A direct connection between the magnitude of the violation of the fluctuation response relation (FRR) and the rate of energy dissipation is presented in terms of field variables of nonequilibrium systems. Here, we consider the density field of a colloidal suspension either in a relaxation process or in a nonequilibrium steady state driven by an external field. Using a path-integral representation of the temporal evolution of the density field, we find an equality that relates the magnitude of the violation of the FRR for scalar and vector potentials of the velocity field to the rate of energy dissipation for the entire system. Our result demonstrates that the violation of the FRR for field variables captures the entropic component of the dissipated free energy.

Elementary smooth functions (beyond contact) are employed to construct pair correlation functions that mimic jammed disordered sphere packings. Using the $g_2$-invariant optimization method of Torquato and Stillinger [J. Phys. Chem. B 106, 8354 (2002)], parameters in these functions are optimized under necessary realizability conditions to maximize the packing fraction $\varphi$ and average number of contacts per sphere $Z$. A pair correlation function that incorporates the salient features of a disordered packing and that is smooth beyond contact is shown to permit a $\varphi$ of 0.6850: this value represents a 45% reduction in the difference between the maximum for congruent hard spheres in three dimensions, $\pi /\sqrt{18}\approx 0.7405$ and 0.64, the approximate fraction associated with maximally random jammed packings in three dimensions. We show that, surprisingly, the continued addition of elementary functions consisting of smooth sinusoids decaying as $r^{-4}$ permits packing fractions approaching $\pi /\sqrt{18}$. A translational order metric is used to discriminate between degrees of order in the packings presented. We find that to achieve higher packing fractions, the degree of order must increase, which is consistent with the results of a previous study [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)].

We report the formation of axial segregation patterns of bidisperse granular mixtures of glass beads in a spherical container which is rotated about a central axis. When the rotation axis is horizontal, three distinct segregation bands are formed for a broad range of geometrical and dynamical parameters. We find two distinct regimes: at low fill levels the small size beads of the mixture are collected at the poles and the large size beads in a central band. At high fill levels the pole regions are occupied by large beads, while the small beads form the central band. The critical fill level for this structural transition decreases with increasing container size. For a container with 37 mm inner diameter, containing a mixture of 0.5 and 1.5 mm beads, the transition occurs between 40% and 50% fill level. When the rotation axis is tilted, the band positions are shifted and two-band structures are formed with the smaller particles at the lower pole. In our experiments the granulate is submersed in water; this allows NMR imaging of the complete three-dimensional band structures. We compare the observed segregation structures to those in cylindrical mixers and propose a model for the qualitative explanation of the pattern formation process.

We investigate dynamical self-arrest in a diblock copolymer melt using a replica approach within a self-consistent local method based on dynamical mean-field theory (DMFT). The local replica approach effectively predicts ${\left(\chi N\right)}_A$ for dynamical self-arrest in a block copolymer melt for symmetric and asymmetric cases. We discuss the competition of the cubic and quartic interactions in the Landau free energy for a block copolymer melt in stabilizing a glassy state depending on the chain length. Our local replica theory provides a universal value for the dynamical self-arrest in block copolymer melts with ${\left(\chi N\right)}_A\sim 10.5+64N^{-3/10}$ for the symmetric case.

The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion, we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move, and the end results are similar. For adherent cells, simulations suggest that the actin cytoskeleton must play an active role for the cells to establish cell-cell contact regions similar to those observed in vitro.

Voltage-gated ion channels are key molecules for the generation and propagation of electrical signals in excitable cell membranes. The voltage-dependent switching of these channels between conducting and nonconducting states is a major factor in controlling the transmembrane voltage. In this study, a statistical mechanics model of these molecules has been discussed on the basis of a two-dimensional spin model. A new Hamiltonian and a new Monte Carlo simulation algorithm are introduced to simulate such a model. It was shown that the results well match the experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon using the cut-open axon technique.

Trajectory data from observations of a random-walk process are often used to characterize macroscopic transport coefficients and to make inferences about motility mechanisms. Continuum equations describing the average moments of the position of an agent in an exclusion process are derived and validated with simulation data. Unlike standard noninteracting random walks, the moment equations for the exclusion process explicitly represent the interaction of agents since they depend on the averaged macroscopic agent density. Key issues associated with the validity of the continuum equations and interpretation of experimental data are discussed.

If the mean-square displacement of a stochastic process is proportional to $t^{\beta }$, $\beta \ne 1$, then it is said to be anomalous. We construct a family of Markovian stochastic processes with independent nonstationary increments and arbitrary but a priori specified mean-square displacement. We label the family as an extended Brownian motion and show that they satisfy a Langevin equation with time-dependent diffusion coefficient. If the time derivative of the variance of the process is homogeneous, then by computing the fractal dimension it can be shown that the complexity of the family is the same as that of the Brownian motion. For two particles initially separated by a distance $x$, the finite-size Lyapunov exponent (FSLE) measures the average rate of exponential separation to a distance $ax$. An analytical expression is developed for the FSLEs of the extended Brownian processes and numerical examples presented. The explicit construction of these processes illustrates that contrary to what has been stated in the literature, a power-law mean-square displacement is not necessarily related to a breakdown in the classical central limit theorem (CLT) caused by, for example, correlation (fractional Brownian motion or correlated continuous-time random-walk schemes) or infinite variance (Levy motion). The classical CLT, coupled with nonstationary increments, can and often does give rise to power-law moments such as the mean-square displacement.

Fundamental thermodynamics and an earlier elastic solid-state point defect model [P. Varotsos and K. Alexopoulos, Phys. Rev. B 15, 4111 (1977); Phys. Rev. B 18, 2683 (1978)] are employed to formulate an analytical second-order polynomial function describing the density scaling of the diffusion coefficient in viscous liquids. The function parameters are merely determined by the scaling exponent, which is directly connected with the Grüneisen constant. Density scaling diffusion coefficient isotherms obtained at different pressures collapse on a unique master curve, in agreement with recent computer simulation results of Lennard-Jones viscous liquids [D. Coslovich and C. M. Roland, J. Phys. Chem. 112, 1329 (2008)].

In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.

This paper studies the statistical properties of the web of import-export relationships among world countries using a weighted-network approach. We analyze how the distributions of the most important network statistics measuring connectivity, assortativity, clustering, and centrality have coevolved over time. We show that all node-statistic distributions and their correlation structure have remained surprisingly stable in the last $20\text{years}$—and are likely to do so in the future. Conversely, the distribution of (positive) link weights is slowly moving from a log-normal density towards a power law. We also characterize the autoregressive properties of network-statistics dynamics. We find that network-statistics growth rates are well-proxied by fat-tailed densities like the Laplace or the asymmetric exponential power. Finally, we find that all our results are reasonably robust to a few alternative, economically meaningful, weighting schemes.

Through the use of analytical and numerical techniques, we investigate the interaction between the trivial off-state and the continuous-wave (CW) operation of a semiconductor laser subject to conventional optical feedback. More specifically, using numerical continuation tools, the stability and bifurcations of the CW states, or external-cavity modes (ECMs), are analyzed in dependence on the parameters of feedback phase, feedback strength, pump current, and the linewidth enhancement factor. In this way, curves of codimension-one Hopf bifurcations are shown to destabilize the off-state and lead to stable ECM operation. Moreover, self-intersections of these Hopf curves in codimension-two Hopf-Hopf bifurcation points are seen to give rise to curves of codimension-one torus bifurcations (Hopf bifurcations of the ECMs), and degenerate-Hopf points to the birth of saddle-node bifurcations of the ECMs, as parameters are varied. These codimension-two points are shown to come together at a codimension-three degenerate Hopf-Hopf point (a Bogdanov-Takens bifurcation of the ECMs): a limiting point for which a stable off-state can exist.

This paper investigates the efficiency of the implicit restart Lanczos and simple (without reorthogonalization) Lanczos algorithms, as eigensolvers for large scale computations in molecular and chemical physics. Using the cardioid billiard and the hydrogen cyanide/hydrogen isocyanide (HCN/HNC) molecule as model systems we demonstrate superior efficiency of implicit restart Lanczos compared to the simple Lanczos algorithm. A modified implementation of implicit restart Lanczos is also presented which works with a smaller Krylov space—with associated savings in memory—and can handle larger basis sets than the usual implicit restart Lanczos. It also enables getting all eigenpairs of a matrix, or all eigenvalues below a threshold (where the number of such is not known before hand), which is more difficult with the usual implicit restart algorithm.

Many recent papers have questioned Irving and Kirkwood’s atomistic expression for stress. In Irving and Kirkwood’s approach both interatomic forces and atomic velocities contribute to stress. It is the velocity-dependent part that has been disputed. To help clarify this situation we investigate (i) a fluid in a gravitational field and (ii) a steadily rotating solid. For both problems we choose conditions where the two stress contributions, potential and kinetic, are significant. The analytic force-balance solutions of both these problems agree very well with a smooth-particle interpretation of the atomistic Irving-Kirkwood stress tensor.

We propose that, for materials having positive dielectric anisotropy, the biaxiality can be clearly verified or excluded by measuring the transmitted light intensity as a function of electric field. If the material is biaxial and is observed in homeotropically aligned cells, the schlieren texture should not disappear (transmitted intensity is not zero) even at very high fields, since the field does not affect the distribution of the second director normal to the main director. On the other hand, if the material is uniaxial the transmitted intensity should decrease with increasing field and a perfect homeotropic texture can be achieved at high fields. We have studied a bent-core compound in which a uniaxial-biaxial nematic $\left(N_u\text{−}{N}_b\right)$ transition has been reported. This material has a positive dielectric anisotropy at low frequencies, so we could apply the technique described above. Our studies indicate that the material is uniaxial in the entire nematic range.

A theoretical study of dynamical phenomena induced by linearly polarized light incident perpendicularly on a planar aligned nematic layer with the light intensity as the control parameter is reported. We find the threshold of the optically induced twist Fréedericksz transition as a function of the problem parameters. The critical light intensity was found substantially lower than predicted earlier by Santamato et al. [Phys. Rev. A 36, 2389 (1987)]. We have demonstrated by a rigorous stability analysis that the bifurcation is stationary only for a thickness of the nematic layer smaller than a certain critical value and becomes a Hopf bifurcation in the opposite case. Above the Hopf bifurcation an oscillatory state appears. It becomes unstable at a secondary threshold through a heteroclinic bifurcation, and the director settles to a new stationary distorted state.

The structural properties and phase behavior of a self-avoiding polymer chain on an adhesive substrate, subject to pulling at the chain end, are described by means of a grand canonical ensemble approach. We derive analytical expressions for the probability distributions of the basic structural units of an adsorbed polymer, such as loops, trains, and tails, in terms of the adhesive potential $ϵ$ and applied pulling force $f$. In contrast to conventional, $f=0$, polymer adsorption, the chain detachment transition under pulling turns out to be of first (rather than second) order, albeit it is dichotomic, i.e., no coexistence of different phase states exists. Also, the hitherto controversial value of the critical adsorption exponent $\varphi$ is found to depend essentially on the degree of interaction between different loops so that $0.34⩽\varphi ⩽0.59$. The theoretical predictions are verified by means of extensive Monte Carlo simulations.

We elucidate the microscopic mechanism of the weakening of the hydrophobicity at low temperatures by investigating cold denaturation of a protein. We employ an elaborate statistical-mechanical theory combined with a realistic water model. At low temperatures, the ordered structure with enhanced hydrogen bonds of water molecules is formed near nonpolar groups, leading to entropic loss and energy gain which are both quite large. However, they are canceled out and make no contribution to the free-energy change. We argue that a different factor, which is responsible for the weakening of the hydrophobicity at low temperatures, induces cold denaturation.

In a spatially periodic temperature profile, directed transport of an overdamped Brownian particle can be induced along a periodic potential. With a load force applied to the particle, this setup can perform as a heat engine. For a given load, the optimal potential maximizes the current and thus the power output of the heat engine. We calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures, the optimal potential leads to a divergent current. This divergence, being an effect of both the overdamped limit and the infinite temperature gradient at the interface, would be cut off in any real experiment.

We show that there are two classes of the closure equations for the Ornstein-Zernike equation: The analytical equations for the bridge functional $B=B^{\left(\mathit{an}\right)}$ like hypernetted-chain approximation, Percus-Yevick approximation, etc., and nonanalytic equation $B=B^{\left(\mathit{nan}\right)}$, where $B^{\left(\mathit{nan}\right)}=B^{\left(\mathit{rg}\right)}+B^{\left(\mathit{cr}\right)}$ and $B^{\left(\mathit{rg}\right)}$ is the regular (analytical) component of the bridge functional, and $B^{\left(\mathit{cr}\right)}$ is the critical (nonanalytical) component of $B^{\left(\mathit{nan}\right)}$. The closure equation $B^{\left(\mathit{an}\right)}$ defines coordinates of the critical point and other individual features of critical phenomena, and $B^{\left(\mathit{nan}\right)}$ defines all the known relations between critical exponents. It is shown, that the necessary condition for existence of the nonanalytic solution of the OZ equation is the equality $5-\eta =\delta (1+\eta )$, where $\eta ,\delta$ are the critical exponents, values of which can change in a narrow interval. We also show that the transition from the analytical solution to the nonanalytic one is accompanied by a break of the pressure derivative. The boundaries between the areas, where each of these solutions exists, are indicated on the phase diagram.