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In this paper, we introduce a novel approach to study reaction-diffusion systems -- dynamic transition theory approach developed in Ma and Wang 2015. This approach generalizes Turing's classical result (linear stability analysis) on pattern…
Transport at microscopic length scales is essential in biological systems and various technologies, including microfluidics. Recent experiments achieved self-organized transport phenomena in microtubule active matter using light to modulate…
In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…
We report an approach to obtain effective pair potentials which describe the structure of two-dimensional systems of active Brownian particles. The pair potential is found by an inverse method, which matches the radial distribution function…
Quantum collision models normally consist of a system interacting with a set of ancillary units representing the environment. While these ancillary systems are usually assumed to be either two level systems (TLS) or harmonic oscillators, in…
The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order…
The principles of statistical mechanics and information theory play an important role in learning and have inspired both theory and the design of numerous machine learning algorithms. The new aspect in this paper is a focus on integrating…
Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their…
Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's…
We develop a nonequilibrium Green's function theory for dispersion interactions between two nanostructures, each an open quantum system driven into a nonequilibrium steady state by an applied bias voltage. Starting from the two-particle…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact,…
We develop a thermodynamic framework for closed and open chemical networks applicable to non-elementary reactions that do not need to obey mass action kinetics. It only requires the knowledge of the kinetics and of the standard chemical…
We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms…
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…
We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained…
Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for…
Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…