Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations.

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale, long-time kinetics in such systems are effective, scale-dependent renormalized parameters that need to be either measured experimentally or computed by means of a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters.

Effects of lattice dilution on the nonequilibrium phase transition in the stochastic susceptible-infectious-recovered model.

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing nonequilibrium phase transition in the paradigmatic susceptible-infectious-recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents.

Critical dynamics of the antiferromagnetic O(3) nonlinear sigma model with conserved magnetization.

We study the near-equilibrium critical dynamics of the O(3) nonlinear sigma model describing isotropic antiferromagnets with a nonconserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen-De Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics, at least to one-loop order in a perturbative treatment with respect to the static and dynamical nonlinearities.

Dynein-Inspired Multilane Exclusion Process with Open Boundary Conditions.

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases.

Social distancing and epidemic resurgence in agent-based susceptible-infectious-recovered models.

Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak) and long-distance connections are maintained on a low level (limited to less than five percent of the overall connectivity).

Critical dynamics of anisotropic antiferromagnets in an external field.

We numerically investigate the nonequilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The nonconserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field.

Coupled two-species model for the pair contact process with diffusion.

The contact process with diffusion (PCPD) defined by the binary reactions B+B→B+B+B, B+B→∅ and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies have indicated that an explicit account of particle pair degrees of freedom may be required to properly capture this system's effective long-time, large-scale behavior. We introduce a two-species representation for the PCPD in which single particles B and particle pairs A are dynamically coupled according to the stochastic reaction processes B+B→A, A→A+B, A→∅, and A→B+B, with each particle type diffusing independently.

Feedback control of surface roughness in a one-dimensional Kardar-Parisi-Zhang growth process.

Control of generically scale-invariant systems, i.e., targeting specific cooperative features in nonlinear stochastic interacting systems with many degrees of freedom subject to strong fluctuations and correlations that are characterized by power laws, remains an important open problem.

Transverse temperature interfaces in the Katz-Lebowitz-Spohn driven lattice gas.

We explore the intriguing spatial patterns that emerge in a two-dimensional spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with attractive nearest-neighbor interactions. The domain is split into two regions with hopping rates governed by different temperatures T>T_{c} and T_{c}, respectively, where T_{c} indicates the critical temperature for phase ordering, and with the temperature boundaries oriented perpendicular to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region.

Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation.

We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation toward its "frozen" state with quasistationary spiral structures. We study the transition kinetics from either the defect turbulence regime or random initial configurations to the frozen state with a well-defined low density of quasistationary topological defects. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts.

Effects of inhibitory and excitatory neurons on the dynamics and control of avalanching neural networks.

The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. We consider a neural network model based on the work of Lombardi, Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how tuning the fraction of inhibitory neurons in this model alters the connectivity of the network over time, removes exponential cut-offs present in the distributions of avalanche size and duration, and transitions the power spectral density of the network into an "epileptic" regime.

The spatiotemporal system dynamics of acquired resistance in an engineered microecology.

Great strides have been made in the understanding of complex networks; however, our understanding of natural microecologies is limited. Modelling of complex natural ecological systems has allowed for new findings, but these models typically ignore the constant evolution of species. Due to the complexity of natural systems, unanticipated interactions may lead to erroneous conclusions concerning the role of specific molecular components.

Ligand-receptor binding kinetics in surface plasmon resonance cells: a Monte Carlo analysis.

Surface plasmon resonance (SPR) chips are widely used to measure association and dissociation rates for the binding kinetics between two species of chemicals, e.g., cell receptors and ligands.

Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model.

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate.

Relaxation dynamics of vortex lines in disordered type-II superconductors following magnetic field and temperature quenches.

We study the effects of rapid temperature and magnetic field changes on the nonequilibrium relaxation dynamics of magnetic vortex lines in disordered type-II superconductors by employing an elastic line model and performing Langevin molecular dynamics simulations. In a previously equilibrated system, either the temperature is suddenly changed or the magnetic field is instantaneously altered which is reflected in adding or removing flux lines to or from the system. The subsequent aging properties are investigated in samples with either randomly distributed pointlike or extended columnar defects, which allows us to distinguish the complex relaxation features that result from either type of pinning centers.

Pinning time statistics for vortex lines in disordered environments.

We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes.

Nonequilibrium relaxation and aging scaling of the Coulomb and Bose glass.

We employ Monte Carlo simulations to investigate the nonequilibrium relaxation properties of the two- and three-dimensional Coulomb glass with different long-range repulsive interactions. Specifically, we explore the aging scaling laws in the two-time density autocorrelation function. We find that, in the time window and parameter range accessible to us, the scaling exponents are not universal, depending on the filling fraction and temperature: As either the temperature decreases or the filling fraction deviates more from half filling, the exponents reflect markedly slower relaxation kinetics.

Environmental versus demographic variability in two-species predator-prey models.

We investigate the competing effects and relative importance of intrinsic demographic and environmental variability on the evolutionary dynamics of a stochastic two-species Lotka-Volterra model by means of Monte Carlo simulations on a two-dimensional lattice. Individuals are assigned inheritable predation efficiencies; quenched randomness in the spatially varying reaction rates serves as environmental noise. We find that environmental variability enhances the population densities of both predators and prey while demographic variability leads to essentially neutral optimization.

Nonequilibrium relaxation and critical aging for driven Ising lattice gases.

We employ Monte Carlo simulations to study the nonequilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density autocorrelation function in the nonequilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time autocorrelations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.

Slow relaxation and aging kinetics for the driven lattice gas.

We numerically investigate the long-time behavior of the density-density autocorrelation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay. We compare the crossover functions obtained from our simulations with various analytic results in the literature and analyze the characteristic oscillations that occur in finite systems away from half-filling.

Spatial rock-paper-scissors models with inhomogeneous reaction rates.

We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices. Specifically, we investigate the influence of spatial variability of the reaction rates and site occupancy restrictions on the transient oscillations of the species densities and on spatial correlation functions in the quasistationary coexistence state. For small systems, we also numerically determine the dependence of typical extinction times on the number of lattice sites.

Spatial variability enhances species fitness in stochastic predator-prey interactions.

We study the influence of spatially varying reaction rates on a spatial stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using two-dimensional Monte Carlo simulations. The effects of this quenched randomness on population densities, transient oscillations, spatial correlations, and invasion fronts are investigated. We find that spatial variability in the predation rate results in more localized activity patches, which in turn causes a remarkable increase in the asymptotic population densities of both predators and prey and accelerated front propagation.