Related papers: Energy Minimizing Configurations for Single-Direct…
We study the occurrence of domain branching in a class of $(d+1)$-dimensional sharp interface models featuring the competition between an interfacial energy and a non-local field energy. Our motivation comes from branching in uniaxial…
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…
We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general 6-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
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 investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider…
We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary…
We study the $p$-variational capacity of interior condensers in a bounded open set $\Omega\subset\mathbb R^n$ when both plates are determined by a single phase $\theta:\Omega\to\mathbb R$ in $W^{1,\infty}(\Omega)$ through sublevel and…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the…
We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $\Gamma$-convergence we derive a one-dimensional limit theory and show that…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogeneities of the coefficient field, and the equation is solved…
We study a class of Landau-de Gennes energy functionals with a sextic bulk energy density in a three-dimensional domain. We examine the asymptotic behavior of uniformly bounded minimizers in two distinct scenarios: one where their energy…
We study point configurations on the torus $\mathbb T^d$ that minimize interaction energies with tensor product structure which arise naturally in the context of discrepancy theory and quasi-Monte Carlo integration. Permutation sets on…
In this paper, we consider the problem of optimal demand response and energy storage management for a power consuming entity. The entity's objective is to find an optimal control policy for deciding how much load to consume, how much power…
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…
We present the results of analytical study and Molecular Dynamics simulation of low energy nonlinear non-stationary dynamics of single-walled carbon nanotubes (CNTs). New phenomena of intensive energy exchange between different parts of CNT…
Reduced-density-matrix-functional theory is applied to open-shell systems. We introduce a spin-restricted formulation by appropriately expressing approximate correlation-energy functionals in terms of spin-dependent occupation numbers and…
The use of energy functionals based on density as the basic variable is advocated for ab initio molecular dynamics. It is demonstrated that the constraint of positivity of density can be incorporated easily by using square root density for…