Related papers: A Minimization Method for The Double-Well Energy F…
This paper considers the network flow stabilization problem in power systems and adopts an output regulation viewpoint. Building upon the structure of a heterogeneous port-Hamiltonian model, we integrate network aspects and develop a…
We investigate two unconditionally energy stable invariant energy quadratization (IEQ) finite element methods (FEMs) [Chen et al. Numerical Algorithms, DOI: 10.1007/s11075-024-01910-z, 2024] for solving the Cahn-Hilliard-Navier-Stokes…
Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel under an integral constraint. The corresponding minimizers…
We present an energy functional for a Thomas-Fermi type two-fluid model of a self-gravitating non-rotating charged body, with a non-relativistic kinetic energy. We prove that, under certain conditions on the total number of positively…
We study properties of an attractive-repulsive energy functional based on power-kernels, which can be used for halftoning of images. In the first part of this work, using a variational framework for probability measures, we examine…
We consider a general energy functional for phase coexistence models, which comprises the case of Banach norms in the gradient term plus a double-well potential. We establish density estimates for $Q$-minima. Namely, the state parameters…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…
The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented…
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic lattice. The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins, respectively. By constraining the deformed configurations to…
A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularization. However, in arXiv:2510.17296 we introduced a novel…
In this work, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model consists of a Cahn-Hilliard equation, a Navier-Stokes equation and…
We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…
We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional in two and three dimensions, which corresponds to the $H^1$ projection of measure-preserving maps. Our result introduces a new criteria on the…
In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be…
An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the…
This paper presents a detailed asymptotic and numerical investigation of the phase diagram for global minimizers to a Cahn-Hilliard functional with long-range interactions in two space dimensions. We introduce a small parameter measuring…
In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation. The $O(1/n)$-energy convergence of the proposed method is proven, where $n$ is the number of iterations. In…
In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear rate of the scheme is also…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
The stretch energy is a fully nonlinear energy functional that has been applied to the numerical computation of area-preserving mappings. However, this approach lacks theoretical support and the analysis is complicated due to the full…