We report the effect of applied pressure on the dielectric properties of the $B$2 phase of a bent-core liquid crystal. This study on bent-core banana-shaped molecules shows that while the dielectric anisotropy hardly varies with pressure, the relaxation parameters associated with the rotation around the long axes of the molecules are significantly influenced. These studies also bring out the fact that there are additional phases between the $B$2 phase and the true crystalline solid. Indeed, the existence of another variant of the $B$2 phase (labeled $B{2}^{\prime }$), is revealed only in dielectric studies but not seen in x-ray and calorimetric measurements. Employing the dependence of the relaxation frequency along isobaric as well as isothermal paths, different activation parameters are determined and their behavior is compared with those of rodlike systems. The influence of dc bias on the dielectric behavior obtained at atmospheric pressure is also presented, which exhibits features similar to chiral antiferroelectric smectics, and further shows an additional relaxation over a small window of dc voltages.

We propose a statistical machine-learning approach to derive low-dimensional models by integrating noisy time-series data from partial observation of high-dimensional systems, aiming to utilize quantitative data on biological phenomena in the cell. In particular, the method estimates a model from data at different values of a bifurcation parameter in order to characterize biological functions as bifurcation types that are insensitive to system details and experimental errors. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations and the learned systems are shown to robustly inherit the bifurcation types.

We reanalyze transfer-matrix and Monte Carlo results for the critical Binder cumulant $U^{*}$ of an anisotropic two-dimensional Ising model on a square lattice in a square geometry with periodic boundary conditions. Spins are coupled between nearest-neighboring sites and between next-nearest-neighboring sites along one of the lattice diagonals. We find that $U^{*}$ depends only on the asymptotic critical long-distance features of the anisotropy, irrespective of its realization through ferromagnetic or antiferromagnetic next-nearest-neighbor couplings. We modify an earlier renormalization-group calculation to obtain a quantitative description of the anisotropy dependence of $U^{*}$. Our results support our recent claim towards the validity of universal finite-size scaling for critical phenomena in the presence of a weak anisotropy.

Many body dissipative particle dynamics (MDPD) is a particle-based simulation method in which the interaction potential is a sum of self energies depending on locally sampled density variables. This functional form gives rise to density-dependent pairwise forces; however, not all such force laws are derivable from a potential, and the integrability condition for this to be the case provides a strong constraint. A strategy to assess the implications of this constraint is illustrated here by the derivation of a useful no-go theorem for multicomponent MDPD.

In this Comment, we point out that the Euler-Lagrange equations, which are referred to as the general equilibrium equations by Zhao et al. [Phys. Rev. E 74, 032801 (2006)] are incorrect along with the equations which are derived from them. The correct equations are provided in this Comment. We produce new numerical results with the use of the correct equations.

One of the most noticeable collective motion of noncohesive granular matter is clustering under certain conditions. In particular, when a quasi-two-dimensional monolayer of monodispersed noncohesive particles is vertically vibrated, a solid-liquid-like transition occurs when the driving amplitude exceeds a critical value. Here the physical mechanism underlying particle clustering relies on the strong interactions mediated by grain collisions, rather than on grain-grain cohesive forces. In average, the solid cluster resembles a drop, with a striking circular shape. We experimentally investigate the coarse-grained solid-liquid interface fluctuations, which are characterized through the static and dynamic correlation functions in the Fourier space. These fluctuations turn out to be well described by the capillary wave theory, which allows us to measure the solid-liquid interface surface tension and mobility once the granular “thermal” kinetic energy is determined. Despite that the system is strongly out of equilibrium and that the granular temperature is not uniform, there is energy equipartition at the solid-liquid interface, for a relatively large range of angular wave numbers. Furthermore, both surface tension and mobility are consistent with a simple order of magnitude estimation considering the characteristic energy, length, and time scales, which is very similar to what can be done for atomic systems.

In the thin-double-layer limit $\kappa a\gg 1$, electrokinetic flows about free surfaces are driven by a combination of an electro-osmotic slip and effective shear-stress jump. An intriguing case is that of a highly conducting liquid drop of radius $a$, where the inability to balance the viscous shear by Maxwell stresses results in an $O\left(\kappa a\right)$ velocity amplification relative to the familiar electro-osmotic scale. To illuminate the inherent nonlinearity we consider uncharged drops, where the induced surface-charge distribution results in a fore-aft symmetric electrokinetic flow profile with no attendant drop translation. This problem is analyzed using a macroscale model, where the double layer is represented by effective boundary conditions. Because of the intense flow, ionic convection within the $O(1/\kappa )$-wide diffuse-charge layer is manifested by a moderate-zeta-potential surface-conduction effect. The drop deforms to a prolate shape in response to the combination of hydrodynamic forces and the effective electrocapillary reduction of the surface-tension coefficient, both mechanisms being asymptotically comparable. The flow field and the concomitant drop deformation are calculated using both a weak-field approximation and numerical simulations of the nonlinear macroscale model.

The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bidispersed disks subject to quasistatic, uniaxial compression without vibrational disturbances (zero granular temperature). Three primary results are presented in this experimental study. First, using disks with different static friction coefficients ($\mu$), we experimentally verify numerical results that predict jamming onset at progressively lower packing fractions with increasing friction. Second, we show that the first compression cycle measurably differs from subsequent cycles. The first cycle is fragile—a metastable configuration with simultaneous jammed and unjammed clusters—over a small packing fraction interval (${\varphi }_1<\varphi <{\varphi }_2$) and exhibits simultaneous exponential rise in pressure and exponential decrease in disk displacements over the same packing fraction interval. This fragile behavior is explained through a percolation mechanism of stressed contacts where cluster growth exhibits spatial correlation with disk displacements and contributes to recent results emphasizing fragility in frictional jamming. Control experiments show that the fragile state results from the experimental incompatibility between the requirements for zero friction and zero granular temperature. Measurements with several disk materials of varying elastic moduli $E$ and friction coefficients $\mu$ show that friction directly controls the start of the fragile state but indirectly controls the exponential pressure rise. Finally, under repetitive loading (compression) and unloading (decompression), we find the system exhibits pressure hysteresis, and the critical packing fraction ${\varphi }_c$ increases slowly with repetition number. This friction-induced hysteretic creep is interpreted as the granular pack's evolution from a metastable to an eventual structurally stable configuration. It is shown to depend on the quasistatic step size $\Delta \varphi$, which provides the only perturbative mechanism in the experimental protocol, and the friction coefficient $\mu$, which acts to stabilize the pack.

We present here experimental results on the progressive development of a fluidized zone in a bed of grains, immersed in a liquid, under the effect of a localized upward flow injected through a small orifice at the bottom of the bed. Visualization inside the model granular medium consisting of glass beads is made possible by the combined use of two optical techniques: refractive index matching between the liquid and the beads and planar laser-induced fluorescence. Gradually increasing the injection rate, three regimes are successively observed: static bed, fluidized cavity that does not open to the upper surface of the granular bed, and finally fluidization over the entire height of the granular bed inside a fluidized chimney. The phase diagram is plotted and partially interpreted using a model previously developed by Zoueshtiagh and Merlen [F. Zoueshtiagh and A. Merlen, Phys. Rev. E 75, 053613 (2007)]. A typical sequence, where the flow rate is first increased and then decreased back to zero, reveals a strong hysteretic behavior since the stability of the fluidized cavity is considerably strengthened during the defluidization phase. This effect can be explained by the formation of force arches within the granular packing when the chimney closes up at the top of the bed. A study of the expansion rate of the fluidized cavity was also conducted as well as the analysis of the interaction between two injection orifices with respect to their spacing.

The degree of order within nanoparticle monolayers deposited through electrophoretic deposition on lithographically patterned and unpatterned substrates was analyzed using four complementary measures of order: Voronoi-cell edge-fraction entropy, local bond-orientation order parameter, translational order parameter, and anisotropy order parameter. From these measures of order, we determined that the pattern had an influence on some aspects of the ordering within the nanoparticle monolayer but had no effect on others. The Voronoi-cell edge-fraction entropy did not measurably change due to the pattern, indicating that the pattern has no effect on the number of defects present. The translational order parameter also had no change due to the pattern. The local bond-orientation order parameter had a measurable change, indicating the pattern increased the bond ordering slightly. Also, the anisotropy order parameter developed herein indicated an increase in order. The direction of the increased order corresponded with the direction of the anisotropy designed on the patterned substrate, strongly suggesting that the pattern drives the particles to become more ordered.

Electrode polarization analysis is frequently used to determine free-ion diffusivity and number density in ionic conductors. In the present study, this approach is critically examined in a wide variety of electrolytes, including aqueous and nonaqueous solutions, polymer electrolytes, and ionic liquids. It is shown that the electrode polarization analysis based on the Macdonald-Trukhan model [J. Chem. Phys. 124, 144903 (2006); J. Non-Cryst. Solids 357, 3064 (2011)] progressively fails to give reasonable values of free-ion diffusivity and number density with increasing salt concentration. This should be expected because the original model of electrode polarization is designed for dilute electrolytes. An empirical correction method which yields ion diffusivities in reasonable agreement with pulsed-field gradient nuclear magnetic resonance measurements is proposed. However, the analysis of free-ion diffusivity and number density from electrode polarization should still be exercised with great caution because there is no solid theoretical justification for the proposed corrections.

In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types; the resulting measurements thus give only averages over the different cell types present. Based on fluctuations in the mixture proportions from sample to sample it is in principle possible to reconstruct the underlying expression levels of each cell type: to deconvolute the sample. We use a statistical mechanics approach to the problem of deconvoluting such partial concentrations from mixed samples, explore this approach using Markov chain Monte Carlo simulations, and give analytical results for when and how well samples can be unmixed.

Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.

The imposition of a cost constraint for constructing the optimal navigation structure surely represents a crucial ingredient in the design and development of any realistic navigation network. Previous works have focused on optimal transport in small-world networks built from two-dimensional lattices by adding long-range connections with Manhattan length $r_{ij}$ taken from the distribution $P_{ij}\sim r_{ij}^{-\alpha }$, where $\alpha$ is a variable exponent. It has been shown that, by introducing a cost constraint on the total length of the additional links, regardless of the strategy used by the traveler (independent of whether it is based on local or global knowledge of the network structure), the best transportation condition is obtained with an exponent $\alpha =d+1$, where $d$ is the dimension of the underlying lattice. Here we present further support, through a high-performance real-time algorithm, on the validity of this conjecture in three-dimensional regular as well as in two-dimensional critical percolation clusters. Our results clearly indicate that cost constraint in the navigation problem provides a proper theoretical framework to justify the evolving topologies of real complex network structures, as recently demonstrated for the networks of the US airports and the human brain activity.

We study the failure of disordered materials by numerical simulations of the random fuse model. We identify emergent patterns of localized damage prior to catastrophic failure by statistically averaging the density of damage around the eventual failure nucleation point. The resulting pattern depends on fracture density and obeys the same scaling relations as would be expected for the stress field generated by a critical crack nucleating in a finite, disorder-free effective medium of varying size. The growth of this critical crack absorbs preexisting clusters according to a well-defined scaling relation. Unfortunately, in single model runs such precursory signals are not obvious. Our results imply that reliable and accurate prediction of failure in time-independent, microscopically brittle random materials in a real case is inherently problematic, and degrades with system size.

Adaptive networks, which combine topological evolution of the network with dynamics on the network, are ubiquitous across disciplines. Examples include technical distribution networks such as road networks and the internet, natural and biological networks, and social science networks. These networks often interact with or depend upon other networks, resulting in coupled adaptive networks. In this paper we study susceptible-infected-susceptible (SIS) epidemic dynamics on coupled adaptive networks, where susceptible nodes are able to avoid contact with infected nodes by rewiring their intranetwork connections. However, infected nodes can pass the disease through internetwork connections, which do not change with time: The dependencies between the coupled networks remain constant. We develop an analytical formalism for these systems and validate it using extensive numerical simulation. We find that stability is increased by increasing the number of internetwork links, in the sense that the range of parameters over which both endemic and healthy states coexist (both states are reachable depending on the initial conditions) becomes smaller. Finally, we find a new stable state that does not appear in the case of a single adaptive network but only in the case of weakly coupled networks, in which the infection is endemic in one network but neither becomes endemic nor dies out in the other. Instead, it persists only at the nodes that are coupled to nodes in the other network through internetwork links. We speculate on the implications of these findings.

We identify universal spatial fluctuations in systems with nontrivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations, and spin currents, both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction. We support our claim of universality with the excellent agreement between the numerical results and system-independent spatial correlations of a random field defined on both the spatial and spin degrees of freedom. A rigorous identity relating our universal predictions with response functions provides a direct physical interpretation of our results in the framework of linear response theory.

Employing Monte Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing temperature. The corresponding transition temperature depends separately on the number of particles $N$ and the box size $L$, implying nonextensivity due to the long-range character of the interactions. The probability density of the spacing between the particles exhibits at low temperatures an accumulation of discrete peaks with an overall asymmetric shape. In the vicinity of the transition temperature it is of a Gaussian form, whereas in the high-temperature regime an exponential decay is observed. The high-temperature behavior shows a cluster phase with a mean cluster size that first increases with the temperature and then saturates. The crossover is clearly identifiable also in the nonlinear behavior of the heat capacity with varying temperature. The influence of the trapping potential on the observed results as well as possible experimental realizations are briefly addressed.

The three-dimensional jamming of neutrally buoyant monodisperse, bidisperse, and tridisperse mixtures of particles flowing through a restriction under fluid flow has been studied. During the transient initial accumulation of particles at the restriction, a low probability of a jamming event is observed, followed by a transition to a steady-state flowing backlog of particles, where the jamming probability per particle reaches a constant. Analogous to the steady-state flow in gravity-driven jams, this results in a geometric distribution describing the number of particles that discharge prior to a jamming event. We develop new models to describe the transition from an accumulation to a steady-state flow, and the jamming probability after the transition has occurred. Predictions of the behavior of the geometric distribution see the log-probability of a jam occurring proportionally to $(R_2^2-1)$, where $R_2$ is the ratio of opening diameter to the second moment number average particle diameter. This behavior is demonstrated to apply to more general restriction shapes, and collapses for all mixture compositions for the restriction sizes tested.