We mobilize both a generating function approach and the theory of finite Markov processes to compute the probability of irreversible absorption of a randomly diffusing species on a lattice with competing reaction centers. We consider an N-site lattice populated by a single deep trap, and $N-1$ partially absorbing traps (absorption probability $0<s<1$). The influence of competing reaction centers on the probability of reaction at a target site (the deep trap) and the mean walk length of the random walker before localization (a measure of the reaction efficiency) are computed for different geometries. Both analytic expressions and numerical results are given for reactive processes on two-dimensional surfaces of Euler characteristic $\Omega =0$ and $\Omega =2$. The results obtained allow a characterization of catalyst deactivation processes on planar surfaces and on catalyst pellets where only a single catalytic site remains fully active (deep trap), the other sites being only partially active as a result of surface poisoning. The central result of our study is that the predicted dependence of the reaction efficiency on system size $N$ and on $s$ is in qualitative accord with previously reported experimental results, notably catalysts exhibiting selective poisoning due to surface sites that have different affinities for chemisorption of the poisoning agent (e.g., acid zeolite catalysts). Deviations from the efficiency of a catalyst with identical sites are quantified, and we find that such deviations display a significant dependence on the topological details of the surface (for fixed values of $N$ and $s$ we find markedly different results for, say, a planar surface and for the polyhedral surface of a catalyst pellet). Our results highlight the importance of surface topology for the efficiency of catalytic conversion processes on inhomogeneous substrates, and in particular for those aimed at industrial applications. From our exact analysis we extract results for the two limiting cases $s\approx 1$ and $s\approx 0$, corresponding respectively to weak and strong catalyst poisoning (decreasing $s$ leads to a monotonic decrease in the efficiency of catalytic conversion). The results for the $s\approx 0$ case are relevant for the dual problem of light-energy conversion via trapping of excitations in the chlorophyll antenna network. Here, decreasing the probability of excitation trapping $s$ at sites other than the target molecule does not result in a decrease of the efficiency as in the catalyst case, but rather in enhanced efficiency of light-energy conversion, which we characterize in terms of $N$ and $s$. The one-dimensional case and its connection with a modified version of the gambler's ruin problem are discussed. Finally, generalizations of our model are described briefly.

We revisit the relation between the shear-stress relaxation modulus $G\left(t\right)$, computed at finite shear strain $0<\gamma \ll 1$, and the shear-stress autocorrelation functions ${C\left(t\right)|}_{\gamma }$ and ${C\left(t\right)|}_{\tau }$ computed, respectively, at imposed strain $\gamma$ and mean stress $\tau$. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general ${G\left(t\right)=C\left(t\right)|}_{\tau }{=C\left(t\right)|}_{\gamma }+G_{\mathrm{eq}}$ for $t>0$ with $G_{\mathrm{eq}}$ being the static equilibrium shear modulus. $G\left(t\right)$ and ${C\left(t\right)|}_{\gamma }$ thus must become different for solids and it is impossible to obtain $G_{\mathrm{eq}}$ alone from ${C\left(t\right)|}_{\gamma }$ as often assumed. We comment briefly on self-assembled transient networks where $G_{\mathrm{eq}}\left(f\right)$ must vanish for a finite scission-recombination frequency $f$. We argue that ${G\left(t\right)=C\left(t\right)|}_{\tau }{=C\left(t\right)|}_{\gamma }$ should reveal an intermediate plateau set by the shear modulus $G_{\mathrm{eq}}(f=0)$ of the quenched network.

When corroding or otherwise aggressive particles are incident on a surface, pits can form. For example, under certain circumstances rock surfaces that are exposed to salts can form regular tessellating patterns of pits known as “tafoni.” We introduce a simple lattice model in which a gas of corrosive particles, described by a discrete, biased diffusion equation, drifts onto a surface. Each gas particle has a fixed probability of being absorbed and causing damage at each contact. The surface is represented by a lattice of strength numbers which reduce after each absorbtion event, with sites being removed when their strength becomes negative. Regular formations of pits arise spontaneously, with each pit having a characteristic trapezoidal geometry determined by the particle bias, absorbtion probability, and surface strength. The formation of this geometry may be understood in terms of a first order partial differential equation and is a consequence of particle concentration gradients which arise in the pits. By viewing pits as particle funnels, we are able to relate the gradient of pit walls to absorbtion probability and particle bias.

Network robustness against attacks is one of the most fundamental researches in network science as it is closely associated with the reliability and functionality of various networking paradigms. However, despite the study on intrinsic topological vulnerabilities to node removals, little is known on the network robustness when network defense mechanisms are implemented, especially for networked engineering systems equipped with detection capabilities. In this paper, a sequential defense mechanism is first proposed in complex networks for attack inference and vulnerability assessment, where the data fusion center sequentially infers the presence of an attack based on the binary attack status reported from the nodes in the network. The network robustness is evaluated in terms of the ability to identify the attack prior to network disruption under two major attack schemes, i.e., random and intentional attacks. We provide a parametric plug-in model for performance evaluation on the proposed mechanism and validate its effectiveness and reliability via canonical complex network models and real-world large-scale network topology. The results show that the sequential defense mechanism greatly improves the network robustness and mitigates the possibility of network disruption by acquiring limited attack status information from a small subset of nodes in the network.

A linear stability analysis of a thin liquid film flowing over a plate is performed. The plate is considered as impermeable and adiabatic. The upper surface of the film is assumed to be a free boundary with a non-negligible surface tension, characterized by a Robin thermal boundary condition. The thermoconvective instability is generated by the interplay between the heating due to viscous dissipation and the temperature-dependent surface tension at the free boundary. A basic parallel flow, arbitrarily oriented, is assumed and the basic temperature profile is determined analytically. In order to investigate the linear stability of the system, the normal mode method is employed. A system of ordinary differential equations defining an eigenvalue problem is thus obtained. The case of longitudinal rolls, where the base flow velocity is parallel to the axis rolls, is solved both analytically and numerically. Other possible inclinations of the base flow are investigated by means of a numerical procedure based on combining the Runge-Kutta and the shooting methods.

Recent efforts to demonstrate significant self-heating of the fuel and eventual ignition at the National Ignition Facility make use of plastic (CH) ablators [O. A. Hurricane et al., Phys. Plasmas 21, 056314 (2014)]. Mainline simulation techniques for modeling CH capsule implosions treat the ablator as an average-atom fluid and neglect potential species separation phenomena. The mass-ablation process for a mixture is shown to lead to the potential for species separation, parasitic energy loss according to thermodynamic arguments, and reduced rocket efficiency. A generalized plasma barometric formula for a multispecies concentration gradient that includes collisionality and steady flows in spherical geometry is presented. A model based on plasma expansion into a vacuum is used to interpret reported experimental evidence for ablator species separation in an inertial-confinement-fusion target [J. S. Ross et al., Rev. Sci. Instrum. 83, 10E323 (2012)]. The possibility of “runaway” hydrogen ions in the thermoelectric field of the ablation front is conjectured.

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact $N$-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around $-1.8$, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

A method of finding entropic form for a given stationary probability distribution and specified potential field is discussed, using the steady-state Fokker-Planck equation. As examples, starting with the Boltzmann and Tsallis distribution and knowing the force field, we obtain the Boltzmann-Gibbs and Tsallis entropies. Also, the associated entropy for the gamma probability distribution is found, which seems to be in the form of the gamma function. Moreover, the related Fokker-Planck equations are given for the Boltzmann, Tsallis, and gamma probability distributions.

The dynamics of adhesion of a spherical microparticle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions, and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high Péclet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations where thermal fluctuations are completely ignored. The role of wall hydrodynamic interactions on the steady-state motion of a particle, when the particle is close to the wall, has also been explored. At high Péclet numbers, the shear induced force that arises due to the stresslet part of the Stokes dipole plays a dominant role, reducing the particle velocity significantly and affecting the states of motion of the particle. The coupling between the translational and rotational degrees of freedom of the particle, brought about by the presence of hydrodynamic interactions, is found to have no influence on the binding dynamics. On the other hand, the drag coefficient, which depends on the distance of the particle from the wall, plays a crucial role at low rates of bond formation. A significant difference in the effect of both the shear force and the position-dependent drag force on the states of motion of the particle is observed when the Péclet number is small.

Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J. F. Lutsko and M. A. Durán-Olivencia, Classical nucleation theory from a dynamical approach to nucleation, J. Chem. Phys. 138, 244908 (2013).]. The present work extends this effort to the case of nucleation in confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nucleation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate.

Concentration gradients of signaling molecules are essential for patterning during development and they have been observed in both unicellular and multicellular systems. In subcellular systems, clustering of the signaling molecule has been observed. We develop a theoretical model of cluster-mediated concentration gradient formation based on the Becker-Döring equations of aggregation-fragmentation processes. We show that such a mechanism produces robust concentration gradients on realistic time and spatial scales so long as the process of clustering does not significantly stabilize the signaling molecule. Finally, we demonstrate that such a model is applicable to the pom1p subcellular gradient in fission yeast.

A robust method for inferring the structure of networks is presented based on the one-to-one correspondence between the expected composition of cascades of bursts of activity, called crackling noise or avalanches, and the weight matrix. Using a model of neuronal avalanches as a paradigmatic example, we derive this correspondence exactly by calculating the closed-form expression of the joint probability distribution of avalanche sizes obtained by counting separately the number of elements active in each subnetwork during avalanches.

The Richtmyer-Meshkov instability (RMI) develops when a shock front hits a rippled contact surface separating two different fluids. After the incident shock refraction, a transmitted shock is always formed and another shock or a rarefaction is reflected back. The pressure-entropy-vorticity fields generated by the rippled wave fronts are responsible for the generation of hydrodynamic perturbations in both fluids. In linear theory, the contact surface ripple reaches an asymptotic normal velocity which is dependent on the incident shock Mach number, fluids density ratio, and compressibilities. It was speculated in the past about the possibility of getting a zero value for the asymptotic normal velocity, a phenomenon that was called “freeze-out” [G. Fraley, Phys. Fluids 29, 376 (1986); K. Mikaelian, Phys. Fluids 6, 356 (1994), A. L. Velikovich et al., Phys. Plasmas 8, 592 (2001)]. In a previous paper, freeze-out was studied for the case when a shock is reflected at the contact surface [J. G. Wouchuk and K. Nishihara, Phys. Rev. E 70, 026305 (2004)]. In this work the freeze-out of the RMI is studied for the case in which a rarefaction is reflected back. Two different regimes are found: nearly equal preshock densities at the interface at any shock intensity, and very large density difference for strong shocks. The contour curves that relate shock Mach number and preshock density ratio are obtained in both regimes for fluids with equal and different compressibilities. An analysis of the temporal evolution of different cases of freeze-out is shown. It is seen that the freeze-out is the result of the interaction between the unstable interface and the rippled wave fronts. As a general and qualitative criterion to look for freeze-out situations, it is seen that a necessary condition for freeze-out is the same orientation for the tangential velocities generated at each side of the contact surface at $t=0+$. A comparison with the results of previous works is also shown.

The effective dynamically screened potential of a classical ion in a stationary flowing quantum plasma at finite temperature is investigated. This is a key quantity for thermodynamics and transport of dense plasmas in the warm-dense-matter regime. This potential has been studied before within hydrodynamic approaches or based on the zero temperature Lindhard dielectric function. Here we extend the kinetic analysis by including the effects of finite temperature and of collisions based on the Mermin dielectric function. The resulting ion potential exhibits an oscillatory structure with attractive minima (wakes) and, thus, strongly deviates from the static Yukawa potential of equilibrium plasmas. This potential is analyzed in detail for high-density plasmas with values of the Brueckner parameter in the range $0.1\le r_s\le 1$ for a broad range of plasma temperature and electron streaming velocity. It is shown that wake effects become weaker with increasing temperature of the electrons. Finally, we obtain the minimal electron streaming velocity for which attraction between ions occurs. This velocity turns out to be less than the electron Fermi velocity. Our results allow for reliable predictions of the strength of wake effects in nonequilibrium quantum plasmas with fast streaming electrons showing that these effects are crucial for transport under warm-dense-matter conditions, in particular for laser-matter interaction, electron-ion temperature equilibration, and stopping power.

The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab initio calculations on molecules are evaluated. Compact, arbitrarily accurate expressions are obtained. They are expressed through molecular auxiliary functions and evaluated with the numerical Global-adaptive method for arbitrary values of parameters in the noninteger Slater-type orbitals. Highly accurate benchmark values are presented for these integrals. The convergence properties of new molecular auxiliary functions are investigated. The comparison for two-center two-electron integrals is made with results obtained from single center expansions by translation of the wave function to a single center with integer principal quantum numbers and results obtained from the Cuba numerical integration algorithm, respectively. The procedures discussed in this work are capable of yielding highly accurate two-center two-electron integrals for all ranges of orbital parameters.

In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics in complex geometries.

We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the probabilities (Green's functions) $P(x,t)$ describing a particle's random walk are found. The membrane, which can be asymmetrical, is characterized by the two probabilities of stopping a random walker by the membrane when it tries to pass through the membrane in both opposite directions. Green's functions are transformed to the system in which the variables are continuous, and then the membrane permeability coefficients are given by special formulas which involve the probabilities mentioned above. From the obtained Green's functions, we derive boundary conditions at the membrane. One of the conditions demands the continuity of a flux at the membrane, but the other one is rather unexpected and contains the Riemann-Liouville fractional time derivative $P(x_N^{-},t)={\lambda }_{1}P(x_N^{+},t)+{\lambda }_2{\partial }^{\alpha /2}P(x_N^{+},t)/\partial t^{\alpha /2}$, where ${\lambda }_1,{\lambda }_2$ depending on membrane permeability coefficients (${\lambda }_1=1$ for a symmetrical membrane), $\alpha$ is a subdiffusion parameter, and $x_N$ is the position of the membrane. This boundary condition shows that the additional “memory effect,” represented by the fractional derivative, is created by the membrane. This effect is also created by the membrane for a normal diffusion case in which $\alpha =1$.

Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this paper, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is due to dislocation avalanche motions in Cu and Ni. A different mechanism of dislocation pinning is found in Al. These different stress relaxation mechanisms give different power-law exponents. We propose a probabilistic model to describe the novel dislocation motion in Al and analytically deduce the power-law behavior.

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e., alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be proarrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e., from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.