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Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
Diffusion studies of adsorbates moving on a surface are often analyzed using 2D Langevin simulations. These simulations are computationally cheap and offer valuable insight into the dynamics, however, they simplify the complex interactions…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…
Understanding mechanisms of rare but important events in complex molecular systems, such as protein folding or ligand (un)binding, requires accurately mapping transition paths from an initial to a final state. The committor is the ideal…
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous…
Building on the phenomenological and microscopic models reviewed in Part I, this second part focuses on network-level mechanisms that generate emergent temperature response curves. We review deterministic models in which temperature…
We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of…
We consider reaction-diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using Lyapunov functional and duality arguments, we establish…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
The role of dimensionality (Euclidean versus fractal), spatial extent, boundary effects and system topology on the efficiency of diffusion-reaction processes involving two simultaneously-diffusing reactants is analyzed. We present…
This paper provides a theoretical framework of deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and chemical reaction. Very general forms of the…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by…
We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…