Conserved lattice-gas models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents $\beta =1=\nu =\eta$, whereas the same on a ladder belong to directed percolation (DP) universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder forces the APT to be in the DP class. To substantiate this we introduce a class of restricted conserved lattice-gas models on a multichain system ($M\times L$ square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains, in the thermodynamic limit $L\to \infty ,$ these models exhibit APT at ${\rho }_c=\frac{1}{2}(1+\frac{1}{M})$ with $\beta =1.$ On the other hand, for even-chain systems transition occurs at ${\rho }_c=\frac{1}{2}$ with $\beta =1,2$ for $M=2,4$, respectively, and $\beta =3$ for $M\ge 6.$ We illustrate this unusual critical behavior analytically using a transfer-matrix method.

Understanding the influence of the structure of a dispersal network on the species persistence and modeling a realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the persistence of interacting ecological systems was studied [M. D. Holland and A. Hastings, Nature (London) 456, 792 (2008)], where it was shown that a randomization of the structure of a dispersal network in a metapopulation model of prey and predator increases the species persistence via clustering, prolonged transient dynamics, and amplitudes of population fluctuations. In this paper, by contrast, we show that a deterministic network topology in a metapopulation can also favor asynchrony and prolonged transient dynamics if species dispersal obeys a long-range interaction governed by a distance-dependent power law. To explore the effects of power-law coupling, we take a realistic ecological model, namely, the Rosenzweig-MacArthur model in each patch (node) of the network of oscillators, and show that the coupled system is driven from synchrony to asynchrony with an increase in the power-law exponent. Moreover, to understand the relationship between species persistence and variations in power-law exponent, we compute a correlation coefficient to characterize cluster formation, a synchrony order parameter, and median predator amplitude. We further show that smaller metapopulations with fewer patches are more vulnerable to extinction as compared to larger metapopulations with a higher number of patches. We believe that the present work improves our understanding of the interconnection between the random network and the deterministic network in theoretical ecology.

A positive Lyapunov exponent is the most convincing signature of chaos. However, existing methods for estimating the Lyapunov exponent from a time series often give unreliable estimates because they trace the time evolution of the distance between a pair of initially neighboring trajectories in phase space. Here, we propose a mathematical method for estimating the degree of dynamical instability, as a surrogate for the Lyapunov exponent, without tracing initially neighboring trajectories on the basis of the information entropy from a symbolic time series. We apply the proposed method to numerical time series generated by well-known chaotic systems and experimental time series and verify its validity.

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

The permeability of the bacterial outer membrane, enclosing Gram-negative bacteria, depends on the interactions of the outer, lipopolysaccharide (LPS) layer, with surrounding ions and molecules. We present a coarse-grained model for describing how cationic amphiphilic molecules (e.g., antimicrobial peptides) interact with and perturb the LPS layer in a biologically relevant medium, containing monovalent and divalent salt ions (e.g., ${\text{Mg}}^{\text{2+}}$). In our approach, peptide binding is driven by electrostatic and hydrophobic interactions and is assumed to expand the LPS layer, eventually priming it for disruption. Our results suggest that in parameter ranges of biological relevance (e.g., at micromolar concentrations) the antimicrobial peptide magainin 2 effectively disrupts the LPS layer, even though it has to compete with ${\text{Mg}}^{\text{2+}}$ for the layer. They also show how the integrity of LPS is restored with an increasing concentration of ${\text{Mg}}^{\text{2+}}$. Using the approach, we make a number of predictions relevant for optimizing peptide parameters against Gram-negative bacteria and for understanding bacterial strategies to develop resistance against cationic peptides.

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form $f^{\prime \prime }+{\left(\beta f^{\prime }\right)}^2+f=0$, where $\beta$ is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.

It is well known that Brownian motion can be described using Langevin equation. In this paper we extend the application of the Langevin equation to the Rayleigh-Bénard (RB) flow, assuming that each molecule in the system is a Brownian particle colliding with its surrounding molecules. The phenomenon of thermal instability, changing from a conductive to a convective state, is well reproduced by Langevin dynamics simulations. The roles of the drag force and the random force terms in the Langevin equation in triggering thermal instability are elucidated via numerical tests. Furthermore, we demonstrate that the strength of the fluctuation correlations increases as the Rayleigh number approaches the critical value, and the characteristics of the fluctuation correlations below the onset of instability foreshadow the form of the convective patterns emerging above the critical point. The Langevin equation, together with the form of the fluctuation correlations, sheds new light on the mechanism of the RB instability.

Inertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy's law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy's law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy's law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical justification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy's law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.

We describe a model for the study of the interaction of short x-ray free-electron laser (XFEL) pulses with large finite samples. Hydrodynamics is solved in one-dimensional planar geometry with consideration of the electron-ion energy exchange and of the possible elastoplastic behavior. From a time-dependent calculation of the complex refractive index and of the underlying atomic physics, XFEL energy deposition is modeled through a calculation of the radiation field in the material. In the case of hard x-ray irradiation, energetic electrons induced by the XFEL absorption can propagate and deposit their energy outside the interaction region. Simulations of the interaction of hard x-ray ultrashort pulses with solid materials Ru and Si at different grazing incidence angles are presented and discussed. The results obtained demonstrate the potential of this approach to predict damage dynamics for materials of interest for x-ray optics.

We have derived a hypernetted-chain-like (HNC-like) approximate closure of the Ornstein-Zernike equation for multibody dissipative particle dynamics (MDPD) system in which the classic closures are not directly practicable. We first point out that the Percus's method is applicable to MDPD system in which particles interact with a density-dependent potential. And then an HNC-like closure is derived using Percus's idea and the saddle-point approximation of particle free energy. This HNC-like closure is compared with results of previous researchers, and in many cases, it demonstrates better agreement with computer simulation results. The HNC-like closure is used to predict the cluster crystallization in MDPD. We determine whether the cluster crystallization will happen in a system utilizing the widely applicable Hansen-Verlet freezing criterion and by observing the radial distribution function. The conclusions drawn from the results of the HNC-like closure are in agreement with computer simulation results. We evaluate different weight functions to determine whether they are prone to cluster crystallization. A new effective density-dependent pairwise potential is also proposed to help to explain the tendency to cluster crystallization of MDPD systems.

It is difficult to obtain a core sample and information for digital core reconstruction of mature sandstone reservoirs around the world, especially for an unconsolidated sandstone reservoir. Meanwhile, reconstruction and division of clay minerals play a vital role in the reconstruction of the digital cores, although the two-dimensional data-based reconstruction methods are specifically applicable as the microstructure reservoir simulation methods for the sandstone reservoir. However, reconstruction of clay minerals is still challenging from a research viewpoint for the better reconstruction of various clay minerals in the digital cores. In the present work, the content of clay minerals was considered on the basis of two-dimensional information about the reservoir. After application of the hybrid method, and compared with the model reconstructed by the process-based method, the digital core containing clay clusters without the labels of the clusters’ number, size, and texture were the output. The statistics and geometry of the reconstruction model were similar to the reference model. In addition, the Hoshen-Kopelman algorithm was used to label various connected unclassified clay clusters in the initial model and then the number and size of clay clusters were recorded. At the same time, the $K$-means clustering algorithm was applied to divide the labeled, large connecting clusters into smaller clusters on the basis of difference in the clusters’ characteristics. According to the clay minerals’ characteristics, such as types, textures, and distributions, the digital core containing clay minerals was reconstructed by means of the clustering algorithm and the clay clusters’ structure judgment. The distributions and textures of the clay minerals of the digital core were reasonable. The clustering algorithm improved the digital core reconstruction and provided an alternative method for the simulation of different clay minerals in the digital cores.

A solvable, minimal model of diffusion in the presence of a reversible adsorption site is investigated. We show that the diffusive particles are influenced by the adsorbing site on transient times when they have anomalous subdiffusive behavior. However, the particle dispersion law crosses over to the normal diffusive regime on asymptotically long times. The subdiffusive regime is characterized by a $t^{1/4}$ transient scaling with the same exponent as for the irreversible adsorption. On this transient time scale dominated by particle adsorption, there is a depletion of particles near the adsorbing site, and the typical width of the depletion zone grows in time as $t^{1/4}$ with the same exponent as the subdiffusive dispersion. We show that having a nonzero desorption probability for the adsorbed particles produces a crossover towards normal diffusion on time scales larger than a characteristic reactive time, which we show scales with diffusivity and the adsorption site reactivity.

We develop a functional renormalization group (FRG) approach for the two-dimensional $XY$ model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)] with a duality transformation that explicitly introduces vortices via an integer-valued field. We show that the hierarchy of FRG flow equations for the infinite set of relevant and marginal couplings of the model can be reduced to the well-known Kosterlitz-Thouless renormalization group equations for the renormalized temperature and the vortex fugacity. Within our approach it is straightforward to include weak amplitude as well as out-of-plane fluctuations of the spins, which lead to additional interactions between the vortices that do not spoil the Berezinskii-Kosterlitz-Thouless transition. This demonstrates that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.

We propose a geometrical characterization of amorphous liquid structures that suppress crystallization by competing locally with crystalline order. We introduce for this purpose the crystal affinity of a liquid, a simple measure of its propensity to accumulate local crystalline structures on cooling. This quantity is explicitly related to the high-temperature structural covariance between local fluctuations in crystal order and that of competing liquid structures: favoring a structure that, due to poor overlap properties, anticorrelates with crystalline order reduces the affinity of the liquid. Using a lattice model of a liquid, we show that this quantity successfully predicts the tendency of a liquid to either accumulate or suppress local crystalline fluctuations with increasing supercooling. We demonstrate that the crystal affinity correlates strongly with the crystal nucleation rate and the crystal-liquid interfacial free energy of the low-temperature liquid, making our theory a predictive tool to determine which amorphous structures enhance glass-forming ability.

We present numerical solutions to the Landau-de Gennes free-energy model under the one-constant approximation for systems of single and double spherical colloidal particles immersed in an otherwise uniformly aligned nematic liquid crystal. A perfect homeotropic surface anchoring of liquid-crystal molecules on the spherical surface is considered. A large parameter space is carefully examined, including those in the free-energy model and those describing the dimer configurations and the background liquid-crystal orientation. The stability of the resulting liquid-crystal defects appearing in the neighborhood of the colloidal dimer pair is analyzed in light of the numerical results for their free energies. A number of scenarios are considered: a free dimer pair in a nematic fluid where the free-energy ground states are described in terms of a phase diagram, and a constrained dimer pair where the interparticle distance and the relative orientation of the distance vector to the nematic director can be manipulated. We pay particular attention to the nonsymmetric solutions, which yield several metastable defect states that can be observed in real systems. The high-precision numerical calculations are based on a spectral method, which is an enabling factor that allows us to compare the subtle difference in the free energies of different defect structures.

The manner in which transport properties vary over the entire parameter-space of coupling and magnetization strength is explored. Four regimes are identified based on the relative size of the gyroradius compared to other fundamental length scales: the collision mean free path, Debye length, distance of closest approach, and interparticle spacing. Molecular dynamics simulations of self-diffusion and temperature anisotropy relaxation spanning the parameter space are found to agree well with the predicted boundaries. Comparison with existing theories reveals regimes where they succeed, where they fail, and where no theory has yet been developed.

Recent theory has demonstrated a novel physics regime for magnetic reconnection in high-energy-density plasmas where the magnetic field is advected by heat flux via the Nernst effect. Here we elucidate the physics of the electron dissipation layer in this regime. Through fully kinetic simulation and a generalized Ohm's law derived from first principles, we show that momentum transport due to a nonlocal effect, the heat-flux-viscosity, provides the dissipation mechanism for magnetic reconnection. Scaling analysis, and simulations show that the reconnection process comprises a magnetic field compression stage and quasisteady reconnection stage, and the characteristic width of the current sheet in this regime is several electron mean-free paths. These results show the important interplay between nonlocal transport effects and generation of anisotropic components to the distribution function.

Oscillation of particles in a dust crystal formed in a low-pressure radio-frequency gas discharge under microgravity conditions is studied. Analysis of experimental data obtained in our previous study shows that the oscillations are highly isotropic and nearly homogeneous in the bulk of a dust crystal; oscillations of the neighboring particles are significantly correlated. We demonstrate that the standard deviation of the particle radius vector along with the local particle number density fully define the coupling parameter of the particle subsystem. The latter proves to be of the order of 100, which is two orders of magnitude lower than the coupling parameter estimated for the Brownian diffusion of particles with the gas temperature. This means significant kinetic overheating of particles under stationary conditions. A theoretical interpretation of the large amplitude of oscillation implies the increase of particle charge fluctuations in the dust crystal. The theoretical estimates are based on the ionization equation of state for the complex plasma and the equation for the plasma perturbation evolution. They are shown to match the results of experimental data processing. Estimated order of magnitude of the coupling parameter accounts for the existence of the solid-liquid phase transition observed for similar systems in experiments.

We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional confinements across the crossover from solid- to liquid-like behaviors. While static correlations that investigate the translational and bond orientational order in the confinements show the footprints of hexatic-like phase at low temperatures, dynamics of the particles slow down considerably in this phase, reminiscent of a supercooled liquid. Using density correlations, we probe long-lived heterogeneities arising from the interplay of the irregularity in the confinement and long-range Coulomb interactions. The relaxation at multiple time scales show stretched-exponential decay of spatial correlations in irregular traps. Temperature dependence of characteristic time scales, depicting the structural relaxation of the system, show striking similarities with those observed for the glassy systems, indicating that some of the key signatures of supercooled liquids emerge in confinements with lower spatial symmetries.