Related papers: Localization Study of a Regularized Variational Da…
Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack…
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous occurrence of a steady front between two spatially homogeneous equilibria and a supercritical Turing…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
The existence, stability properties, and bifurcation diagrams of localized patterns and hole solutions in one-dimensional extended systems is studied from the point of view of front interactions. An adequate envelope equation is derived…
We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to the generality of this model usually…
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as…
This paper studies the problem of integrated distributed network localization and formation maneuver control. We develop an integrated relative-measurement-based scheme, which only uses relative positions, distances, bearings, angles,…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
This paper studies 3-D distributed network localization using mixed types of local relative measurements. Each node holds a local coordinate frame without a common orientation and can only measure one type of information (relative position,…
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…
In this paper we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
This paper investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and inter-node relative measurements in local coordinate frames. It is assumed that the local frames…
The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…
This contribution presents a model order reduction strategy for fast parametric modelling of problems with cracks formulated on spline discretizations. In the context of damage detection, parametric reduced order models (ROMs) are well…
Strain localization is responsible for mesh dependence in numerical analyses concerning a vast variety of fields such as solid mechanics, dynamics, biomechanics and geomechanics. Therefore, numerical methods that regularize strain…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potentials in multiple spatial dimensions. While the standard…