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Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of…
In this paper we analyze a PDE system modelling (non-isothermal) phase transitions and damage phenomena in thermoviscoelastic materials. The model is thermodynamically consistent: in particular, no {\em small perturbation assumption} is…
Fundamental properties of the multicomponent diffuse-interface model (DIM), such as the maximum entropy principle and conservation laws, are used to explore the basic interfacial dynamics and phase transitions in fluids. Flat interfaces…
We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models…
Dense mixture of granules and liquid often shows a sever shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of…
A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in…
Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of…
This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…
We study the deployment of a first-order multi-agent system over a desired smooth curve in 3D space. We assume that the agents have access to the local information of the desired curve and their displacements with respect to their closest…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
Sea ice is highly complex due to the inhomogeneity of the physical properties (e.g. temperature and salinity) as well as the permeability and mixture of water and a matrix of sea ice and/or sea ice crystals. Such complexity has proven…
A transient analysis for vesicle deformation under DC electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the…
We consider a quasilinear degenerate diffusion-reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law degeneracy as one of the dependent variables vanishes and a super diffusion singularity…
In this work, we investigate the existence and uniqueness properties of a composite structure (multilayered) fluid interaction PDE system which arises in multi-physics problems, and particularly in biofluidic applications related to the…
The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…
We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g. a shell) or…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
We present here a multilayer model for shallow grain-fluid mixtures with dilatancy effects. It can be seen as a generalization of the depth-averaged model presented in Bouchut et al. (2016), that includes dilatancy effects by considering a…