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We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different…
We establish the global well-posedness of overdamped dynamic density functional theory (DDFT): a nonlinear, nonlocal integro-partial differential equation used in statistical mechanical models of colloidal fluids, and other applications…
We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the…
Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from the sound produced by a violin to the screeching of chalk…
We consider an elastic/viscoelastic transmission problem for the Bresse system with fully Dirichlet or Dirichlet-Neumann-Neumann boundary conditions. The physical model consists of three wave equations coupled in certain pattern. The system…
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…
We study three different experiments that involve dry friction and periodic driving, and which employ both single and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects,…
We present a Brownian dynamics model of driven polymer translocation, in which non-equilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
In the paper, a mathematical model assembling a "driver - mobile vehicle - road environment" system and capable of simulating the process of mobile vehicles skid in traction movement mode is proposed. The usage of non-linear drift models…
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
If a porous media is being damaged by excessive stress, the elastic matrix at every infinitesimal volume separates into a 'solid' and a 'broken' component. The 'solid' part is the one that is capable of transferring stress, whereas the…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
We develop further a new geometrical model of a discretized string, proposed in [1] and establish its basic physical properties. The model can be considered as the natural extention of the usual Feynman amplitude of the random walks to…
Robotic systems operating in unstructured environments must operate under significant uncertainty arising from intermittent contacts, frictional variability, and unmodeled compliance. While recent model-free approaches have demonstrated…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…