Related papers: Construction of a two-phase flow with singular ene…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded domain. One phase is assumed to be magnetic, the other phase…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
Variational models of phase transitions take into account double-well energies singularly perturbed by gradient terms, such as the Cahn-Hilliard free energy. The derivation by $\Gamma$-convergence of a sharp-interface limit for such energy…
The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is…
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the…
We demonstrate that the uniqueness of solutions to a broad class of parabolic geometric evolution equations can be proven via a direct and essentially classical energy argument which avoids the DeTurck trick entirely. Previously, we have…
Fluid elements deform in turbulence by stretching and folding. In this work, by projecting the material deformation tensor onto the largest stretching direction, the dynamics of folding is depicted through the evolution of the material…
In this paper, we consider a compressible two-fluid system with a common velocity field and algebraic pressure closure in dimension one. Existence, uniqueness and stability of global weak solutions to this system are obtained with…
We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…
We prove the convergence of an implicit time discretization for the one-phase Mullins-Sekerka equation, possibly with additional non-local repulsion, proposed in [F. Otto, Arch. Rational Mech. Anal. 141 (1998) 63--103]. Our simple argument…
We study time-dependent density segregation of granular mixtures flowing over an inclined plane. Discrete Element Method (DEM) simulations in a periodic box are performed for granular mixtures of same size and different density particles…
We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure…
Hydrodynamics describes the evolution of macroscopic states in non--equilibrium thermodynamics. Following Onsager reciprocal relations, one can formulate a large class of hydrodynamic equations as gradient flows of free energies. In recent…
The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…
We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a…
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…