We numerically study the process of quasistatic invasion of a nonwetting fluid in 2D and 3D porous layers from multiple inlet injection sources and show that a porous layer acts as a two-phase filter as a result of the repeated convergence of flow paths: The probability for a pore at the outlet to be a breakthrough point is significantly lower than the fraction of active injection points at the inlet owing to the merging within the porous layer of liquid paths originating from different inlet injection points. The study of the breakthrough point statistics indicates that the number of breakthrough points diminishes with the system thickness and that the behavior of thin layers, defined here as systems of typical thicknesses of less than 15 lattice spacing units (≈15 pore or grain mean sizes), is distinct from thicker layers. For thicker systems, it is found that the probability of an outlet pore to be a breakthrough pore scales as $l^{1-d}$ where $l$ is the system thickness and $d$ is the space dimensionality, whereas, a power law behavior is not obtained with a thin system. Other properties, such as the invading phase occupancy profiles are studied. We also described a kinetic algorithm that allowed us to compute the occurrence times of breakthrough points. The distribution of these times is markedly different in 2D and in 3D.

We perform molecular dynamics simulations to investigate dynamical properties of a supercritical Lennard-Jones fluid. We find that in the supercritical region there is a short-ranged deviation in dynamic character. We further find that this anomalous change is associated with the presence of the Widom line, the locus of specific heat maxima, of the liquid-vapor phase transition. The salient change in dynamics is consistent with a crossover in the correlation of the diffusion coefficient with the excess entropy. Our results lead to an interpretation that, even though a supercritical fluid excludes a singularity, its dynamical properties can be significantly affected by the existence of thermodynamic response maxima.

We employ a continuum theory of solvent-free ionic liquids accounting for both short-range electrostatic correlations and steric effects (finite ion size) [Bazant et al., Phys. Rev. Lett. 106, 046102 (2011)] to study the response of a model microelectrochemical cell to a step voltage. The model problem consists of a 1-1 symmetric ionic liquid between two parallel blocking electrodes, neglecting any transverse transport phenomena. Matched asymptotic expansions in the limit of thin double layers are applied to analyze the resulting one-dimensional equations and study the overall charge-time relation in the weakly nonlinear regime. One important conclusion is that our simple scaling analysis suggests that the length scale $\sqrt{{\lambda }_D^{*}{l}_c^{*}}$ accurately characterizes the double-layer structure of ionic liquids with strong electrostatic correlations where $l_c^{*}$ is the electrostatic correlation length (in contrast, the Debye screening length ${\lambda }_D^{*}$ is the primary double-layer length for electrolytes) and the response time of ${\lambda }_D^{*3/2}{L}^{*}/\left(D^{*}{l}_c^{1/2}\right)$ (not ${\lambda }_D^{*}{L}^{*}/D^{*}$ that is the primary charging time of electrolytes) is the correct charging time scale of ionic liquids with strong electrostatic correlations where $D^{*}$ is the diffusivity and $L^{*}$ is the separation length of the cell. With these two new scales, data of both electric potential versus distance from the electrode and the total diffuse charge versus time collapse onto each individual master curve in the presence of strong electrostatic correlations. In addition, the dependance of the total diffuse charge on steric effects, short-range correlations, and driving voltages is thoroughly examined. The results from the asymptotic analysis are compared favorably with those from full numerical simulations. Finally, the absorption of excess salt by the double layer creates a depletion region outside the double layer. Such salt depletion may bring a correction to the leading order terms and break down the weakly nonlinear analysis. A criterion which justifies the weakly nonlinear analysis is verified with numerical simulations.

Nonlinear wrinkling of a compressed film on a soft substrate in the presence of inhomogeneous swelling actuation strain caused by solvent diffusion is studied. The simulation relies on a continuum model which integrates phase field microelasticity and Föppl–von Kármán plate theory. We show that the wrinkling morphologies developed in the diffusive domain exceeding a critical compression are confined and become shape and size dependent. A rich variety of wrinkling patterns observed in experiments including hexagonal ordered, dimple, or peanut structures, are numerically recovered, depending on the distribution of diffusion-mediated actuation strain. A cascade feature of the diffusion-coupled wrinkle is demonstrated as well: There are two ranges of solvent concentration within which the sequences of wrinkling pattern are different.

When dealing with the dissemination of epidemics, one important question that can be asked is the location where the contamination began. In this paper, we analyze three spreading schemes and propose and validate an effective methodology for the identification of the source nodes. The method is based on the calculation of the centrality of the nodes on the sampled network, expressed here by degree, betweenness, closeness, and eigenvector centrality. We show that the source node tends to have the highest measurement values. The potential of the methodology is illustrated with respect to three theoretical complex network models as well as a real-world network, the email network of the University Rovira i Virgili.

This work is devoted to pattern identification in systems with $S\left(1\right)$ symmetry based on limited experimental data. As we demonstrate, such pattern identification is complicated by the lack of a theoretical basis as well as by the presence of experimental uncertainties, and possible overlapping and missing points in the data. The study is motivated by a recent finding of physical systems where instabilities of different wave numbers may coexist and thus lead to several single-wave-number patterns superimposed with a random phase-shift between them. As shown in this work, such patterns cannot be identified with Fourier analysis as well as direct measurement of the wave numbers is not possible. We present both a constructive theoretical approach, which establishes the conditions under which the structure of such patterns is identifiable, and an example of application—the crown structure analysis in the drop splash problem. For the latter study, an experimental setup is developed based on high-speed stereo photography, which produces data suitable for a quantitative analysis of the observed patterns.

We present a dynamical analysis of chiral object motions to explain physical mechanisms and give quantitative predictions on the shear-induced drift motions of chiral objects and the chiral separation of enantiomers using shear flows. For objects well represented by the uniaxial approximation, such as DNA and chiral disk hexamers, dynamical motions in low-Reynolds-number shear flows are solved analytically, in terms of steady-state object-flow interacting parameters, which can be calculated numerically by well-established methods. The shear-induced drifting speed of long helices are evaluated. Good agreements are found between our results and those obtained from dynamical simulations [Makino and Doi, Phys. Fluids 17, 103605 (2005)]. We also compare our results with those obtained experimentally [Marcos, Fu, Powers, and Stocker, Phys. Rev. Lett. 102, 158103 (2009)]. The analysis may also be extended to study other important chiral-flow interactions in nature environments and microfluidic devices, such as the particle-wall and interparticle interactions.

The equation of state (EOS) for partially ionized carbon, oxygen, and carbon-oxygen mixtures at temperatures $3\times {10}^5\text{K}\lesssim T\lesssim 3\times {10}^6$ K is calculated over a wide range of densities, using the method of free energy minimization in the framework of the chemical picture of plasmas. The free energy model is an improved extension of our model previously developed for pure carbon [Potekhin, Massacrier, and Chabrier, Phys. Rev. E 72, 046402 (2005)]. The internal partition functions of bound species are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model, recently improved, in particular for the case of mixtures. We also propose a simple but accurate method of calculation of the EOS of partially ionized binary mixtures based on detailed ionization balance calculations for pure substances.

We explore the existence of moving nonradiating kinks in nonlocal generalizations of ${\phi }^4$ and ${\phi }^4$-${\phi }^6$ models. These models are described by nonlocal nonlinear Klein-Gordon equation, $u_{tt}-\mathcal{L}u+F\left(u\right)=0$, where $\mathcal{L}$ is a Fourier multiplier operator of a specific form and $F\left(u\right)$ includes either just a cubic term (${\phi }^4$ case) or cubic and quintic (${\phi }^4$-${\phi }^6$ case) terms. The general mechanism responsible for the discretization of kink velocities in the nonlocal model is discussed. We report numerical results obtained for these models. It is shown that, contrary to the traditional ${\phi }^4$ model, the nonlocal ${\phi }^4$ model does not admit moving nonradiating kinks but admits solitary waves that do not exist in the local model. At the same time the nonlocal ${\phi }^4$-${\phi }^6$ model describes moving nonradiating kinks. The set of velocities allowed for these kinks is discrete with the highest possible velocity $c_1$. This set of velocities is unambiguously determined by the parameters of the model. Numerical simulations show that a kink launched at the velocity $c$ higher than $c_1$ starts to decelerate, and its velocity settles down to the highest value of the discrete spectrum $c_1$.

We present a systematic analysis of the outcome of soliton collisions upon variation of the relative phase $\phi$ of the solitons, in the two-dimensional cubic-quintic complex Ginzburg-Landau equation in the absence of viscosity. Three generic outcomes are identified: merger of the solitons into a single one, creation of an extra soliton, and quasielastic interaction. The velocities of the merger soliton and the extra soliton can be effectively controlled by $\phi$. In addition, the range of the outcome of creating an extra soliton decreases to zero with the reduction of gain or the increasing of loss. The above features have potential applications in optical switching and logic gates based on interaction of optical solitons.

We analyze the electromagnetic field generated by a point charge intersecting the interface between vacuum and a nonmagnetic anisotropic medium with a plasma-type dispersion of the dielectric permittivity tensor. After penetrating the medium, the charge moves along its main axis. The total field is presented as a sum of a self-field (i.e., a charge field in a corresponding unbounded medium) and a scattered field associated with the boundary influence. We show that the self-field in the considered anisotropic medium is divided into a quasistatic field and a wave field (the so-called “plasma trace” is absent in the case under consideration). Under certain conditions, the Vavilov-Cherenkov radiation generated in the medium is reversed (i.e., the energy flux density vector forms an obtuse angle with the direction of the charge motion). Accordingly, so-called reversed Cherenkov-transition radiation (RCTR) can be generated. We analytically and numerically investigate both the scattered field and the total one, and we show that RCTR exists in the vacuum region if the charge velocity exceeds a certain threshold value associated with total internal reflection. Computations of the Fourier harmonics of the field as well as the total field itself demonstrate that RCTR in vacuum can be a dominant effect. Some properties of RCTR can be useful for diagnostics of particle bunches and determination of medium characteristics.

The problem of evaluating dissipative effects in Josephson junctions loaded by transmission lines is reexamined, for either the symmetric or the asymmetric case, with particular consideration of the time domain in which the interaction between junction and load system occurs.

The rich variety of densest columnar structures of identical hard spheres inside a cylinder can surprisingly be constructed from a simple and computationally fast sequential deposition of cylinder-touching spheres, if the cylinder-to-sphere diameter ratio is $D\in [1,2.7013]$. This provides a direction for theoretically deriving all these densest structures and for constructing such densest packings with nano-, micro-, colloidal, or charged particles, which all self-assemble like hard spheres.

We discuss vesicle-shaped transformations induced by an adhering spherical particle of different sizes using the classical Helfrich bending energy model. We focus on studying a model of an oblate vesicle with no spontaneous curvature in terms of fixed enclosing volume and surface area. Numerical solutions allow us to map out a complex phase diagram for such a simple, yet fundamental, physical system.

We study the (analytic) finite-size corrections in the Ising model on the strip with free, fixed ($++$), and mixed boundary conditions. For fixed ($++$) boundary conditions, the spins are fixed to the same values on two sides of the strip. We find that subdominant finite-size corrections to scaling should be to the form $a_p/N^{2p-1}$ for the free energy $f_N$ and $b_p/N^{2p-1}$ for inverse correlation length ${\xi }_N^{-1}$, with integer value of $p$. We investigate the set $\{a_p,b_p\}$ by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios $b_p/a_p$ remain constant upon varying coupling anisotropy. Such universal behavior is correctly reproduced by the conformal perturbative approach.

We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states.

In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over GF($q$), the Galois Field of order $q$. We present a scheme of low complexity and near-optimal empirical performance. The compression step is based on a reduction of a sparse low-density parity-check code over GF($q$) and is done through the so-called reinforced belief-propagation equations. These reduced codes appear to have a nontrivial geometrical modification of the space of codewords, which makes such compression computationally feasible. The computational complexity is $O\left(dnq{\log }_{2}q\right)$ per iteration, where $d$ is the average degree of the check nodes and $n$ is the number of bits. For our code ensemble, decompression can be done in a time linear in the code's length by a simple leaf-removal algorithm.

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

The effect of noise on nonlinear systems is analyzed, considering the case of slow-fast systems. It is known that small noise perturbations can induce a deterministic limit cycle in excitable systems when a specific scaling between the noise strength and the time-scale separation is achieved, a mechanism called self-induced stochastic resonance (SISR). The present study is focused on the impact of order 1 noise using the stochastic averaging principle. We introduce an elementary system of two coupled FitzHugh-Nagumo equations, which display the following nontrivial noise-induced behavior: (i) in the noise-free case, or for very small noise, the system fluctuates around its resting state; (ii) for small noise, oscillations appear due to SISR; (iii) for intermediate noise, the system fluctuates again around its resting state; (iv) for larger noise, new oscillations are observed and their explanation requires the application of the stochastic averaging principle. It is suggested that in the perspective of biological systems, time-scale separation may act as a “noise averager,” enabling a noise-controlled dynamical behavior through the averaging principle.

By incorporating ecological dynamics into evolutionary games, we introduce natural and unnatural death to the spatial prisoner's dilemma game in which individuals can play mixed strategies. This introduction can give a simple explanation for the emergence and abundance of cooperation in animal and human societies. We found that individuals are more likely to cooperate in a highly competitive environment. In addition, our simulation results suggest that the individuals would tend to cooperate when the temptation to defect is small.