The results of dielectric measurements for a mixture of chiral liquid crystal 5*CB with ${\mathrm{Al}}_2{\mathrm{O}}_3$ powder are given. A detailed analysis of the dielectric spectra enabled us to obtain information about the influence of the ${\mathrm{Al}}_2{\mathrm{O}}_3$ grains on the dynamics of the liquid-crystal molecules. Numerical analysis of the results confirmed that the dielectric spectra obtained are complex. In the low-frequency range they are dominated by ionic conductivity while in the whole frequency range two maxima appear. One of them is related to rotations of the molecules around their short axes. In the isotropic phase the corresponding values of the relaxation times are very close to those for bulk 5*CB. Relaxation and conduction processes can be described by a Vogel-Fulcher-Tammann function. In the cholesteric phase, rotation of 5*CB molecules trapped in the pores of ${\mathrm{Al}}_2{\mathrm{O}}_3$ occurs. Another relaxation process results from dynamics of 5*CB molecules anchoring to ${\mathrm{Al}}_2{\mathrm{O}}_3$ grains. The temperature dependence of relaxation times related to this process is nonmonotonic.

We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a nonequilibrium state with the desired final volume fraction $\varphi$ for which we can obtain a well-defined nonequilibrium static structure factor $S_0(k;\varphi )$. The evolution of the $\alpha$-relaxation time ${\tau }_{\alpha }(k)$ and long-time self-diffusion coefficient $D_L$ as a function of the evolution time $t_w$ is then monitored for an array of volume fractions. For a given waiting time the plot of ${\tau }_{\alpha }(k;\varphi ,t_w)$ as a function of $\varphi$ exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time [$\varphi ⩽\varphi {}^{(c)}(t_w)$] and to samples for which equilibration is not yet complete [$\varphi ⩾\varphi {}^{(c)}(t_w)$]. The crossover volume fraction $\varphi {}^{(c)}(t_w)$ increases with $t_w$ but seems to saturate to a value $\varphi {}^{(a)}\equiv \varphi {}^{(c)}(t_w\to \infty )\approx 0.582$. We also find that the waiting time $t_w^{\mathrm{eq}}(\varphi )$ required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, $t_w^{\mathrm{eq}}(\varphi )\approx 0.27[{\tau }_{\alpha }^{\mathrm{eq}}(k;\varphi )]{}^{1.43}$, and that both characteristic times increase strongly as $\varphi$ approaches $\varphi {}^{(a)}$, thus suggesting that the measurement of equilibrium properties at and above $\varphi {}^{(a)}$ is experimentally impossible.

Within an exact microcanonical (MC) ensemble, we study the nonanalyticities of thermodynamic functions research in finite noninteracting Bose gases in traps. The results show that there exists a rich oscillatory behavior of MC thermodynamical quantities as a function of a system’s total energy $E$ (e.g., nonmonotonous temperature, nonanalytic and negative specific heats, and microscopic phase transitions). The origin of these nonanalyticities comes directly from the inverted curvature entropy $S(E)$ with respect to $E$ and the behaviors are different in different trap geometries, boundary conditions, and energy spectrum configurations. Contrary to the usual grandcanonical and canonical results, there exists Bose condensation and the nonanalyticities in the two-dimensional finite noninteracting Bose systems with different traps. We also discuss the critical temperature dependence on the particle number $N$ with different ensembles, traps, and boundary conditions. In large enough $N$, almost all the results of the thermodynamical quantities become smooth, which are similar to the usual canonical behaviors. We emphasize the finite-size effects on the MC entropy change, which should, in principle, be observable in suitably designed experiments of the small systems.

We study hysteresis in antiferromagnetic random-field Ising model at zero temperature. The external field is cycled adiabatically between $-\infty$ and $\infty$. Two different distributions of the random field are considered: (i) a uniform distribution of width $2\Delta$ centered at the origin and (ii) a Gaussian distribution with average value zero and standard deviation $\sigma$. In each case the hysteresis loop is determined exactly in one dimension and compared with numerical simulations of the model.

In this work, we provide exact solutions for the ideal boson lattice gas on the infinitely ramified star and wheel graphs. Within a tight-binding description, we show that Bose-Einstein condensation (BEC) takes place at a finite temperature after a proper rescaling of the hoping integral $\varepsilon$ connecting a central site to the peripheral ones. Analytical expressions for the transition temperature, the condensed gas fraction, and the specific heat are given for the star graph as a function of the density of particles $n$. In particular, the specific heat has a mean-field character, being null in the high-temperature noncondensed phase with a discontinuity at $T_c$. In the wheel graph, on which the peripheral sites form a closed chain with hopping integral $t$, BEC takes place only above a critical value of the ratio $\varepsilon /t$ for which a gap $\Delta E$ appears between the ground state and a one-dimensional band. A detailed analysis of the BEC characteristics as a function of $n$ and $\Delta E$ is provided. The specific heat in the high-temperature phase of the wheel graph remains finite due to correlations among the peripheral sites.

Inspired by the collective phenomenon of territorial emergence, whereby animals move and interact through the scent marks they deposit, we study the dynamics of a 1D Brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously. We show how to reduce, in certain parameter regimes, the non-Markovian, many-body problem of territoriality to the analytically tractable one-body problem studied here. The mean square displacement (MSD) of the 1D Brownian walker within subdiffusing boundaries is calculated exactly and generalizes well known results when the boundaries are immobile. Furthermore, under certain conditions, if the boundary dynamics are strongly subdiffusive, we show the appearance of an interesting nonmonotonicity in the time dependence of the MSD, giving rise to transient negative diffusion.

We report a study of the paths formed by a finite volume of air gently injected at the base of an immersed granular material. A two-dimensional model, based on experimental observations, shows that the typical height and width of the region explored by the branched path depends not only on the injected volume $V$, but also on a dimensionless parameter $\chi$ which accounts for the relative effects of the gravity and capillarity. For a given injected volume $V$, larger gravity effects lead to taller and narrower structures; for a given $\chi$, the typical height and width of the structure scale like $V^{1/2}$ and $V^{1/4}$, respectively, while the typical gaseous fraction in the corresponding region increases accordingly like $V^{1/4}$. Such results can be of practical importance: For instance, gas can be trapped on purpose in an underground natural container below a granular slurry. Our results can help in predicting if the gas is likely to reach the free surface and escape the system if the container presents a defect (hole or fracture).

Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We also present numerical solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge, and reaction rates in response to an applied voltage.

The results of a theoretical investigation of the energy loss of charged particles in a magnetized classical plasma due to the electric-field fluctuations are reported. The energy loss for a test particle is calculated through the linear-response theory. At vanishing magnetic field, the electric-field fluctuations lead to an energy gain of the charged particle for all velocities. It has been shown that in the presence of strong magnetic field, this effect occurs only at low velocities. In the case of high velocities, the test particle systematically loses its energy due to the interaction with a stochastic electric field. The net effect of the fluctuations is the systematic reduction of the total energy loss (i.e., the sum of the polarization and stochastic energy losses) at vanishing magnetic field and reduction or enhancement at strong field, depending on the velocity of the particle. It is found that the energy loss of the slow heavy ion contains an anomalous term that depends logarithmically on the projectile mass. The physical origin of this anomalous term is the coupling between the cyclotron motion of the plasma electrons and the long-wavelength, low-frequency fluctuations produced by the projectile ion. This effect may strongly enhance the stochastic energy gain of the particle.

We study the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the $K(l,p)$ Rosenau-Hyman (RH) equation for $l=p=2$, with compacton-anticompacton solutions of the $L(l,p)$ Cooper-Shepard-Sodano (CSS) equation for $p=1$ and $l=3$. This study is performed using a Padé discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton-anticompacton scattering. For the CSS equation, the scattering can be interpreted as “annihilation” as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision, which eventually lead to “blowup” of the resulting wave form.

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [S. Pratt, Phys. Rev. Lett. 84, 4255 (2000)] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body interactions, makes possible the inclusion of conservation laws, and requires low computational time. In this Brief Report, we show that such recursion relations can be obtained from generating functions, without any restriction in relation to the number of conservation laws (e.g., total energy or angular momentum).

We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as a functional of a trial many-body distribution. This functional is minimized in two stages. The first step consists of a constrained search of all many-body distributions that generate a given one-body density. The result can be split into internal and external contributions to the total grand potential. In contrast to the original approach by Mermin and Evans, here the intrinsic Helmholtz free-energy functional is defined by an explicit expression that does not refer to an external potential in order to generate the given one-body density. The second step consists of minimizing with respect to the one-body density. We show that this framework can be applied in a straightforward way to the canonical ensemble.

Heat transfer is investigated on three levels of description: Fourier, Cattaneo, and Peierls. The microscopic nature of the heat that becomes important, in particular in nanoscale systems, is characterized by a vector field related to the heat flux on the Cattaneo level and by the phonon distribution function on the Peierls level. All dynamical theories discussed in the paper are fully nonlinear and all are proven to be compatible among themselves, with equilibrium thermodynamics, and with mechanics. An investigation of the first two compatibilities gives rise to potentials having the physical interpretation of nonequilibrium entropies. The compatibility with mechanics is manifested by the Hamiltonian structure of the time-reversible part of the time evolution.

Using a modified Bak-Tang-Wiesenfeld model for sand piles, we simulate a Casimir-like effect in a granular pile with avalanches. Results obtained in the simulation are in good agreement with results previously acquired experimentally: two parallel walls are attracted to each other at small separation distances, with a force decreasing with increasing distance. In the simulation only, at medium distances a weak repulsion exists. Additionally, with the aim of avalanche prevention, the possibility of suppressing self-organized criticality with an array of walls placed on the slope of the pile is investigated, but the prevention effect is found to be negligible.

We investigate the cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field numerically by the Brownian dynamics method, focusing on the cases of ϕ $=$ 0.01 and 0.03 and Ma $=$ 0, 0.001, 0.01, and 0.1, where ϕ is the area fraction of superparamagnetic particles and Ma is the Mason number, i.e., the ratio of viscous drag to magnetic force acting on a magnetic particle. We clarify the effect of ϕ and Ma on the cluster-cluster aggregation process from the point of view of dynamic scaling law.

Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions. Starting from microscopic density functional theory, we derive a phase-field-crystal expression for the free-energy density that involves three local order-parameter fields, namely the translational density, the polarization, and the nematic order parameter. Various coupling terms between the order-parameter fields are obtained, which are in line with macroscopic considerations. Since the coupling constants are brought into connection with the molecular correlations, we establish a bridge from microscopic to macroscopic modeling. Our theory provides a starting point for further numerical calculations of the stability of polar liquid-crystalline phases and is also relevant for modeling of microswimmers, which are intrinsically polar.

High-resolution x-ray diffraction was used to investigate how polymer networks affect the tilt angle in the smectic-$C$* (Sm$C$*) phase of the ferroelectric liquid crystal 4-[(S,S)-2,3-epoxyhexyloxy]-phenyl-4-(decyloxy)-benzoate (W46 or EPHDBPE). Blends comprising W46, a monomer, and a photoinitiator were prepared and photopolymerized at temperatures that correspond to isotropic and the Sm$C$* phases of W46. When compared to the pure material, the tilt in the Sm$C$* phase was found to decrease in both polymerized samples. The effect, however, is greater for the sample that was polymerized while it was in the Sm$C$* phase. Also, the Sm$A$*-Sm$C$* transition in pure W46 is a weak first-order transition that becomes continuous if traces of polymer are added to W46.

Thermalization of systems described by the discrete nonlinear Schrödinger equation, in the strong disorder limit, is investigated both theoretically and numerically. We show that introducing correlations in the disorder potential, while keeping the “effective” disorder fixed (as measured by the localization properties of wave-packet dynamics), strongly facilitates the thermalization process and leads to a standard grand canonical distribution of the probability norms associated with each site.

Identifying overlapping communities in networks is a challenging task. In this work we present a probabilistic approach to community detection that utilizes a Bayesian non-negative matrix factorization model to extract overlapping modules from a network. The scheme has the advantage of soft-partitioning solutions, assignment of node participation scores to modules, and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection.

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.