Search results for "VARIATION"

A parabolic hemivariational inequality

1996

Nonlocal elasticity and related variational principles

2001

Abstract The Eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied. The model is refined by assuming an attenuation function depending on the `geodetical distance' between material particles, such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented. A suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model. The nonlocal elasticity boundary-value problem for infinitesimal displacements and quasi-static loads is addressed and the conditions for the solution uniqueness are established. Three variational principles, nonlocal…

Numerical Algorithms Based on Characteristic Domain Decomposition for Obstacle Problems

1997

A new numerical solution algorithm for obstacle problems is proposed, where the characteristic domain decomposition into active and inactive subdomains separated by the free boundary is approximated by a Schwarz method. Such an approach gives an opportunity to apply fast linear system solvers to genuinely non-linear obstacle problems. Other solution algorithms, like projected relaxation methods and active set strategies, are compared to the new solution algorithm. Numerical experiments related to the elastoplastic torsion problem are included showing the efficiency of the new approach.

The Nitsche phenomenon for weighted Dirichlet energy

2018

Abstract The present paper arose from recent studies of energy-minimal deformations of planar domains. We are concerned with the Dirichlet energy. In general the minimal mappings need not be homeomorphisms. In fact, a part of the domain near its boundary may collapse into the boundary of the target domain. In mathematical models of nonlinear elasticity this is interpreted as interpenetration of matter. We call such occurrence the Nitsche phenomenon, after Nitsche’s remarkable conjecture (now a theorem) about existence of harmonic homeomorphisms between annuli. Indeed the round annuli proved to be perfect choices to grasp the nuances of the problem. Several papers are devoted to a study of d…

Finite element approximation of parabolic hemivariational inequalities

1998

In this paper we introduce a finite element approximation for a parabolic hemivariational initial boundary value problem. We prove that the approximate problem is solvable and its solutions converge on subsequences to the solutions of the continuous problem

Diversification of CYCLOIDEA-like TCP genes in the basal eudicot families Fumariaceae and Papaveraceae s.str.

2006

CYCLOIDEA-like genes belong to the TCP family of transcriptional regulators and have been shown to control different aspects of shoot development in various angiosperm lineages, including flower monosymmetry in asterids and axillary meristem growth in monocots. Genes related to the CYC gene from ANTIRRHINUM show independent duplications in both asterids and rosids. However, it remains unclear to what extent this affected the evolution of flower symmetry and shoot branching in these and other eudicot lineages. Here, we show that CYC-like genes have also undergone duplications in two related Ranunculales families, Fumariaceae and Papaveraceae s.str. These families exhibit morphological divers…

Microgeographic Variation of Genetic Polymorphism in Argyresthia mendica (Lep.: Argyresthiidae)

1988

Field studies on the genetic structure of populations show a considerable amount of heterogeneity in space and time. In many cases, these heterogeneities can be related to structures in the environment, such as properties of soil, availability of special food resources, topographic conditions or climate. In other cases the genetic structure can be explained by properties of the plant and animal species under study, e.g. ability and speed of migration and colonization (Karlin and Nevo 1976; Endler 1977; Nevo 1978; Nevo and Yang 1979; Nevo et al. 1981; Seitz and Komma 1984; Wohrmann 1984).

Wronskian Addition Formula and Darboux-Pöschl-Teller Potentials

2013

For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant.

Refitting Solutions Promoted by $$\ell _{12}$$ Sparse Analysis Regularizations with Block Penalties

2019

International audience; In inverse problems, the use of an l(12) analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased solution. This is done through the use of refitting block penalties that only act on the co-support of the estimation. Based on an analysis of related works in the literature, we propose a new penalty that is well suited for refitting purposes. We also present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good be…

Effects of Interobserver Variability on 2D and 3D CT- and MRI-Based Texture Feature Reproducibility of Cartilaginous Bone Tumors

2021

AbstractThis study aims to investigate the influence of interobserver manual segmentation variability on the reproducibility of 2D and 3D unenhanced computed tomography (CT)- and magnetic resonance imaging (MRI)-based texture analysis. Thirty patients with cartilaginous bone tumors (10 enchondromas, 10 atypical cartilaginous tumors, 10 chondrosarcomas) were retrospectively included. Three radiologists independently performed manual contour-focused segmentation on unenhanced CT and T1-weighted and T2-weighted MRI by drawing both a 2D region of interest (ROI) on the slice showing the largest tumor area and a 3D ROI including the whole tumor volume. Additionally, a marginal erosion was applied…