining potential and on the high-frequency distribution of the noise. The asymptotic expression of the probability distribution function in phase space is calculated analytically. The results are extended to the case where small dissipative effects are taken into account.

Experimental results and their interpretations are presented on the nonlinear acoustic effects of multiple scattered elastic waves in unconsolidated granular media. Short wave packets with a central frequency higher than the so-called cutoff frequency of the medium are emitted at one side of the statically stressed slab of glass beads, and received at the other side after multiple-scattering and nonlinear elastic effects. Typical signals are strongly distorted compared to their initially radiated shape both due to nonlinearity and scattering. It is shown that acoustic waves with a deformation amplitude much lower than the mean static deformation of the contacts in the medium can modify the elastic properties of the medium. This addresses the problem of acoustic wave action on granular matter during and after acoustic excitation, which is necessary to understand in the nondestructive testing of the elastic properties of granular media by acoustic methods. Coda signal analysis is shown to be a powerful time-resolved tool in monitoring slight modifications in the elastic response of an unconsolidated granular structure.