Related papers: Sharp Interface Limit for the Cahn-Larch\'e System
We present an extension of the Allen-Cahn/Cahn-Hilliard system which incorporates a geometrically linear ansatz for the elastic energy of the precipitates. The model contains both the elastic Allen-Cahn system and the elastic Cahn-Hilliard…
We introduce a diffused interface formulation of the Plateau problem, where the Allen--Cahn energy $\mathcal{AC}_\varepsilon$ is minimized under a volume constraint $v$ and a spanning condition on the level sets of the densities. We discuss…
We show convergence of solutions of a convective Allen-Cahn equation for a given smooth and divergence free velocity field to a transport equation for an evolving interface in the case when the thickness of the diffuse interface tends to…
We study a quasi-incompressible Navier--Stokes/Cahn--Hilliard coupled system which describes the motion of two macroscopically immiscible incompressible viscous fluids with partial mixing in a small interfacial region and long-range…
We consider the Allen-Cahn equation with nonlinear anisotropic diffusion and derive anisotropic direction-dependent curvature flow under the sharp interface limit. The anisotropic curvature flow was already studied, but its derivation is…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn--Hilliard type allow for dynamic…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
We derive a posteriori error estimate for a fully discrete adaptive finite element approximation of the stochastic Cahn-Hilliard equation with rough noise. The considered model is derived from the stochastic Cahn-Hilliard equation with…
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
Violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality certifies genuine quantum correlations. In this work, we formalize in Lean 4 the rigidity theorem -- any strategy achieving near-optimal CHSH value must be locally isometric to…
This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a…
In this paper the well-posedness of some degenerate parabolic equations with a dynamic boundary condition is considered. To characterize the target degenerate parabolic equation from the Cahn-Hilliard system, the nonlinear term coming from…
The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and…
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the…
In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ). This intruiguing result is related to recent developments in…
In this article, we fill a gap in the literature on Hawkes processes. In particular, we derive a CLT for a non linear compound marked Hawkes process. We also provide an upper bound on the convergence rate using the functional 1-Wasserstein…