Related papers: Dimension reduction for $-\Delta_1$
A 3D-2D dimension reduction for a nonlinear optimal design problem with a perimeter penalization is performed in the realm of $\Gamma$-convergence, providing an integral representation for the limit functional.
This paper presents a method for reducing a three-dimensional gradient damage model to a one-dimensional model for slender rods (with a small radius-to-length ratio, $\delta = R/L \to 0$). The 3D model minimizes an energy functional that…
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
$3d-2d$ dimensional reduction for hyperelastic thin films modeled through energies with point dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of $\Gamma$-convergence. Integral…
An application of dimensional reduction results for gradient constrained problems is provided for 3D-2D dimension reduction for supremal functionals, in the case when the domain is convex.
This paper is devoted to dimensional reductions via the norm resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Recent developments in higher order calculations within the framework of Dimensional Reduction, the preferred regularization scheme for supersymmetric theories, are reported on. Special emphasis is put on the treatment of evanescent…
Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…
In this contribution we present the results of a series of investigations of dimensional reduction, applied to SU(3) gauge theory in 2 + 1 dimensions. We review earlier results, present a new reduced model with Z(3) symmetry, and discuss…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…
We consider the minimization of theta functions $\theta\_\Lambda(\alpha)=\sum\_{p\in\Lambda}e^{-\pi\alpha|p|^2}$ amongst lattices $\Lambda\subset \mathbb R^d$, by reducing the dimension of the problem, following as a motivation the case…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $\Gamma$-convergence, providing an integral…
In a previous paper an asymptotic expansion for lambda_d in powers of 1/d was developed. The results of computer computations for some terms in the expansion, as well as various quantities associated to the expansion, are herein presented.…
This paper introduces the $(\alpha, \Gamma)$-descent, an iterative algorithm which operates on measures and performs $\alpha$-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used…
Three density theorems for three suitable subspaces of $SBD$ functions, in the strong $BD$ topology, are proven. The spaces are $SBD$, $SBD^p_\infty$, where the absolutely continuous part of the symmetric gradient is in $L^p$, with $p>1$,…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…