Related papers: Approximation of the Helfrich's functional via Dif…
This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.
Understanding the interface dynamics in non-equilibrium quantum systems remains a challenge. We study the interface dynamics of strongly coupled immiscible binary superfluids by using holographic duality. The full nonlinear evolution of the…
We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…
We propose to model physical effects at the sharp density interface between atmosphere and ocean with the help of diffuse interface approaches for multiphase flows with variable densities. We use the variable-density model proposed in…
We conduct a theoretical study of a two-phase-fluid-structure interaction problem in which air is driven at constant volume flux into a liquid-filled Hele-Shaw channel whose upper boundary is an elastic sheet. A depth-averaged model in the…
We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties…
Hypothesis: Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
Simulations of liquid-gas systems with extended interfaces are observed to fail to give accurate results for two reasons: the interface can get ``stuck'' on the lattice or a density overshoot develops around the interface. In the first case…
An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…
We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parameter tends to zero. Our result is of implicit function…
Motivated by recent results in spin chains we study dissipation and relaxation in a two-dimensional holographic interface conformal field theory (ICFT) in which degrees of freedom on one side of the interface are coupled to an external…
In this work I derive analytic expressions for the curvature dependent fluid-substrate surface tension of a hard sphere fluid on a hard curved wall. In a first step, the curvature thermodynamic properties are found as truncated power series…
A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test…
We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to an in-plane applied electric field. We develop a spectrally accurate boundary integral method where a coupled integral equation system is formulated.…
We derive a connection between the intrinsic tribological properties and the electronic properties of a solid interface. In particular, we show that the adhesion and frictional forces are dictated by the electronic charge redistribution…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
We consider a dynamical random interface on the infinite lattice $\mathbb{N}$ evolving according to a "corner flip" dynamic above a hard wall, with an additional pinning at the origin. We study the stationary fluctuations under a diffusive…