Related papers: Isotropic diffeomorphisms: solutions to a differen…

Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach.…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select a specific translate of the striped patterns and induce…

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…

In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…

We provide a new formulation of nonrelativistic diffeomorphism invariance. It is generated by localising the usual global Galilean Symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the…

The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented…

This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…

The deformation principle admits one to obtain a very broad class of nonuniform geometries as a result of deformation of the proper Euclidean geometry. The Riemannian geometry is also obtained by means of a deformation of the Euclidean…

We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…

We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…

We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to…

The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…