Related papers: Anomalous diffusion in nonlinear transformations o…

We present new simulation results on a hard sphere system at high densities. Using three-time correlations, we can account for the anomalous diffusion, which results from a homogeneous back-dragging effect. Furthermore, we calculate the…

This mini-review presents extensions of the voter model that incorporate various plausible features of real decision-making processes by individuals. Although these generalizations are not calibrated by empirical data, the resulting…

We propose a modified voter model with locally conserved magnetization and investigate its phase ordering dynamics in two dimensions in numerical simulations. Imposing a local constraint on the dynamics has the surprising effect of speeding…

Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement…

The filtering distribution is a time-evolving probability distribution on the state of a dynamical system, given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly…

In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the…

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a…

We study the ordering dynamics of nonlinear voter models with multiple states, also providing a discussion of the two-state model. The rate with which an individual adopts an opinion scales as the $q$-th power of the number of the…

In recent years, some researchers have applied diffusion models to multivariate time series anomaly detection. The partial diffusion strategy, which depends on the diffusion steps, is commonly used for anomaly detection in these models.…

We study the finite-momentum spin dynamics in the one-dimensional XXZ spin chain within the Ising-type regime at high temperatures using density autocorrelations within linear response theory and real-time propagation of nonequilibrium…

The onset of the Rayleigh-Benard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion…

In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights…

We study an adaptive network model driven by a nonlinear voter dynamics. Each node in the network represents a voter and can be in one of two states that correspond to different opinions shared by the voters. A voter disagreeing with its…

Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of…

Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

We analyze the universality classes of phase transitions in a variety of nonlinear voter models. By mapping several models with symmetric absorbing states onto a canonical model introduced in previous studies, we confirm that they exhibit a…

This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are…

In the voter model, vertices of a graph (interpreted as voters) adopt one out of two opinions (0 and 1), and update their opinions at random times by copying the opinion of a neighbor chosen uniformly at random. This process is dual to a…