We formulate the statistical mechanical description of liquid systems for both polarizable and polar systems in an electric field in the $\mathbf{E}$ ensemble, which is the pendant to the thermodynamic description in terms of the free energy at constant potential. The contribution of the electric field to the configurational integral ${\tilde{Q}}_N\left(\mathbf{E}\right)$ in the $\mathbf{E}$ ensemble is given in an exact form as a factor in the integrand of ${\tilde{Q}}_N\left(\mathbf{E}\right)$. We calculate the contribution of the electric field to the Ornstein-Zernike formula for the scattering function in the $\mathbf{E}$ ensemble. As an application, we determine the field-induced shift of the critical temperature for polarizable and polar liquids and show that the shift is upward for polarizable liquids and downward for polar liquids.

Using the level-spacing (LS) statistics, we have investigated the localization-delocalization transitions (LDTs) in Hessian matrices of a simple fluid with short-ranged interactions. The model fluid is a prototype of topologically disordered systems and its Hessian matrices are recognized as an ensemble of Euclidean random matrices with elements subject to several kinds of constraints. Two LDTs in the Hessian matrices are found, with one in the positive-eigenvalue branch and the other in the negative-eigenvalue one. The locations and the critical exponents of the two LDTs are estimated by the finite-size scaling for the second moments of the nearest-neighbor LS distributions. Within numerical errors, the two estimated critical exponents are almost coincident with each other and close to that of the Anderson model (AM) in three dimensions. The nearest-neighbor LS distribution at each LDT is examined to be in a good agreement with that of the AM at the critical disorder. We conclude that the LDTs in the Hessian matrices of topologically disordered systems exhibit the critical behaviors of orthogonal universality class.

We study the stochastically forced Lorenz model in the parameter zone admitting two coexisting limit cycles under the transition to chaos via period-doubling bifurcations. Noise-induced transitions between both different parts of the single attractor and two coexisting separate attractors are demonstrated. The effects of structural stabilization and noise symmetrization are discussed. We suggest a stochastic sensitivity function technique for the analysis of noise-induced transitions between two coexisting limit cycles. This approach allows us to construct the dispersion ellipses of random trajectories for any Poincare sections. Possibilities of our descriptive-geometric method for a detailed analysis of noise-induced transitions between two periodic attractors of Lorenz model are demonstrated.

Stochastic pooling networks (SPN) are sensor networks where multiple sensors make independently noisy and compressed measurements of the same information source, which are combined via pooling. Examples of SPNs range from nanoelectronics to biological sensory neurons. Here it is shown that optimal information transmission in SPNs with nodes that quantize to a finite number of states requires the input signal distribution to be discrete. This is illustrated numerically for a simple SPN consisting of $N$ binary-quantizing sensors. The resultant information capacity is shown to be independent of the noise distribution when the signal distribution can be freely chosen, but to imply an optimal noise distribution if the signal distribution is fixed. While larger than the best performance of previously studied continuously valued input signals, the capacity does not scale faster than the previous best result of ${\text{log}}_2\left(\sqrt{N}\right)$ bits per channel use. It is also shown that a plot of the optimal input distribution contains bifurcations as $N$ increases, and that suprathreshold stochastic resonance occurs when the mutual information is determined for a suboptimal noise distribution.

The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these functions as determinants of $N\times N$ matrices and then extrapolate to $N\to \infty$. This formulation allows for a quick and accurate numerical evaluation of these quantities for point processes in Euclidean spaces of dimension $d$. We also implement an algorithm due to Hough et al. for generating configurations of determinantal point processes in arbitrary Euclidean spaces, and we utilize this algorithm in conjunction with the aforementioned numerical results to characterize the statistical properties of what we call the Fermi-sphere point process for $d=1–4$. This homogeneous, isotropic determinantal point process, discussed also in a companion paper [S. Torquato, A. Scardicchio, and C. E. Zachary, J. Stat. Mech.: Theory Exp. (2008) P11019.], is the high-dimensional generalization of the distribution of eigenvalues on the unit circle of a random matrix from the circular unitary ensemble. In addition to the nearest-neighbor probability distribution, we are able to calculate Voronoi cells and nearest-neighbor extrema statistics for the Fermi-sphere point process, and we discuss these properties as the dimension $d$ is varied. The results in this paper accompany and complement analytical properties of higher-dimensional determinantal point processes developed in a prior paper.

We study a one-dimensional gas of needlelike objects as a testing ground for a formalism that relates the thermodynamic properties of “hard” potentials to the probabilities for contacts between particles. Specifically, we use Monte Carlo methods to calculate the pressure and elasticity coefficient of the hard-needle gas as a function of its density. The results are then compared to the same quantities obtained analytically from a transfer-matrix approach.

The radiometric force on several configurations of heated plates placed in a stagnant gas is examined experimentally, with a high-resolution thrust stand, and numerically using the direct simulation Monte Carlo method and a discrete ordinate solution of a model kinetic equation. A wide range of pressures from 0.006 to 6 Pa was examined, corresponding to Knudsen numbers from 20 to 0.02, in argon and helium test gases. The radiometric force, important in a number of emerging micro- and nanoscale applications, is shown to be mostly area dependent in the transitional regime where it reaches its maximum at $\text{Kn}\sim 0.1$.

Using methods of statistical physics, we present rigorous theoretical calculations of Eigen’s quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of information carriers. As the mutation rate is increased from small values to large values, one can observe three phases: the first (I) selective (also known as ferromagnetic) phase, the second (II) intermediate phase with some residual order, and the third (III) completely randomized (also known as paramagnetic) phase. We calculate the phase diagram for these phases and the concentration of information carriers in the master sequence (also known as peak configuration) $x_0$ and other classes of information carriers. As the phase point moves across the boundary between phase I and phase II, $x_0$ changes continuously; as the phase point moves across the boundary between phase II and phase III, $x_0$ has a large change. Our results are applicable for the general case of a fitness landscape.

Recent literature has presented evidence that the study of navigation in complex networks is useful to understand their dynamics and topology. Two main approaches are usually considered: navigation of random walkers and navigation of directed walkers. Unlike these approaches ours supposes that a traveler walks optimally in order to minimize the cost of the walking. If this happens, two extreme regimes arise—one dominated by directed walkers and the other by random walkers. We try to characterize the critical point of the transition from one regime to the other in function of the connectivity and the size of the network. Furthermore, we show that this approach can be used to generalize several concepts presented in the literature concerning random navigation and direct navigation. Finally, we defend that investigating the extreme regimes dominated by random walkers and directed walkers is not sufficient to correctly assess the characteristics of navigation in complex networks.

We revisit the classical model for voter dynamics in a two-party system with two basic modifications. In contrast to the original voter model studied in regular lattices, we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance. In addition, we incorporate the rapidly changing nature of the interpersonal relations in the model. At each time step, agents can update their relationships. This update is determined by their own opinion, and by their preference to make connections with individuals sharing the same opinion, or rather with opponents. In this way, the network is built in an adaptive manner, in the sense that its structure is correlated and evolves with the dynamics of the agents. The simplicity of the model allows us to examine several issues analytically. We establish criteria to determine whether consensus or polarization will be the outcome of the dynamics and on what time scales these states will be reached. In finite systems consensus is typical, while in infinite systems a disordered metastable state can emerge and persist for infinitely long time before consensus is reached.

The problem of detection and quantitative characterization of directional couplings in an ensemble of noisy oscillators from a time series is addressed. We suggest estimators for the strengths of couplings which are based on modeling the observed oscillations with a set of stochastic phase oscillators and easily interpreted from a physical viewpoint. Moreover, we present an analytic formula for a statistical significance level allowing to reveal an architecture of couplings reliably from a relatively short time series. The technique applies to weakly coupled nonsynchronized oscillators. It is introduced for oscillators with close basic frequencies but can be readily generalized to the case of arbitrary frequencies. Efficiency of the technique is demonstrated in numerical experiments.

Heterogeneity is one of the most important and ubiquitous types of external perturbations in dissipative systems. To know the behaviors of pulse waves in such media is closely related to studying the collision process between the pulse and the heterogeneity-induced-ordered pattern. In particular, we focus on unidirectional propagation of pulses in a medium with an asymmetric bump heterogeneity. This topic has attracted much interest recently with respect to potential computational aspects of chemical pulse propagation as well as with respect to pulse propagation in biological signal processing. We employ a three-component reaction-diffusion system with one activator and two inhibitor species to illustrate these issues. The reduced dynamics near a drift bifurcation describes the phenomena in the full partial differential equations by ordinary differential equations. Such a reduced dynamics is able to capture unidirectional propagation properties of pulses near an asymmetric heterogeneity in a qualitatively correct way. A remarkable feature is that such unidirectional behavior is linked to the imperfection of global bifurcation structure and the resulting asymmetric locations of critical points.

We have simulated the dynamics of a butane molecule and computed the time evolution of two sets of collective variables: (a) internal variables (stretchings, bendings, and dihedral angle) and (b) variables derived from a principal component analysis (PCA). We have characterized each collective variable by a coherence time, the time needed to develop its chaotic behavior. The coherence times diminish significantly when the temperature is raised into and above the range where conformational transitions of the dihedral angle set in. Below this transition region the coherence times of some variables reach hundreds of picoseconds (principal components) or even nanoseconds (internal variables); moreover, there are large differences among variables, as their coherence time can be much larger or much smaller than the Lyapunov time of the whole molecule. This result reflects the prediction of Nekhoroshev’s theorem. Crossing the transition region, the coherence times of both sets of variables drop to few picoseconds, and the differences among variables diminish. Still, the coordinates and velocities characterized by the largest fluctuations in the PCA appear to be also the most coherent ones, below and above the transition region.

We present a methodology to characterize synchronization in time series based on symbolic representations. Each time series is mapped onto a sequence of $p$-dimensional delay vectors that are subsequently transformed into symbols by means of a rank-ordering of their values. Based on these representations, we propose a transcription scheme between symbols of the respective time series to study synchronization properties. Group-theoretical considerations and the use of information measures allow us to classify regimes of synchronization and to assess its strength. We apply our method to a prototype nonlinear system, which reveals a rich variety of coupled dynamics. We investigate in detail the robustness of the derived synchronization measure against noise and compare its value with that of the established measures.

We discuss an elementary model of a turbulent boundary layer over a flat surface given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a nonslip boundary-condition line. We are able to reproduce several important features of realistic flows, such as the viscous and logarithmic boundary sublayers, and the general behavior of the first statistical moments (turbulent intensity, skewness, and flatness) of the streamwise velocity fluctuations. As an application, we advance some heuristic considerations on the boundary layer underlying kinematics that could be associated with the phenomenon of drag reduction by polymers, finding a suggestive support from its experimental signatures.

A carbon nanotube (CNT) can be viewed as a molecular nozzle. It has a cylindrical shape of atomistic regularity, and the diameter can be even less than 1 nm. We have conducted molecular-dynamics simulations of water jet from a (6,6) CNT that confines water in a form of single-file molecular chain. The results show that the water forms nanoscale clusters at the outlet and they are released intermittently. The jet breakup is dominated by the thermal fluctuations, which leads to the strong dependence on the temperature. The cluster size $n$ decreases and the release frequency $f$ increases at higher temperatures. The $f$ roughly follows the reaction kinetics by the transition state theory. The speed of a cluster is proportional to the $1/\sqrt{n}$ because of the central limit theorem. These properties make great contrast with the macroscopic liquid jets.

A theoretical model shows that in the context of a Ginzburg-Landau equation with rapidly varying, mean-zero dispersion, stable and attracting self-similar breathers are formed with parabolic profiles. These self-similar solutions are the final solution state of the system, not a long-time, intermediate asymptotic behavior. A transformation shows the self-similarity to be governed by a nonlinear diffusion equation with a rapidly varying, mean-zero diffusion coefficient. The alternating sign of the diffusion coefficient, which is driven by the dispersion fluctuations, is critical to supporting the parabolic profiles which are, to leading order, of the Barenblatt form. Our analytic model proposes a mechanism for generating physically realizable temporal parabolic pulses in the Ginzburg-Landau model.

We analyze the scattering of the classical sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well. We show that the breather can pass through the well and exit with a speed different, sometimes larger, from the initial one. It can also be trapped and very slowly decay inside the well or bounce out of the well and go back to where it came from. We also show that the breather can split into a kink–antikink pair when it hits the well.

To control numerical errors accumulated over tens of millions of time steps during the integration of a set of highly coupled equations of motion is not a trivial task. In this paper, we propose a parallel algorithm for spin dynamics and the newly developed spin-lattice dynamics simulation [P. W. Ma et al., Phys. Rev. B 78, 024434 (2008)]. The algorithm is successfully tested in both types of dynamic calculations involving a million spins. It shows good stability and numerical accuracy over millions of time steps $\left(\sim 1\text{ns}\right)$. The scheme is based on the second-order Suzuki-Trotter decomposition (STD). The usage can avoid numerical energy dissipation despite the trajectory and machine errors. The mathematical base of the symplecticity, for properly decomposed evolution operators, is presented. Due to the noncommutative nature of the spin in the present STD scheme, a unique parallel algorithm is needed. The efficiency and stability are tested. It can attain six to seven times speed up when eight threads are used. The run time per time step is linearly proportional to the system size.

We study the behavior of the Casimir force in $O\left(n\right)$ systems with a diffuse interface and slab geometry ${\infty }^{d-1}\times L$, where $2<d<4$ is the dimensionality of the system. We consider a system with nearest-neighbor anisotropic interaction constants $J_{\parallel }$ parallel to the film and $J_{\perp }$ across it. We argue that in such an anisotropic system the Casimir force, the free energy, and the helicity modulus will differ from those of the corresponding isotropic system, even at the bulk critical temperature, despite that these systems both belong to the same universality class. We suggest a relation between the scaling functions pertinent to the both systems. Explicit exact analytical results for the scaling functions, as a function of the temperature $T$, of the free energy density, Casimir force, and the helicity modulus are derived for the $n\to \infty$ limit of $O\left(n\right)$ models with antiperiodic boundary conditions applied along the finite dimension $L$ of the film. We observe that the Casimir amplitude ${\Delta }_{\text{Casimir}}(d\mid J_{\perp },J_{\parallel })$ of the anisotropic $d$-dimensional system is related to that of the isotropic system ${\Delta }_{\text{Casimir}}\left(d\right)$ via ${\Delta }_{\text{Casimir}}(d\mid J_{\perp },J_{\parallel })={(J_{\perp }∕J_{\parallel })}^{(d-1)∕2}{\Delta }_{\text{Casimir}}\left(d\right)$. For $d=3$ we derive the exact Casimir amplitude ${\Delta }_{\text{Casimir}}(3,\mid J_{\perp },J_{\parallel })=[{\mathrm{Cl}}_2(\pi ∕3)∕3-\zeta \left(3\right)∕\left(6\pi \right)](J_{\perp }∕J_{\parallel })$, as well as the exact scaling functions of the Casimir force and of the helicity modulus ${\rm Y}(T,L)$. We obtain that ${\beta }_c{\rm Y}(T_c,L)=(2∕{\pi }^2)[{\mathrm{Cl}}_2(\pi ∕3)∕3+7\zeta \left(3\right)∕\left(30\pi \right)](J_{\perp }∕J_{\parallel })L^{-1}$, where $T_c$ is the critical temperature of the bulk system. We find that the contributions in the excess free energy due to the existence of a diffuse interface result in a repulsive Casimir force in the whole temperature region.