The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.

When nonequilibrium extended homogeneous systems exhibit multistability, it leads to the presence of domain walls between the existing equilibria. Depending on the stability of the steady states, the dynamics differs. Here, we consider the interface dynamics in the case of a spatially inhomogeneous system, namely, an optical system where the control parameter is spatially Gaussian. Then interfaces connect the monostable and the bistable nonuniform states that are associated with two distinct spatial regions. The coexistence of these two regions of different stability induces relaxation dynamics and the propagation of a wall with a time-dependent speed. We emphasize analytically these two dynamical behaviors using a generic bistable model. Experimentally, an inhomogeneous Gaussian light beam traveling through either a dye-doped liquid crystal cell or a Kerr cavity depicts these behaviors, in agreement with the theoretical predictions.

The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGGs) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarios—like in the analysis of a disease propagating through plants—the shape of the plots and fields where the host of the disease is located may play a fundamental role in the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots or fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph and we consider a lower bound for the epidemic threshold of a susceptible-infected-susceptible model or a susceptible-infected-recovered model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot or field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots or fields of the same area and different shapes.

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, an accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum-likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean-square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions that give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.

Interlinking a positive feedback loop (PFL) with a negative feedback loop (NFL) constitutes a typical motif in genetic networks, performing various functions in cell signaling. How time delay in feedback regulation affects the dynamics of such systems still remains unclear. Here, we investigate three systems of interlinked PFL and NFL with time delays: a synthetic genetic oscillator, a three-node circuit, and a simplified single-node model. The stability of steady states and the routes to oscillation in the single-node model are analyzed in detail. The amplitude and period of oscillations vary with a pointwise periodicity over a range of time delay. Larger-amplitude oscillations can be induced when the PFL has an appropriately long delay, in comparison with the PFL with no delay or short delay; this conclusion holds true for all the three systems. We unravel the underlying mechanism for the above effects via analytical derivation under a limiting condition. We also develop a stochastic algorithm for simulating a single reaction with two delays and show that robust oscillations can be maintained by the PFL with a properly long delay in the single-node system. This work presents an effective method for constructing robust large-amplitude oscillators and interprets why similar circuit architectures are engaged in timekeeping systems such as circadian clocks.

The glass transition region in nonconfined polymeric and low-molecular-weight supercooled liquids is probed by temperature-modulated calorimetry at a frequency of 3.3 mHz. From the distribution of relaxation times derived by analyzing the complex heat capacity, the number $N_{\alpha }$ of cooperatively rearranging units is estimated. This is done by resorting to a method in which cooperative motion is viewed as a result of a spontaneous regression of energy fluctuations. After a first, local, structural transition occurs, the energy threshold for the rearrangement of adjacent molecular units decreases progressively. This facilitation process is associated to a corresponding evolution of the density of states in a canonical representation and may be considered as a continuous spanning through different dynamic states toward a condition in which configurational constraints disappear. A good agreement is found with the $N_{\alpha }$ values obtained from the same calorimetric data within the framework of Donth's fluctuation theory. It is shown that, at variance from previous treatments, $N_{\alpha }$ can be estimated from just the relaxation function, without resorting to the knowledge of the configurational entropy. Examples point to a modest dependence of the $N_{\alpha }$ estimates on the experimental method used to derive the relaxation function.

We study the rheology of a soft particulate system where the interparticle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions ($\varphi$), attraction strengths ($u$), and imposed shear rates ($\dot{\gamma }$). In striking contrast to repulsive systems, we find that at small shear rates generically a fragile isostatic solid is formed even if we go to $\varphi \ll {\varphi }_J$. Further, with increasing shear rates, even at these low $\varphi$, nonmonotonic flow curves occur which lead to the formation of persistent shear bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough $\varphi$, we also observe structural changes via the interplay of low shear rates and attraction with the formation of microclusters and voids. Finally, we characterize the properties of the emergent shear bands, and thereby, we find surprisingly small mobility of these bands, leading to prohibitively long time scales and extensive history effects in ramping experiments.

We employ noncontact optical techniques to generate and measure stress waves in uncompressed, one-dimensional microscopic granular chains, and support our experiments with discrete numerical simulations. We show that the wave propagation through dry particles (150 μm radius) is highly nonlinear and it is significantly influenced by the presence of defects (e.g., surface roughness, interparticle gaps, and misalignment). We derive an analytical relation between the group velocity and gap size, and define bounds for the formation of highly nonlinear solitary waves as a function of gap size and axial misalignment.

Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed $c$ depending on position $\mathbf{r}$. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ${\ell }^{*}$, scattering phase function $f$, and anisotropy factor $g$. Discarding the operator term in the wave equation is shown to have a significant impact on $f$ and $g$, yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ${\ell }_c$ is smaller than or comparable to the wavelength $\lambda$. More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ${\ell }^{*}$ whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around $300\%$ in the low-frequency regime, and still above $30\%$ for ${\ell }_c/\lambda ={10}^3$ no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.

We provide Reynolds averaged azimuthal velocity profiles, measured in a Taylor-Couette system in turbulent flow, at medium Reynolds (7800 $<$ Re $<$ 18000) number with particle image velocimetry technique. We find that in the wall regions, close to the inner and outer cylinders, the azimuthal velocity profile reveals a significant deviation from classical logarithmic law. In order to propose a new law of the wall, the profile of turbulent mixing length was estimated from data processing; it was shown to behave nonlinearly with the radial wall distance. Based on this turbulent mixing length expression, a law of the wall was proposed for the Reynolds averaged azimuthal velocity, derived from momentum balance and validated by comparison to different data. In addition, the profile of viscous dissipation rate was investigated and compared to the global power needed to maintain the inner cylinder in rotation.

It is shown that the contributions of all partially resolved transition arrays (PRTAs) to the spectrum of a supertransition array (STA) may be summed by an efficient analytical method. The method is similar to the configurationally resolved super transition array method [G. Hazak and Y. Kurzweil, High Energy Density Phys. 8, 290 (2012)] and avoids the Gaussianity assumption of the partially resolved super transition arrays method [B. G. Wilson, C. A. Iglesias, and M. H. Chen High Energy Density Phys. 14, 67 (2015)], thus yielding an STA spectrum which is resolved down to the PRTA level.

We propose a multidomain grid refinement technique with extensions to entropic incompressible, thermal, and compressible lattice Boltzmann models. Its validity and accuracy are assessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal, and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the setups of turbulent channel flow, flow past a sphere, Rayleigh-Bénard convection, as well as the supersonic flow around an airfoil. Special attention is paid to analyzing the adaptive features of entropic lattice Boltzmann models for multigrid simulations.

The distribution of ions near a charged surface is an important quantity in many biological and material processes, and has been therefore investigated intensively. However, few theoretical and simulation approaches have included the influence of concentration-induced variations in the local dielectric permittivity of an underlying electrolyte solution. Such local variations have long been observed and known to affect the properties of ionic solution in the bulk and around the charged surface. We propose a hybrid computational model that combines Monte Carlo simulations with continuum electrostatic modeling to investigate such properties. A key component in our hybrid model is a semianalytical formula for the ion-ion interaction energy in a dielectrically inhomogeneous environment. This formula is obtained by solving for the Green's function Poisson's equation with ionic-concentration-dependent dielectric permittivity using a harmonic interpolation method and spherical harmonic series. We also construct a self-consistent continuum model of electrostatics to describe the effect of ionic-concentration-dependent dielectric permittivity and the resulting self-energy contribution. With extensive numerical simulations, we verify the convergence of our hybrid simulation scheme, show the qualitatively different structures of ionic distribution due to the concentration-induced dielectric variations, and compare our simulation results with the self-consistent continuum model. In particular, we study the differences between weakly and strongly charged surfaces and multivalencies of counterions. Our hybrid simulations conform particularly the depletion of ionic concentrations near a charged surface and also capture the charge inversion. We discuss several issues and possible further improvement of our approach for simulations of large charged systems.

The helical magnetorotational instability is known to work for resistive rotational flows with comparably steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear are continuously connected when some axial electrical current is allowed to flow through the rotating fluid. Using a local approximation we demonstrate that the magnetohydrodynamic behavior of this dissipation-induced instability is intimately connected with the nonmodal growth and the pseudospectrum of the underlying purely hydrodynamic problem.

One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence—the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive—the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.

Recent papers have shown that spatial (quenched) disorder can suppress discontinuous absorbing phase transitions. Conversely, the scenario for temporal disorder is still unknown. To shed some light in this direction, we investigate its effect in three different two-dimensional models which are known to exhibit discontinuous absorbing phase transitions. The temporal disorder is introduced by allowing the control parameter to be time dependent $p\to p\left(t\right)$, either varying as a uniform distribution with mean $\overline{p}$ and variance $\sigma$ or as a bimodal distribution, fluctuating between a value $p$ and a value $p_l\ll p$. In contrast to spatial disorder, our numerical results strongly suggest that such uncorrelated temporal disorder does not forbid the existence of a discontinuous absorbing phase transition. We find that all cases are characterized by behaviors similar to their pure (without disorder) counterparts, including bistability around the coexistence point and common finite-size scaling behavior with the inverse of the system volume, as recently proposed [M. M. de Oliveira et al., Phys. Rev. E 92, 062126 (2015)]. We also observe that temporal disorder does not induce temporal Griffiths phases around discontinuous phase transitions, at least not for $d=2$.

We study a stochastic lattice model for cell colony growth, which takes into account proliferation, diffusion, and rotation of cells, in a culture medium with quenched disorder. The medium is composed of sites that inhibit any possible change in the internal state of the cells, representing the disorder, as well as by active medium sites that do not interfere with the cell dynamics. By means of Monte Carlo simulations we find that the velocity of the growing interface, which is taken as the order parameter of the model, strongly depends on the density of active medium sites (${\rho }_A$). In fact, the model presents a (continuous) second-order pinning-depinning transition at a certain critical value of ${\rho }_A^{\mathrm{crit}}$, such as, for ${\rho }_A>{\rho }_A^{\mathrm{crit}}$, the interface moves freely across the disordered medium, but for ${\rho }_A<{\rho }_A^{\mathrm{crit}}$ the interface becomes irreversible pinned by the disorder. By determining the relevant critical exponents, our study reveals that within the depinned phase the interface can be rationalized in terms of the Kardar-Parisi-Zhang universality class, but when approaching the critical threshold, the nonlinear term of the Kardar-Parisi-Zhang equation tends to vanish and then the pinned interface belongs to the quenched Edwards-Wilkinson universality class.

The concept of the effective potential is suggested as an efficient instrument to get a uniform analytical description of stochastic high-temperature on-off flashing and rocking ratchets. The analytical representation for the average particle velocity, obtained within this technique, allows description of ratchets with sharp potentials (and potentials with jumps in particular). For sawtooth potentials, the explicit analytical expressions for the average velocity of on-off flashing and rocking ratchets valid for arbitrary frequencies of potential energy fluctuations are derived; the difference in their high-frequency asymptotics is explored for the smooth and cusped profiles, and profiles with jumps. The origin of the difference as well as the appearance of the jump behavior in ratchet characteristics are interpreted in terms of self-similar universal solutions which give the continuous description of the effect. It is shown how the jump behavior in motor characteristics arises from the competition between the characteristic times of the system.

Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on a $2M\times 2N$ checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using the exact partition function and finite-size corrections for the dimer model on a finite checkerboard lattice, we obtain finite-size scaling functions for the free energy, the internal energy, and the specific heat of the dimer model. We investigate the properties of the specific heat near the critical point and find that the specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent $\lambda$ is equal to $\infty$. We have also considered the limit $N\to \infty$ for which we obtain the expansion of the free energy for the dimer model on the infinitely long cylinder. From a finite-size analysis we have found that two conformal field theories with the central charges $c=1$ for the height function description and $c=-2$ for the construction using a mapping of spanning trees can be used to describe the dimer model on the checkerboard lattice.

Macroscopic extended systems with dissipation and injection of energy can exhibit particlelike solutions. Dissipative kinks with an oscillatory cloak and a family of localized states that connect uniform symmetric states in a magnetic wire forced with a transversal oscillatory magnetic field and in a parametrically driven damped pendula chain are studied. The oscillatory cloak is composed of evanescent waves emitted at the kink position and generated by a resonant mechanism. These waves mediate the kink interaction and generate a family of localized states.