The two-species symbiotic contact process (2SCP) is a stochastic process in which each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.

Bacterial biofilms are a risk to human health, playing critical roles in persistent infections. Recent studies have observed electrical signaling in biofilms and thus biofilms represent a new class of active excitable matter in which cell division is the active process and the spiking of the individual bacterial cells is the excitable process. Electrophysiological models have predominantly been developed to describe eukaryotic systems, but we demonstrate their use in understanding bacterial biofilms. Our agent-based fire-diffuse-fire (ABFDF) model successfully simulates the propagation of both centrifugal (away from the center) and centripetal (toward the center) electrical signals through biofilms of Bacillus subtilis. Furthermore, the ABFDF model allows realistic spatial positioning of the bacteria in two dimensions to be included in the fire-diffuse-fire model and this is the crucial factor that improves agreement with experiments. The speed of propagation is not constant and depends on the radius of the propagating electrical wave front. Centripetal waves are observed to move faster than centrifugal waves, which is a curvature driven effect and is correctly captured by our simulations.

Combining Poiseuille flow with an external electric field is a demonstrated method to drive transverse migration in capillary electrophoresis. Despite both computational and experimental studies, a number of questions about how to best model polymers under these conditions remains. Attempts have been made to develop a kinetic theory for a bead-spring dumbbell model, but these have only been accurate at low electric field strength and have not captured the nonmonotonic relationship between migration and electric field strength. In this paper, we revisit the development of a kinetic theory for a bead-spring dumbbell in a combination of parabolic flow and an external electric field. The resultant theory yields a compact formula that predicts polymer concentration profiles that agree excellently with our Brownian dynamics simulations including the aforementioned nonmonotonic relationship. Furthermore, we compare our theoretical results to experimental data and find that our model nearly quantitatively predicts the position of the maximum in migration.

We propose and study theoretically a colloidal system in two dimensions with attractive critical Casimir and repulsive magnetic dipole forces, wherein the strength of attraction and repulsion can be easily and independently tuned by adjusting the temperature and an external magnetic field, respectively. We expect this setup to be experimentally accessible and are confident that it can serve to deepen our understanding of the mechanisms behind microphase separation due to competing interactions. We develop a density functional theory for our model and present first results of our calculations in the form of a phase diagram for fixed temperature, but varying magnetic fields and bulk densities. For certain values of these parameters, we are able to confirm the existence of thermodynamically stable inhomogeneous density profiles in the bulk, such as parallel lamellar stripes, as well as clusters and voids on a hexagonal lattice.

In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063 (1965)], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at wavenumber band $(k_f,k_f+1)$ in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for $k<k_f$, where the fluxes exhibit significant fluctuations. We show that these fluctuations arise due to the unsteady nature of the flow at small wavenumbers. For $k<k_f$, the shell-to-shell energy transfers computed using numerical data show forward energy transfers among the neighboring shells, but backward energy transfers among other shells.

The coupled Maxwell and time-dependent Kohn-Sham equations are solved using the Riemann-Silberstein vectors to represent the electromagnetic fields. Momentum-space time propagation of the Riemann-Silberstein vectors are proposed and test calculations are presented to show the accuracy of the approach.

We present an efficient and very flexible numerical fast Fourier-Laplace transform that extends the logarithmic Fourier transform introduced by Haines and Jones [Geophys. J. Int. 92, 171 (1988)] for functions varying over many scales to nonintegrable functions. In particular, these include cases of the asymptotic form $f(\nu \to 0)\sim {\nu }^a$ and $f\left(\right|\nu |\to \infty )\sim {\nu }^b$ with arbitrary real $a>b$. Furthermore, we prove that the numerical transform converges exponentially fast in the number of data points, provided that the function is analytic in a cone $\left|\mathrm{Im}\nu \right|<\theta \left|\mathrm{Re}\nu \right|$ with a finite opening angle $\theta$ around the real axis and satisfies $\left|f\left(\nu \right)f(1/\nu )\right|<{\nu }^c$ as $\nu \to 0$ with a positive constant $c$, which is the case for the class of functions with power-law tails. Based on these properties we derive ideal transformation parameters and discuss how the logarithmic Fourier transform can be applied to convolutions. The ability of the logarithmic Fourier transform to perform these operations on multiscale (nonintegrable) functions with power-law tails with exponentially small errors makes it the method of choice for many physical applications, which we demonstrate on typical examples. These include benchmarks against known analytical results inaccessible to other numerical methods, as well as physical models near criticality.

Recently a useful finite-difference scheme was proposed in [Phys. Rev. E 98, 033302 (2018)] to solve Fokker-Planck equations with drift-admitting jumps. However, while the scheme is fifth order for the case with smooth drifts, it is only second order for the case with discontinuous drifts. To rectify this, we propose in this paper an improved scheme that achieves a fifth-order convergence rate for the case with drift-admitting jumps. Numerical experiments are also employed to verify the validity of the scheme.

We revisit the optimization of performance of finite-time Carnot machines satisfying the low-dissipation assumption. The standard procedure seeks to optimize an objective function, such as power output of the engine, over the durations of contacts between the working medium and the heat reservoirs. This procedure may lead to unwieldy equations at the optimum of some objective functions. We propose an alternate scheme in which the output or input work is first optimized for a given cycle time, followed by an optimization of another objective function over the cycle time. This optimization problem is solved in a much simplified manner, with closed-form expressions for figures of merit. The approach is demonstrated for various objective functions, both for engines as well as refrigerators.

We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core–penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents' conductivities and volume concentrations; the latter account for the statistical microstructure of the system. The theory effectively incorporates many-particle effects and is expected to be rigorous in the static limit. Using the well-tested statistical physics results for the shell volume concentration, this conclusion is backed up by mapping the theory on available 3D random resistor network simulations for hard spheres coated with fully penetrable concentric shells. Finally, the theory is shown to fit experimental data for real composite solid electrolytes. The fitting results indicate that the effect of enhanced electrical conduction is generally contributed to by several mechanisms. These are effectively taken into account through the shell conductivity profile.

We consider transport in two billiard models, the infinite horizon Lorentz gas and the stadium channel, presenting analytical results for the spreading packet of particles. We first obtain the cumulative distribution function of traveling times between collisions, which exhibits nonanalytical behavior. Using a renewal assumption and the Lévy walk model, we obtain the particles' probability density. For the Lorentz gas, it shows a distinguished difference when compared with the known Gaussian propagator, as the latter is valid only for extremely long times. In particular, we show plumes of particles spreading along the infinite corridors, creating power-law tails of the density. We demonstrate the slow convergence rate via summation of independent and identically distributed random variables on the border between Lévy and Gauss laws. The renewal assumption works well for the Lorentz gas with intermediate-size scattering centers, but fails for the stadium channel due to strong temporal correlations. Our analytical results are supported with numerical samplings.

We consider a spin $s$ subjected to both a static and an orthogonally applied oscillating, circularly polarized magnetic field while being coupled to a heat bath and analytically determine the quasistationary distribution of its Floquet-state occupation probabilities for arbitrarily strong driving. This distribution is shown to be Boltzmannian with a quasitemperature which is different from the temperature of the bath and independent of the spin quantum number. We discover a remarkable formal analogy between the quasithermal magnetism of the nonequilibrium steady state of a driven ideal paramagnetic material and the usual thermal paramagnetism. Nonetheless, the response of such a material to the combined fields is predicted to show several unexpected features, even allowing one to turn a paramagnet into a diamagnet under strong driving. Thus, we argue that experimental measurements of this response may provide key paradigms for the emerging field of periodic thermodynamics.

We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill the appropriate fluctuation-dissipation relation, the probability density on a finite interval converges for long times towards the expected uniform distribution prescribed by thermal equilibrium. In contrast, on a semi-infinite interval with a reflecting wall at the origin, the probability density shows pronounced deviations from the Gaussian behavior observed for normal diffusion. If the correlations of the random force are persistent (positive), particles accumulate at the reflecting wall while antipersistent (negative) correlations lead to a depletion of particles near the wall. We compare and contrast these results with the strong accumulation and depletion effects recently observed for nonthermal fractional Brownian motion with reflecting walls, and we discuss broader implications.

The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.

The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction kinetics by exploring the effect of a jump discontinuity within piecewise constant kinetic parameters, using various methods to identify and confirm the diffusion-driven instability conditions. Essentially, the presence of stability or instability in Turing models is a local property for piecewise constant kinetic parameters and, as such, may be analyzed locally. In particular, a local assessment of whether parameters are within the Turing space provides a strong indication that for a large enough region with these parameters, an instability can be induced.

Simulations and experiments of granular mixtures comprising two different sizes flowing over an inclined plane under the influence of gravity show segregation, where large particles rise to the free surface. The segregation results from differential forces acting on the particles. The buoyancy force experienced by the particles is an important component of the total force acting on the particles and, in this work, we theoretically calculate the buoyant force on intruder particles of different sizes in a flowing granular medium. The effective particle volume for buoyancy force calculation is obtained as the partial molar volume of the large particle from the equation of state for a binary mixture of hard spheres. The theoretical results are in good agreement with results obtained from discrete element method (DEM) simulations. Our calculations show that the buoyancy force on a particle is always smaller than the weight of the particle for larger particles. The ratio of the buoyancy force to the weight of the large particles decreases with increasing size ratio and increases with increasing concentration of the particles. This ratio approaches unity in the limiting cases of size ratio and large particle concentration approaching unity. These theoretical calculations establish a method for obtaining the buoyancy force experienced by particles in flowing mixtures.

We investigate the effect of van der Waals forces on a collection of granular particles by means of molecular dynamics simulations of a vibrated system in three dimensions. The van der Waals interactions introduce two phase coexistences: one between a random close packing and a gas and a second between a polycrystalline dense state and a gas, where the dense, disordered component crystallizes when the driving amplitude exceeds a threshold value. The region of stability of the ordered state in the nonequilibrium phase diagram grows in size as the Hamaker constant increases or the degree of dissipation increases.

We revisit the problem of how energy transfer through the turbulent cascade operates in compressible hydrodynamic turbulence. In general, there is no conservative compressible cascade since the kinetic and internal energy reservoirs can exchange energy through pressure dilatation. Moreover, statistically stationary turbulence at high Mach number can only be maintained in nearly isothermal gas, i.e., if excess heat produced by shock compression and kinetic energy dissipation is continuously removed from the system. We mimic this process by a linear cooling term in numerical simulations of turbulence driven by stochastic forcing. This allows us to investigate turbulence statistics for a broad range of Mach numbers. We compute the rate of change of kinetic and internal energy in wave-number shells caused by advective, compressive, and pressure dilatation effects and constrain power-law fits to compressible turbulence energy spectra to a range of wave numbers in which the total energy transfer is close to zero. The resulting scaling exponents are significantly affected by the forcing. Depending on the root mean square Mach number, we find a nearly constant advective component of the cross-scale flux of kinetic energy at intermediate wave numbers for particular mixtures of solenoidal and compressive modes in the forcing. This suggests the existence of a natural, Mach number dependent mixture of forcing modes. Our findings also support an advection-dominated regime at high Mach numbers with specific scaling exponents (Burgers scaling for the pure velocity fluctuation $u$ and Kolmogorov scaling for the mass-weighted variable $v={\rho }^{1/3}u$).

The computational cost of contracting a tensor network depends on the sequence of contractions, but to decide the sequence of contractions with a minimal computational cost on an arbitrary network has been proved to be an NP-complete problem. In this work, we conjecture that the problem may be a polynomial one if we consider the computational complexity instead. We propose a polynomial algorithm for the optimal contraction complexity of tensor tree network, which is a specific and widely applied network structure. We prove that for any tensor tree network, the proposed algorithm can achieve a sequence of contractions that guarantees the minimal time complexity and a linear space complexity simultaneously. To illustrate the validity of our idea, numerical simulations are presented that evidence the significant benefits when the network scale becomes large. This work will have great potential for the efficient processing of various physical simulations and pave the way for the further exploration of the computational complexity of tensor contraction on arbitrary tensor networks.