Related papers: Dimension reduction in the context of structured d…
We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…
In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by…
We investigate the critical behavior of disordered systems transversely driven at a uniform and steady velocity. An intuitive argument predicts that the long-distance physics of $D$-dimensional driven disordered systems at zero temperature…
We study the response of a granular system at rest to an instantaneous input of energy in a localised region. We present scaling arguments that show that, in $d$ dimensions, the radius of the resulting disturbance increases with time $t$ as…
The vibrating behaviour of thin structures is affected by prestress states. Hence, the effects of thermal prestress are important research subjects in view of ambient vibration monitoring of civil structures. The interaction between…
A new relaxation approach is proposed which allows for the description of stress- and strain-softening at finite strains. The model is based on the construction of a convex hull replacing the originally non-convex incremental stress…
The process of structural relaxation in disordered solids subjected to repeated tension-compression loading is studied using molecular dynamics simulations. The binary glass is prepared by rapid cooling well below the glass transition…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…
We consider a two-dimensional problem in nonlinear elasticity which corresponds to the cubic-to-tetragonal phase transformation. Our model is frame invariant and the energy density is given by the squared distance from two potential wells.…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…
Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems. We study its application to two clustering problems: the facility location problem, and the single-linkage hierarchical clustering…
This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power…
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional…
In the direct approach to continua in reduced space dimensions, a thin shell is described as a mathematical surface in three-dimensional space. An exploratory kinematic study of such surfaces could be very valuable, especially if conducted…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional…
Relaxation theorems which apply to one, two and three-dimensional nonlinear elasticity are proved. We take into account the fact an infinite amount of energy is required to compress a finite line, surface or volume into zero line, surface…