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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.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.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. selleck kinase inhibitor 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.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.Two-dimensional particle-in-cell simulations are presented of the linear and nonlinear developments of stimulated Raman scattering in two overlapping laser beams. The development of the most unstable mode in the linear stage is consistent with a previous paper [C. Z. Xiao et al., Phys. Plasmas 26, 062109 (2019)PHPAEN1070-664X10.1063/1.5096850] where SL mode (two beams share a common scattered light) is dominant in the overlapping region. This mode is enhanced with plasma density and correlation of beam polarizations. When lasers are cross-polarized, it backs to the single-beam Raman backscattering with weak intensity. Trapping-induced nonlinear frequency shift leads to the saturation of SL mode by detuning the coupling and broadening the spectrum. An interesting result that SL mode becomes stronger as the incidence angle increases is contrary to the theoretical prediction and it is a consequence of less efficient saturation in the nonlinear stage.We apply generalizations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional ±1 random-bond Ising model. The behavior of the model is determined by the temperature T and the concentration p of negative (antiferromagnetic) bonds. The ground state is ferromagnetic for 0≤p0, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for p=0 where the clusters are strictly tied to Ising correlations so the percolation transition is in the Ising universality class.A theory explaining how deep learning works is yet to be developed. Previous work suggests that deep learning performs a coarse graining, similar in spirit to the renormalization group (RG). This idea has been explored in the setting of a local (nearest-neighbor interactions) Ising spin lattice. We extend the discussion to the setting of a long-range spin lattice. Markov-chain Monte Carlo (MCMC) simulations determine both the critical temperature and scaling dimensions of the system. The model is used to train both a single restricted Boltzmann machine (RBM) network, as well as a stacked RBM network. Following earlier Ising model studies, the trained weights of a single-layer RBM network define a flow of lattice models. In contrast to results for nearest-neighbor Ising, the RBM flow for the long-ranged model does not converge to the correct values for the spin and energy scaling dimension. Further, correlation functions between visible and hidden nodes exhibit key differences between the stacked RBM and RG flows. The stacked RBM flow appears to move toward low temperatures, whereas the RG flow moves toward high temperature. This again differs from results obtained for nearest-neighbor Ising.An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a "cutoff distance variable" which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain.