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Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
We present a novel picture of a non isothermal solidification process starting from a molecular level, where the microscopic origin of the basic mechanisms and of the instabilities characterizing the approach to equilibrium is rendered more…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
We examine a biomolecular machine involving a driven, observable process coupled to a hidden process in a kinetically cooperative manner. A stochastic thermodynamics framework is employed to analyze a fluctuation theorem for the…
We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
We present a numerical method that consistently implements thermal fluctuations and hydrodynamic interactions to the motion of Brownian particles dispersed in incompressible host fluids. In this method, the thermal fluctuations are…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
We provide a stochastic thermodynamic description across scales for $N$ identical units with all-to-all interactions that are driven away from equilibrium by different reservoirs and external forces. We start at the microscopic level with…
In this theoretical and numerical study, we show how spatially extended fluctuations can influence and dominate the dynamics of a fluid filled elastic blister as is deforms onto a pre-wetted solid substrate. To describe the blister…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus,…
Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
We study non-equilibrium velocity fluctuations in a model for the sedimentation of non-Brownian particles experiencing long-range hydrodynamic interactions. The complex behavior of these fluctuations, the outcome of the collective dynamics…