Two-dimensional arrays of nonlinear electric oscillators are considered theoretically where nearest neighbors are coupled by relatively small constant but nonequal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schrödinger equation with translationally noninvariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the internode coupling as well as on the ratio between time-increasing healing length and lattice spacings. In particular, vortex clusters can be stably trapped for some initial period of time by a circular barrier in the coupling profile, but then, due to gradual dissipative broadening of vortex cores, they lose stability and suddenly start to move.

The focus of this research is to delineate the thermal behavior of a rarefied monatomic gas confined between horizontal hot and cold walls, physically known as rarefied Rayleigh-Bénard (RB) convection. Convection in a rarefied gas appears only for high temperature differences between the horizontal boundaries, where nonlinear distributions of temperature and density make it different from the classical RB problem. Numerical simulations adopting the direct simulation Monte Carlo approach are performed to study the rarefied RB problem for a cold to hot wall temperature ratio equal to $r=0.1$ and different rarefaction conditions. Rarefaction is quantified by the Knudsen number, Kn. To investigate the long-time thermal behavior of the system two ways are followed to measure the heat transfer: (i) measurements of macroscopic hydrodynamic variables in the bulk of the flow and (ii) measurements at the microscopic scale based on the molecular evaluation of the energy exchange between the isothermal wall and the fluid. The measurements based on the bulk and molecular scales agreed well. Hence, both approaches are considered in evaluations of the heat transfer in terms of the Nusselt number, Nu. To characterize the flow properly, a modified Rayleigh number (${\mathrm{Ra}}_m$) is defined to take into account the nonlinear temperature and density distributions at the pure conduction state. Then the limits of instability, indicating the transition of the conduction state into a convection state, at the low and large Froude asymptotes are determined based on ${\mathrm{Ra}}_m$. At the large Froude asymptote, simulations following the onset of convection showed a relatively small range for the critical Rayleigh (${\mathrm{Ra}}_m=1770\pm 15$) that flow instability occurs at each investigated rarefaction degree. Moreover, we measured the maximum Nusselt values ${\mathrm{Nu}}_{\max }$ at each investigated Kn. It was observed that for $\mathrm{Kn}\ge 0.02, {\mathrm{Nu}}_{\max }$ decreases linearly until the transition to conduction at $\mathrm{Kn}\approx 0.03$, known as the rarefaction limit for $r=0.1$, occurs. At the low Froude (parametric) asymptote, the emergence of a highly stratified flow is the prime suspect of the transition to conduction. The critical ${\mathrm{Ra}}_m$ in which this transition occurs is then determined at each Kn. The comparison of this critical Rayleigh versus Kn also shows a linear decrease from ${\mathrm{Ra}}_m\approx 7400$ at $\mathrm{Kn}=0.02$ to ${\mathrm{Ra}}_m\approx 1770$ at $\mathrm{Kn}\approx 0.03$.

Discretizing Maxwell's equations in Galilean (comoving) coordinates allows the derivation of a pseudospectral solver that eliminates the numerical Cherenkov instability for electromagnetic particle-in-cell simulations of relativistic plasmas flowing at a uniform velocity. Here we generalize this solver by incorporating spatial derivatives of arbitrary order, thereby enabling efficient parallelization by domain decomposition. This allows scaling of the algorithm to many distributed compute units. We derive the numerical dispersion relation of the algorithm and present a comprehensive theoretical stability analysis. The method is applied to simulations of plasma acceleration in a Lorentz-boosted frame of reference.

In three-dimensional computer simulations of model non-Brownian jammed suspensions, we compute the time required to reach homogeneous flow upon yielding, by analyzing stresses and particle packing at different shear rates, with and without confinement. We show that the stress overshoot and persistent shear banding preceding the complete fluidization are controlled by the presence of overconstrained microscopic domains in the initial solids. Such domains, identifiable with icosahedrally packed regions in the model used, allow for stress accumulation during the shear startup. Their structural reorganization under deformation controls the emergence and the persistence of the shear banding.

We present a full derivation of capillary fluid equations from the kinetic theory of dense gases. These equations involve van der Waals' gradient energy, Korteweg's tensor, and Dunn and Serrin's heat flux as well as viscous and heat dissipative fluxes. Starting from macroscopic equations obtained from the kinetic theory of dense gases, we use a second-order expansion of the pair distribution function in order to derive the diffuse interface model. The capillary extra terms and the capillarity coefficient are then associated with intermolecular forces and the pair interaction potential.

Dynamic renormalization group (RG) of fluctuating viscoelastic equations is investigated to clarify the cause for numerically reported disappearance of anomalous heat conduction (recovery of Fourier's law) in low-dimensional momentum-conserving systems. RG flow is obtained explicitly for simplified two model cases: a one-dimensional continuous medium under low pressure and incompressible viscoelastic medium of arbitrary dimensions. Analyses of these clarify that the inviscid fixed point of contributing the anomalous heat conduction becomes unstable under the RG flow of nonzero elastic-wave speeds. The dynamic RG analysis further predicts a universal scaling of describing the crossover between the growth and saturation of observed heat conductivity, which is confirmed through the numerical experiments of Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattices.

In this paper we employ methods from statistical mechanics to model temporal correlations in time series. We put forward a methodology based on the maximum entropy principle to generate ensembles of time series constrained to preserve part of the temporal structure of an empirical time series of interest. We show that a constraint on the lag-one autocorrelation can be fully handled analytically and corresponds to the well-known spherical model of a ferromagnet. We then extend such a model to include constraints on more complex temporal correlations by means of perturbation theory, showing that this leads to substantial improvements in capturing the lag-one autocorrelation in the variance. We apply our approach on synthetic data and illustrate how it can be used to formulate expectations on the future values of a data-generating process.

It has long been conjectured that (rapid) fracture propagation dynamics in materials and turbulent motion of fluids are two manifestations of the same physical process. The universality class of turbulence (Kolmogorov dispersion, in particular) is conjectured to be identifiable with the Flory statistics for linear polymers (self-avoiding walks on lattices). These help us to relate fracture statistics to those of linear polymers (Flory statistics). The statistics of fracture in the fiber bundle model (FBM) are now well studied and many exact results are now available for the equal-load-sharing (ELS) scheme. Yet, the correlation length exponent in this model was missing and we show here how the correspondence between fracture statistics and the Flory mapping of Kolmogorov statistics for turbulence helps us to make a conjecture about the value of the correlation length exponent for fracture in the ELS limit of FBM and, also, about the upper critical dimension. In addition, the fracture avalanche size exponent values at lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.

We investigate the relaxation dynamics of a one-dimensional Ising chain via Glauber kinetic Monte Carlo simulations, when the system is cooled slowly from infinite temperature to zero temperature with different cooling protocols. The main quantity of interest is the excess defect density that represents the total defect density minus the equilibrium defect density at varying temperatures. We find that, for three classes of cooling protocols, the time dependence of the excess defect density for various cooling speed shows a dynamic scaling behavior that largely encompasses the Kibble-Zurek mechanism as well as Krapivsky's calculation of the final defect density at zero temperature. We also find distinct features in the behavior of the dynamic scaling when the temperature approaches in a power-law fashion to zero temperature and the excess defect density reaches a peak at finite temperature, where the scaling of the excess defect density at its peak and that at zero temperature exhibits different asymptotic behavior due to different logarithmic corrections. This characteristic behavior can be attributed to the exponential divergence of the relaxation time near zero temperature. While the qualitative theoretical predictions by Krapivsky on the asymptotic exponents are confirmed, the asymptotic predictions for amplitudes overestimate by up to $40\%$ the simulation results.

We derive an extended fluctuation relation for an open system coupled with two reservoirs under adiabatic one-cycle modulation. We confirm that the geometrical phase caused by the Berry-Sinitsyn-Nemenman curvature in the parameter space generates non-Gaussian fluctuations. This non-Gaussianity is enhanced for the instantaneous fluctuation relation when the bias between the two reservoirs disappears.

The dynamic critical behavior of the two-dimensional Ising model with nonextensive Tsallis statistics has been studied. The values of the dynamic critical index $z$ as well as the values of the indices $\nu$ and $\beta$ for different values of the deformation parameter $q$ have been obtained. The emergence of a new type of critical behavior has been revealed.

Arrays of coupled semiconductor lasers are systems possessing radically complex dynamics that makes them useful for numerous applications in beam forming and beam shaping. In this work, we investigate the spatial controllability of oscillation amplitudes in an array of coupled photonic dimers, each consisting of two semiconductor lasers driven by differential pumping rates. We consider parameter values for which each dimer's stable phase-locked state has become unstable through a Hopf bifurcation and we show that, by assigning appropriate pumping rate values to each dimer, high-amplitude oscillations coexist with negligibly low-amplitude oscillations. The spatial profile of the amplitude of oscillations across the array can be dynamically controlled by appropriate pumping rate values in each dimer. This feature is shown to be quite robust, even for random detuning between the lasers, and suggests a mechanism for dynamically reconfigurable production of a large diversity of spatial profiles of laser amplitude oscillations.

Motivated by recent studies of the phenomenon of coherent perfect absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as well as of the recently introduced reflection time difference (RTD). The latter plays the same role for $S$-matrix zeros as the Wigner time delay does for its poles. For systems with broken time-reversal invariance, we derive the $n$-point correlation functions of the zeros in a closed determinantal form, and we study various asymptotics and special cases of the associated kernel. The time-correlation function of the RTD is then evaluated and compared with numerical simulations. This allows us to identify a cubic tail in the distribution of RTD, which we conjecture to be a superuniversal characteristic valid for all symmetry classes. We also discuss two methods for possible extraction of $S$-matrix zeros from scattering data by harmonic inversion.

Unreliable network data can cause community-detection methods to overfit and highlight spurious structures with misleading information about the organization and function of complex systems. Here we show how to detect significant flow-based communities in sparse networks with missing links using the map equation. Since the map equation builds on Shannon entropy estimation, it assumes complete data such that analyzing undersampled networks can lead to overfitting. To overcome this problem, we incorporate a Bayesian approach with assumptions about network uncertainties into the map equation framework. Results in both synthetic and real-world networks show that the Bayesian estimate of the map equation provides a principled approach to revealing significant structures in undersampled networks.

We investigate signed networks with community structure with respect to their spectra and their evolution under a dynamical model of structural balance, a prominent theory of signed social networks. The spectrum of the adjacency matrix generated by a stochastic block model with two equal-size communities shows detectability transitions in which the community structure becomes manifest when its signal eigenvalue appears outside the main spectral band. The spectrum also exhibits “sociality” transitions involving the homogeneous structure representing the average tie value. We derive expressions for the eigenvalues associated with the community and homogeneous structure as well as the transition boundaries, all in good agreement with numerical results. Using the stochastically generated networks as initial conditions for a simple model of structural balance dynamics yields three outcome regimes: two hostile factions that correspond with the initial communities, two hostile factions uncorrelated with those communities, and a single harmonious faction of all nodes. The detectability transition predicts the boundary between the assortative and mixed two-faction states and the sociality transition predicts that between the mixed and harmonious states. Our results may yield insight into the dynamics of cooperation and conflict among actors with distinct social identities.

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness $e$ of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like $1/e$, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

We have designed three-dimensional numerical simulations of a soft spheres model, with size polidispersity and in athermal conditions, to study the transient shear banding that occurs during yielding of jammed soft solids. We analyze the effects of different types of drag coefficients used in the simulations and compare the results obtained using Lees-Edwards periodic boundary conditions with the case in which the same model solid is confined between two walls. The specific damping mechanism and the different boundary conditions indeed modify the load curves and the velocity profiles in the transient regime. Nevertheless, we find that the presence of a stress overshoot and of a related transient banding phenomenon, for large enough samples, is a robust feature for overdamped systems, where their presence do not depend on the specific drag used and on the different boundary conditions.

Fundamental investigations of how boundary slip relative to the no-slip condition for liquid flow in a set of two distinct idealized pore geometries, i.e., a diverging-converging tortuous pore, in contrast to a straight tube capillary pore, contribute to emergent Darcy flow and flow enhancement are presented. Using steady-state solutions to Navier-Stokes equations, a sensitivity study investigates the role of (a) a large variation in boundary slip reported in the literature, and (b) a large variation in pore-throat sizes found in geologic porous media. Results show that both the pore geometry and their pore-throat sizes contribute to differences over several orders of magnitude in the emergent Darcy flow behavior and the flow enhancement. Tortuous pores contribute to a lower flow enhancement relative to the capillary pores, and while the larger pore throats (i.e., $\ge 10\mu \mathrm{m}$) negligibly enhance flow, it increasingly becomes significant for the micron-size pore throats. From capillary pores, flow enhancement is found to increases linearly in an unlimited manner with an increment in boundary slip relative to the no-slip condition. In contrast, flow enhancement from diverging-converging tortuous pores is found to get limited defined by an asymptote for flows with a larger boundary slip. Capillary pores offer no change in resistance to flow due to boundary slip. In contrast, the very nature of diverging-converging tortuous pore geometry offers growth in drag forces and energy dissipation rate, i.e., an increase in resistance to flow, which contributes to the asymptote or the limited flow enhancement. A set of theoretical models are presented, which can be used to predict the flow enhancement as a function of boundary slip and spatial-scale of pore throats. This study may have implications for predicting flow enhancement and pressure loss during fluid injection or recovery from low permeability geologic reservoirs, and relevant to other engineering applications, e.g., hydraulics in corrugated channels or design of carbon nanotube membranes for desalinization purposes.

The dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian dynamics or molecular dynamics simulation, DMC is applicable to systems of spherical and/or anisotropic particles and to equilibrium or out-of-equilibrium processes. In this work, we present a theoretical and methodological framework to extend DMC to the study of heterogeneous systems, where the presence of an interface between coexisting phases introduces an additional element of complexity in determining the dynamic properties. In particular, we simulate a Lennard-Jones fluid at the liquid-vapor equilibrium and determine the diffusion coefficients in the bulk of each phase and across the interface. To test the validity of our DMC results, we also perform Brownian Dynamics simulations and unveil an excellent quantitative agreement between the two simulation techniques.