We introduce and solve a model of hardcore particles on a one-dimensional periodic lattice which undergoes an active–absorbing-state phase transition at finite density. In this model, an occupied site is defined to be active if its left neighbor is occupied and the right neighbor is vacant. Particles from such active sites hop stochastically to their right. We show that both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these nonequilibrium phase transitions belong to a new universality class different from the generic active–absorbing-state phase transition, namely, directed percolation.

We study the diffusive behavior of two-dimensional charged colloidal suspensions subjected to a sinusoidal substrate by means of Brownian dynamics simulations. We mainly focus on the dependence of the mean-square displacement on the substrate strength. Our findings show a variation in the particle diffusion due to a substrate-induced distortion of the dynamic cage of nearest-neighbor colloids. This mechanism leads to a transition from normal diffusion at short times to subdiffusion on intermediate time scales. However, at long times normal diffusion is recovered. We also show that the variation in the long-time self-diffusion coefficient may be associated with the freezing and re-entrant melting transitions.

In this paper, we analyze the influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites (IPMCs). We use the modified Poisson-Nernst-Planck equations to describe the electric potential and mobile counterion distributions within the IPMC for a steady voltage applied across the IPMC rough electrodes. We present an analytical solution of the nonlinear three-dimensional boundary value problem based on the method of matched asymptotic expansions. The distribution of mobile counterions within the polymer region is characterized by thin boundary layers in the proximity to the polymer-electrode interfaces, where enrichment and depletion of mobile charges take place. The presence of rough landscapes drastically increases the polymer-electrode surfaces and thereby significantly improves the overall charge storage. We determine closed-form expressions for the average bending moment produced by the IPMC and for its average stored charge and capacitance. We show that the bending moment produced by an IPMC is linearly proportional to the stored charge, which in turn increases nonlinearly as the voltage applied across the electrodes increases. The average charge stored in the IPMC increases as the electrode surface roughness increases and decreases as steric effects become prominent.

Biological systems need to process information in real time and must trade off accuracy of presentation and coding costs. Here we operationalize this trade-off and develop an information-theoretic framework that selectively extracts information of the input past that is predictive about the output future, obtaining a generalized eigenvalue problem. Thereby, we unravel the input history in terms of structural phase transitions corresponding to additional dimensions of a state space. We elucidate the relation to canonical correlation analysis and give a numerical example. Altogether, this work relates information-theoretic optimization to the joint problem of system identification and model reduction.

We present the results of a numerical study of flow past an inclined flat plate and reveal a route of the transition from steady to chaotic flow. We find that the chaotic flow regime can be reached through the sequential occurrence of successive period-doubling bifurcations and various incommensurate bifurcations. The results provide physical insight into the understanding of fundamental flow behaviors underlying in this flow system and complement the transition phenomenon from steady to chaotic flow.

Volume alteration in solid materials is a common cause of material failure. Here we investigate the crack formation in thin elastic layers attached to a substrate. We show that small variations in the volume contraction and substrate restraint can produce widely different crack patterns ranging from spirals to complex hierarchical networks. The networks are formed when there is no prevailing gradient in material contraction, whereas spirals are formed in the presence of a radial gradient in the contraction of a thin elastic layer.

This paper presents the results of theoretical studies of high-pressure $p$ (tens and hundreds of Torr) direct current (dc) discharges in argon. The diffuse (D), constricted-stratified (CS), and constricted (C) discharge modes are studied using a developed one-dimensional (radial) model. The model includes the conservation equations for electrons, ions (${\text{Ar}}^{+}$ and ${\text{Ar}}_2^{+}$), and excited atoms (metastable and resonant states) for mean electron energy and for the temperature of the high-energy part of the electron-energy distribution function (EEDF), the heat conduction equation for the neutral gas, and Poisson’s equation for the radial electric field. The developed model of a dc discharge allowed us, without any artificial assumptions, to obtain periodic oscillations of plasma parameters for the CS mode and to describe a hysteresis transition between the D mode and the CS mode. Direct transition from the D to the CS mode is accompanied by an increase of several orders of magnitude in the electron density at the discharge axis and the appearance of moving striations. It was shown that the experimentally observed hysteresis of the current-voltage characteristic at the transition between the CS and D modes deals with the nonlocal formation of the EEDF, namely, the diffusion of high-energy electrons from the central constricted region. The effect of the nonlocal formation of the EEDF is taken into account by introducing the effective temperature of the high-energy part of the EEDF and solving the equation for the radial profile of this temperature. The transition from the CS mode to the C mode occurs smoothly, without any jumps of the plasma parameters. Plasma parameters and characteristics of all three modes and transitions between these modes are calculated and compared with experimental data.

This paper presents an investigation of electron density and electron temperature in a dust cloud, subject to radiation, which causes photoelectric emission of electrons. The analysis is based on charge neutrality and number and energy balance of electrons. Appropriate expressions for the photoelectric emission and mean energy of emitted photoelectrons have been employed. The parametric relationship, corresponding to dust of stainless steel (as an illustration) in the near space environment, with dominant Lyman $\alpha$ $\left(1215.7\text{Å}\right)$ radiation in the extreme ultraviolet part of the spectrum, has been investigated.

Stark broadening of hydrogen lines in the presence of a magnetic field is revisited, with emphasis on the role of the ion component under typical conditions of magnetized fusion devices. An impact theory for ions valid at low density $\left(N_e\lesssim {10}^{14}{\text{cm}}^{-3}\right)$ and taking into account the Zeeman degeneracy removal of the atomic states is developed. It is shown that the Stark widths of the Lorentz triplet components strongly depend on the magnetic field. The model is validated by a computer simulation method. For the lateral $\sigma$ components of $\text{Ly}\alpha$, we show that the impact approximation still holds for densities as high as $N_e\sim {10}^{15}{\text{cm}}^{-3}$. In contrast, for the central $\pi$ component as well as for the other lines from low principal quantum number, significant discrepancies between the proposed theory and the simulation results appear at high density. Application to $D\alpha$ in tokamak divertor plasma conditions shows that, in this case, the quasistatic approximation becomes more relevant.

The collisional effects on the current-filamentation instability (CFI) and the two-stream instability (TSI), which appear as a relativistic intense electron beam penetrating into a cold dense plasma, are investigated. It is shown that the growth rate of the CFI mode is first attenuated and then enhanced by the collisional effects as the density ratio of the background plasma to the beam increases. Meanwhile, the maximum CFI growth rate is shifted to the long-wavelength region due to both the bulk plasma density increase and the collisional effects, resulting in larger filaments formation. On the other hand, collisional effects mainly attenuate the TSI and finally stabilize it. Numerical solutions under parameters close to the fast ignition scenario (FIS) are given, which show that the CFI growth rate can be enhanced by 2 orders of magnitude instead of being suppressed in the dense region. Therefore, the CFI-induced electron filaments formation and the resultant kinetic anomalous heating are potentially significant for the target heating in the FIS.

This paper presents numerical simulations that have been carried out to study the thermodynamic and hydrodynamic responses of a solid copper cylindrical target that is facially irradiated along the axis by one of the two Large Hadron Collider (LHC) 7 TeV/$c$ proton beams. The energy deposition by protons in solid copper has been calculated using an established particle interaction and Monte Carlo code, FLUKA, which is capable of simulating all components of the particle cascades in matter, up to multi-TeV energies. These data have been used as input to a sophisticated two-dimensional hydrodynamic computer code BIG2 that has been employed to study this problem. The prime purpose of these investigations was to assess the damage caused to the equipment if the entire LHC beam is lost at a single place. The FLUKA calculations show that the energy of protons will be deposited in solid copper within about 1 m assuming constant material parameters. Nevertheless, our hydrodynamic simulations have shown that the energy deposition region will extend to a length of about 35 m over the beam duration. This is due to the fact that first few tens of bunches deposit sufficient energy that leads to high pressure that generates an outgoing radial shock wave. Shock propagation leads to continuous reduction in the density at the target center that allows the protons delivered in subsequent bunches to penetrate deeper and deeper into the target. This phenomenon has also been seen in case of heavy-ion heated targets [N. A. Tahir, A. Kozyreva, P. Spiller, D. H. H. Hoffmann, and A. Shutov, Phys. Rev. E 63, 036407 (2001)]. This effect needs to be considered in the design of a sacrificial beam stopper. These simulations have also shown that the target is severely damaged and is converted into a huge sample of high-energy density (HED) matter. In fact, the inner part of the target is transformed into a strongly coupled plasma with fairly uniform physical conditions. This work, therefore, has suggested an additional very important application of the LHC, namely, studies of HED states in matter.

The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the Lévy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary in the long-time limit and it represents the Lévy process with a simple scaling. The solution for the drift term in the form $\lambda \text{sgn}\left(x\right)$ possesses two different scales which correspond to the Lévy indexes $\mu$ and $\mu +1$ $\left(\mu <1\right)$. The former component of the solution prevails at large distances but it diminishes with time for a given $x$. The fractional moments, as a function of time, are calculated. They rise with time and the rate of this growth increases with $\lambda$.

Deformation of spheroidal ferrogel bodies caused by a uniform magnetic field is investigated theoretically. The deformation is induced by two competitive mechanisms—magnetostatic and magnetostrictive. The former is due to the demagnetizing field of the sample and hence depends on its shape, while the latter originates from the magnetoelasticity of ferrogel and is shape independent. Both mechanisms are dipolar in nature and contribute—for a body of commensurate dimensions—oppositely to the effect. For an isotropic ferrogel sphere, the magnetostatic contribution still prevails and the magnetic field elongates the body. The two opposing mechanisms balance each other out for a prolate spheroidal sample with the axes aspect ratio $a/b\approx 1.3$. It determines the so-called “Procrustes point” or “Procrustes size”—the magnetic field shrinks the body if $a>1.3b$ and stretches it when $a<1.3b$.

Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the spatial correlations of the field. Comparison to the simulation results for the distribution of the size of the cluster indicates that the distribution of an average field could serve as a useful tool for the estimation of the asymptotic behavior of the distribution of the size of the clusters for “deep” clusters where value of the field on each site is much greater than the rms disorder.

In this paper, we show how a fixed-point-based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we choose a two-species ASEP which has interesting phase transitions not seen in the one-species case. We also apply this method to the single-species problem where the analysis is simple but nevertheless quite insightful.

Extensive Monte Carlo simulations on three qualitatively different model supercritical fluids (square-well fluid, Lennard-Jonesium, and primitive water) have been performed to examine percolation threshold parameters for continuum (correlated) models and their relation to general results valid for random lattice models; random-site percolation simple-cubic lattice has therefore been considered as well. Two different bond criteria, the configurational and self-bound ones, defining a cluster have been used. In addition to the percolation threshold occupation probability $p_c$ and the percolation threshold fluid density ${\rho }_c$, the correlation length exponent $\nu$ and the wrapping probability at the percolation threshold $R_{w,c}$ have also been evaluated. It is found that parameters $\nu$ and $R_{w,c}$ exhibit not only strong temperature dependence but also, unlike the case of lattice systems, dependence on the nature of the system considered and the employed definition of the cluster.

We study the effects of global noise on waves in heterogeneous, spatially clustered, reaction-diffusion systems with possible applications to calcium signaling. We first discuss how clustering of the excitability determines the dynamics by shifting bifurcation points and creating new oscillatory solutions. We then consider the specific situation, where intrinsic noise, due to the smallness of the excitable patches, destroys the global oscillatory state. We show that additional small global fluctuations, however, can partially restore temporal and spatial coherence of the oscillatory signal.

We investigate transport properties of DNA sequences in human chromosome 22 and compare the results with those of a random artificial DNA sequence based on the single- and double-stranded charge transfer models. The statistical quantities, including the Hurst exponent, the distribution of Lyapunov exponent (LE), the central moments, and the scaling parameter, are numerically calculated by using the transfer-matrix approach. It is found that the existence of satellite DNA segments in human chromosome 22 could result in deviations from usual Gaussian distribution of LE. Our results suggest that the presence of the satellite DNA segments, together with the long-range correlations and the base-pairing correlations could lead to the violation of single-parameter scaling hypothesis which holds for the random artificial DNA sequence although the behaviors of the averaged LEs for both DNA sequences are similar. This provides a viewpoint to analyze differences between the genomic DNA sequences and the nonliving random ones on the basis of localization properties of wave functions in the sequences.

A global feedback control of a system that exhibits a subcritical monotonic instability at a nonzero wave number (short-wave or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. This system is studied analytically and numerically. It is shown that feedback control, based on measuring the maximum of the pattern amplitude over the domain, can stabilize the system and lead to the formation of localized unipulse stationary states or traveling solitary waves. It is found that the unipulse traveling structures result from an instability of the stationary unipulse structures when one of the parameters characterizing the coupling between the periodic pattern and the zero mode exceeds a critical value that is determined by the zero mode damping coefficient.