Customarily, the Kirkendall effect is associated with the vacancy-mediated balance of diffusion fluxes of atoms at the interface between two metals. Nowadays, this effect attracts appreciable attention due to its crucial role in the formation of various hollow nanoparticles via oxidation of metal nanocrystallites. The understanding of the physics behind this effect in general and especially in the case of nanoparticles is still incomplete due to abundant complicating factors. Herein, the Kirkendall effect is illustrated in detail at the generic level by performing two-dimensional (2D) lattice Monte Carlo simulations of diffusion of A and B monomers with attractive nearest-neighbor interaction for times up to ${10}^7$ Monte Carlo steps. Initially, A monomers are considered to form a close-packed array, while B monomers are in the 2D-gas state. The A-B interaction is assumed to be stronger compared to the other interactions, so that thermodynamically the $\mathrm{c}(2\times 2)$ A-B phase is preferable compared to the close-packed A phase (as in the case of metal oxidation). Depending on the relative rate of the diffusion jumps of A and B monomers, the patterns observed at the late stage of the formation of the mixed phase are shown to range from a single array without voids to those with appreciable disintegration of the initial array. In this way, the model predicts a single array with numerous small voids, a few moderate voids, or a single large void inside.

In our previous paper [Terekhov et al., Phys. Rev. E 95, 062133 (2017)] we considered the optical channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity for this model. In the present paper we extend the per-sample channel model by introducing the initial signal dependence on time and the output signal detection procedure. The proposed model is a closer approximation of the realistic communications link than the per-sample model where there is no dependence of the initial signal on time. For the proposed model we found the correlators of the output signal both analytically and numerically. Using these correlators we built the conditional probability density function. Then we calculated an entropy of the output signal, a conditional entropy, and the mutual information. Maximizing the mutual information we found the optimal input signal distribution, channel capacity, and their dependence on the shape of the initial signal in the time domain for the intermediate power range.

We investigate the role of a transverse field on the Ising square antiferromagnet with first ($J_1$) and second ($J_2$) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio $J_2/J_1$ in possible experimental realizations of the quantum $J_1\text{−}{J}_2$ Ising antiferromagnet.

Memory effects, sometimes, cannot be neglected. In the framework of continuous-time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the correlated waiting time process, as well as the one of its inverse process, and present the Langevin description of Lévy walk with memory. We call this model a Lévy-walk-type model with correlated waiting times. Based on the built Langevin picture, the properties of aging and nonstationary are discussed. This Langevin system exhibits sub-ballistic superdiffusion $\langle x^2\left(t\right)\rangle \propto t^{2-\frac{{\alpha }^2\beta }{\alpha \beta +1}}$ if the friction force is involved, while it displays superballistic diffusion or hyperdiffusion $\langle x^2\left(t\right)\rangle \propto t^{2+\frac{\alpha }{\alpha \beta +1}}$ if there is no friction. The parameter $0<\alpha <1$ is for the white $\alpha$-stable Lévy noise, while $0\le \beta \le 1$ is to characterize the strength of the correlation of waiting times; $\beta =0$ corresponds to uncorrelated case and $\beta =1$ the strongest correlation. It is discovered that the correlation of waiting times suppresses the diffusion behavior whether a friction is involved or not. The stronger the correlation of waiting times becomes, the slower the diffusion is. In particular, the correlation function, correlation coefficient, ergodicity, and scaling property of the corresponding stochastic process are also investigated.

Spinodal decomposition is a well-known pattern-forming mechanism in metallurgic alloys, semiconductor crystals, and colloidal gels. In metallurgy, if a heated sample of a homogeneous Zn-Al alloy is suddenly quenched below a critical temperature, then the sample can spontaneously precipitate into inhomogenous textures of Zn- and Al-rich regions with significantly altered material properties such as ductility and hardness. Here we report on our recent discovery that a two-dimensional model of the human cortex with inhibitory diffusion can, under particular homogeneous initial conditions, exhibit a form of nonconserved spinodal decomposition in which regions of the cortex self-organize into hexagonally distributed binary patches of activity and inactivity. Fine-scale patterns precipitate rapidly, and then the dynamics slows to render coarser-scale shapes which can ripen into a range of slowly evolving patterns including mazelike labyrinths, hexagonal islands and continents, nucleating “mitotic cells” which grow to a critical size then subdivide, and inverse nucleations in which quiescent islands are surrounded by a sea of activity. One interesting class of activity coalesces into a soliton-like narrow ribbon of depolarization that traverses the cortex at $\sim 4\mathrm{cm}/\mathrm{s}$. We speculate that this may correspond to the thus far unexplained interictal waves of cortical activation that precede grand-mal seizure in an epileptic event. We note that spinodal decomposition is quite distinct from the Turing mechanism for symmetry breaking in cortex investigated in earlier work by the authors [Steyn-Ross et al., Phys. Rev. E 76, 011916 (2007)].

Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly enhance the fluctuations in gene regulatory networks. However, the universal relation between diffusion and stochastic system dynamics remains veiled. Within the approximation of reaction-diffusion master equation (RDME), we find general relation that the steady-state distribution in complex balanced networks is diffusion-independent. Here, complex balance is the nonequilibrium generalization of detailed balance. We also find that for a diffusion-included network with a Poisson-like steady-state distribution, the diffusion can be ignored at steady state. We then derive a necessary and sufficient condition for networks holding such steady-state distributions. Moreover, we show that for linear reaction networks the RDME reduces to the chemical master equation, which implies that the stochastic dynamics of networks is unaffected by diffusion at any arbitrary time. Our findings shed light on the fundamental question of when diffusion can be neglected, or (if nonnegligible) its effects on the stochastic dynamics of the reaction network.

We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e., growth rate) requires a nonzero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.

A mechanism for diffusiophoresis of a charged colloidal particle undergoing surface chemical reaction is proposed. A theoretical model is constructed to describe the dynamics of the particle and the surrounding solution of a weak electrolyte. Theoretical analysis and numerical simulations of the model reveal that phoretic motion of the particle emerges in response to a concentration gradient of electrolyte. The concentration gradient breaks the spherical symmetry of the surface charge distribution, which gives rise to a net force on the particle and leads to directional motion of the particle.

Previous work [Davidovits and Fisch, Phys. Rev. Lett. 116, 105004 (2016)] demonstrated that the compression of a turbulent field can lead to a sudden viscous dissipation of turbulent kinetic energy (TKE), and that paper suggested this mechanism could potentially be used to design new fast-ignition schemes for inertial confinement fusion (ICF). We expand on previous work by accounting for finite Mach numbers, rather than relying on a zero-Mach-limit assumption as previously done. The finite-Mach-number formulation is necessary to capture a self-consistent feedback mechanism in which dissipated TKE increases the temperature of the system, which in turn modifies the viscosity and thus the TKE dissipation itself. Direct numerical simulations with a tenth-order accurate Padé scheme were carried out to analyze this self-consistent feedback loop for compressing turbulence. Results show that, for finite Mach numbers, the sudden viscous dissipation of TKE still occurs, for both the solenoidal and dilatational turbulent fields. As the domain is compressed, oscillations in dilatational TKE are encountered due to the highly oscillatory nature of the pressure dilatation. An analysis of the source terms for the internal energy shows that the mechanical-work term dominates the viscous turbulent dissipation. As a result, the effect of the suddenly dissipated TKE on temperature is minimal for the Mach numbers tested. Moreover, an analytical expression is derived that confirms the dissipated TKE does not significantly alter the temperature evolution for low Mach numbers, regardless of compression speed. The self-consistent feedback mechanism is thus quite weak for subsonic turbulence, which could limit its applicability for ICF.

We present an analysis of a Hall-magnetohydrodynamics model of the magnetospheric plasma with finite Larmor radius effect. Through a bifurcation analysis of the resultant nonlinear system, we show that this nonlinear model does not possess a limit cycle, which rules out regular periodic oscillations with constant amplitude. However, it does result in a train of magnetosonic solitons, localized in space, with amplitudes increasing in time, which are largely in agreement with what is usually observed in the magnetopause region. We call these oscillations aperiodic magnetospheric oscillations. We emphasize that most of the train of solitary oscillations observed by the Cluster fleet and other spacecrafts do not have constant amplitudes: they either continuously increase or decrease. These train of solitons with nonconstant amplitudes is a primary solution of our model.

We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at each node, couples the local spin with the particle. We observe the relaxation of the system toward a stationary paramagnetic or ferromagnetic state and demonstrate that it is related to eigenvectors thermalization and random matrix statistics. The relation between these macroscopic properties and interaction generated entanglement is discussed.

We consider the motion of overdamped particles over random potentials subjected to a Gaussian white noise and a time-dependent periodic external forcing. The random potential is modeled as the potential resulting from the interaction of a point particle with a random polymer. The random polymer is made up, by means of some stochastic process, from a finite set of possible monomer types. The process is assumed to reach a nonequilibrium stationary state, which means that every realization of a random polymer can be considered as an out-of-equilibrium structure. We show that the net flux of particles over this random medium is nonvanishing when the potential profile on every monomer is symmetric. We prove that this ratchetlike phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer. On the contrary, when the process generating the polymer is at equilibrium (thus fulfilling the detailed balance condition) the system is unable to rectify the motion. We calculate the net flux of the particles in the adiabatic limit for a simple model and we test our theoretical predictions by means of Langevin dynamics simulations. We also show that, out of the adiabatic limit, the system also exhibits current reversals as well as nonmonotonic dependence of the diffusion coefficient as a function of forcing amplitude.

We consider the long-time evolution of pulses in the Korteweg–de Vries equation theory for initial distributions which produce no soliton but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.

We study the dynamics of knotted vortices in a bulk excitable medium using the FitzHugh-Nagumo model. From a systematic survey of all knots of at most eight crossings we establish that the generic behavior is of unsteady, irregular dynamics, with prolonged periods of expansion of parts of the vortex. The mechanism for the length expansion is a long-range “wave-slapping” interaction, analogous to that responsible for the annihilation of small vortex rings by larger ones. We also show that there are stable vortex geometries for certain knots; in addition to the unknot, trefoil, and figure-eight knots reported previously, we have found stable examples of the Whitehead link and $6_2$ knot. We give a thorough characterization of their geometry and steady-state motion. For the unknot, trefoil, and figure-eight knots we greatly expand previous evidence that FitzHugh-Nagumo dynamics untangles initially complex geometries while preserving topology.

Previously, the controllability problem of a linear time-invariant dynamical system was mapped to the maximum matching (MM) problem on the bipartite representation of the underlying directed graph, and the sizes of MMs on random bipartite graphs were calculated analytically with the cavity method at zero temperature limit. Here we present an alternative theory to estimate MM sizes based on the core percolation theory and the perfect matching of cores. Our theory is much more simplified and easily interpreted, and can estimate MM sizes on random graphs with or without symmetry between out- and in-degree distributions. Our result helps to illuminate the fundamental connection between the controllability problem and the underlying structure of complex systems.

A drop of lipid lateral self-diffusion coefficient at the liquid-gel phase transition in lipid membranes is calculated. So far this drop was missing theoretical description. Our microscopic model captures so-called subdiffusion regime, which takes place on 1 ps–100 ns timescale and reveals a jump of self-diffusion coefficient. Calculation of the jump is based on our recent study of liquid-gel phase transition. Subdiffusive regime is described within the free volume theory. Calculated values of self-diffusion coefficient are in agreement with quasielastic neutron scattering measurements. Self-diffusion coefficient is found to be composed of two factors: one is related to an area per lipid change at the phase transition, and the other one is due to an order of magnitude change in the stiffness of entropic repulsive potential.

The energy landscape is widely used to quantify the stability of multistable nonlinear systems, such as bistable gene regulation networks. In physics, the potential can be obtained through integration only for gradient systems. However, multidimensional nonlinear systems are often nongradient, for which the potential is calculated by decomposing the dynamics to gradient and nongradient parts. This potential is then called a quasipotential. Given that one-dimensional (1D) systems can be regarded as gradient systems, we attempt to separate the two-dimensional (2D) system into two 1D systems working on distinct timescales, and the potential can be easily calculated for the two 1D systems separately. This method is used in this study to estimate the energy landscape of a two-variable gene autoregulation model. This elegant and comprehensive method is accessible for 2D nonlinear systems in which the dynamics can be divided into slow and fast parts.

Cloaking and scattering cancellation of electromagnetic waves have attracted much attention since they allow control of rf and light waves and are of scientific interest. The analytical results demonstrated in this paper reveal that plasmonic cloaking, which is one of the schemes for scattering cancellation, occurs in the vicinity of Tonks-Dattner resonances in the frequency domain, where resonances enhance wave scattering. This antiresonance-resonance pair for cloaking and scattering is cross-correlated by the symmetrical locations above and below the electron plasma frequency, respectively. However, the cloaking effect is almost independent of electron collisions with neutral particles, whereas scattering at resonance is fairly sensitive to them, leading to unclear resonance. An experimental verification of this analytical prediction is performed for the cloaking effect on working points passing through the cloaking condition and approaching resonance, which is dynamically controlled by changing the electron density. Numerical calculations based on a model configuration similar to the experimental setup confirm scattering cancellation and an increase in scattering as the points get close to the resonance condition. These results are direct evidence of scattering cancellation with a uniform epsilon-near-zero material and demonstrate the effectiveness of plasma as a cloaking material.

The investigation on grid sensitivity for the bifurcation problem of the canonical lid-driven cavity (LDC) flow results is reported here with very fine grids. This is motivated by different researchers presenting different first bifurcation critical Reynolds number (${\text{Re}}_{\text{cr}1}$), which appears to depend on the formulation, numerical method, and choice of grid. By using a very-high-accuracy parallel algorithm, and the same method with which sequential results were presented by Lestandi et al. [Comput. Fluids 166, 86 (2018)] [for (257 $\times$ 257) and (513 $\times$ 513) uniformly spaced grid], we present results using ($1025\times 1025$) and ($2049\times 2049$) grid points. Detailed results presented using these grids help us understand the computational physics of the numerical receptivity of the LDC flow, with and without explicit excitation. The mathematical physics of the investigated problem will become apparent when we identify the roles of numerical errors with the ambient omnipresent disturbances in real physical flows as interchangeable. In physical or in numerical setups, presence of disturbances cannot be ignored. In this context, the need for explicit excitation for the used compact scheme arises for a definitive threshold amplitude, below which the flow relaxes back to quiescent state after the excitation is removed in computations. We also implement the present parallel method to show the physical aspects of primary and secondary instabilities to be maintained for other numerical schemes, and we show the results to reflect the complex physics during multiple subcritical Hopf bifurcation. Also, we relate the various sources of errors during computations that is typical of such shear-driven flow. These results, with near spectral accuracy, constitute universal benchmark results for the solution of Navier-Stokes equation for LDC.

A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size $L$ as $\sim L^{-2/3}$ in the leading order with a diffusive correction of order $\sim L^{-1}$. The crossover length ${\ell }_c$ from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.