Related papers: Energy-minimal Principles in Geometric Function Th…
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…
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems.…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
We present a critical analysis of the classical approaches to energy subjects, based on the work-energy theorem and the conservation of mechanical energy proposed in the courses of the first years of tertiary education. We show how these…
This talk includes a short introduction to Chiral Perturbation Theory in the meson sector concentrating on a number of recent developments. I discuss the latest fit of the low-energy constants. Finite volume corrections are discussed for…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
In the present paper we develop the theory of minimization for energies with multivariate kernels, i.e. energies, in which pairwise interactions are replaced by interactions between triples or, more generally, $n$-tuples of particles. Such…
These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for…
We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results…
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…
The heart of the a priori and a posteriori error control in convex minimization problems is the sharp control of the differences of discrete and exact minimal energy. Conforming finite element discretizations for p-Laplace type minimization…
The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in space-time geometry. We show…
In this talk I review the behaviour of structure functions at low values of Bjorken $x$ and discuss the theoretical underpinnings with particular attention to resummation schemes. I present the need for 'less inclusive' events to…
The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to…
We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…