Related papers: General Solution to the Mixing Problem: Applicatio…
Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the…
Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…
This paper collects the efforts done in our previous works [P. Degond, S. Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L. Mieussens, A Moving…
Physiological whole-body models are valuable tools for the development of novel drugs where understanding the system aspects is important. This paper presents a generalized model that encapsulates the structure and flow of whole-body human…
Multimodal data modeling has emerged as a powerful approach in clinical research, enabling the integration of diverse data types such as imaging, genomics, wearable sensors, and electronic health records. Despite its potential to improve…
Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to…
A general adsorption model is developed to describe the interactions between near-wall fluid molecules and solid surface. This model serves as a framework for the theoretical modelling of the boundary slip phenomena. Based on this…
We study a linear problem that arises in the study of dynamic boundaries, in particular in free boundary problems in connection with fluid dynamics. The equations are also very natural and of interest on their own.
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a non-uniform porous medium. We consider the case of a porous media with a permeability jump across a horizontal…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
In this work we introduce a mixture of GPs to address the data association problem, i.e. to label a group of observations according to the sources that generated them. Unlike several previously proposed GP mixtures, the novel mixture has…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
In microvascular transport, where both blood and drug carriers are involved, plasma skimming has a key role on changing hematocrit level and drug carrier concentration in capillary beds after continuous vessel bifurcation in the…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
Viscous fingering is a well-known hydrodynamic instability that sets in when a less viscous fluid displaces a more viscous fluid. When the two fluids are miscible, viscous fingering introduces disorder in the velocity field and exerts a…
We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method and the advection-diffusion equation for…
We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…