Related papers: Energy minimization using Sobolev gradients: appli…
We develop an alternative formulation in the energy-domain to calculate the second order M{\o}ller-Plesset (MP2) perturbation energies. The approach is based on repeatedly choosing four random energies using a non-separable guiding…
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions…
The present paper is devoted to a theory of profile decomposition for bounded sequences in \emph{homogeneous} Sobolev spaces, and it enables us to analyze the lack of compactness of bounded sequences. For every bounded sequence in…
The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…
Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…
In this article, we propose a unified framework for preconditioned Riemannian gradient (P-RG) methods to minimize Gross-Pitaevskii (GP) energy functionals with rotation on a Riemannian manifold. This framework enables comprehensive analysis…
This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.
The purpose of this short note is to demonstrate uniform logarithmic Sobolev inequalities for the mean field gradient particle systems associated to an energy functional that is convex in the flat sense. A defective log-Sobolev inequality…
We study Sobolev regularity results for minimisers of autonomous, convex variational of linear growth which depend on the symmetric gradient rather than the full gradient. This extends the results available in the literature for the…
The new approach to the microscopic description of the phase transitions starting from the only first principles was developed on an example of the transition normal metal-superconductor. This means mathematically, that the free energy is…
A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the…
We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We…
We numerically solve microscopic deterministic equations of motion for the 2D $\phi^4$ theory with random initial states. Phase ordering dynamics is investigated. Dynamic scaling is found and it is dominated by a fixed point corresponding…
Energy minimality selects among possible configurations of a continuous body with and without cracks those compatible with assigned boundary conditions of Dirichlet-type. Crack paths are described in terms of curvature varifolds so that we…
In recent years, important progress has been made in applying methods and techniques of convex optimization to many fields of applications such as location science, engineering, computational statistics, and computer science. In this paper,…
We prove that, on a planar regular domain, suitably scaled functionals of Ginzburg-Landau type, given by the sum of quadratic fractional Sobolev seminorms and a penalization term vanishing on the unitary sphere, $\Gamma$-converge to…
The earlier-described cluster methods are used to generalize the Ginzburg-Landau gradient expansion for the free energy of an inhomogeneous alloy to the case of not small values of order parameters and variations of composition. The results…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg-Landau…
The recent literature has intensively studied two classes of nonlocal variational problems, namely the ones related to the minimisation of energy functionals that act on functions in suitable Sobolev-Gagliardo spaces, and the ones related…