Related papers: Bead-rod-spring models in random flows
We study the energy distribution during the emergence of a quasi-equilibrium (QE) state in the course of relaxation to equipartition in slow-fast Hamiltonian systems. A bead-spring model where beads (masses) are connected by springs is…
Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional complex systems predict future states individually. This approach struggles to model complex temporal dependencies and fails to…
We prove the existence of large-data global-in-time weak solutions to a general class of coupled bead-spring chain models with finitely extensible nonlinear elastic (FENE) type spring potentials for nonhomogeneous incompressible dilute…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
We introduce a nonlinear, one-dimensional bending-twisting model for an inextensible bi-rod that is composed of a nematic liquid crystal elastomer. The model combines an elastic energy that is quadratic in curvature and torsion with a…
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence and heat transport modification in natural convection, and is one…
The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we…
Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
We investigate mutual local chain order in systems of fully flexible polymer melts in a simple generic bead-spring model. The excluded-volume interaction together with the connectivity leads to local ordering effects which are independent…
The aim of this paper is twofold. First, we set up the theory of elastic matter sources within the framework of general relativity in a self-contained manner. The discussion is primarily based on the presentation of Carter and Quintana but…
We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
This paper investigates solutions of hyperbolic diffusion equations in $\mathbb{R}^3$ with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere $S^2$ are studied. All…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
The role played by a kinetic barrier originated by out-of-plane step edge diffusion, introduced in [Leal \textit{et al.}, \href{https://doi.org/10.1088/0953-8984/23/29/292201}{J. Phys. Condens. Matter \textbf{23}, 292201 (2011)}], is…
The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garz\'o, Brito and Soto, Phys. Fluids \textbf{33}, 023310 (2021)] is considered further to analyze two different problems.…
In light of recent advancements in the constitutive modelling of bidisperse and polydisperse entangled linear polymers, we present a new multi fluid generalization of the classic two fluid approximation for flows of inhomogeneous polymer…
In this paper, we propose a drift-diffusion process on the probability simplex to study stochastic fluctuations in probability spaces. We construct a counting process for linear detailed balanced chemical reactions with finite species such…