Structured Deformations of Continua: Theory and Applications

The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours, as well as fractures and defects can be described in a single setting. Since its introduction in the scientific community of rational mechanicists (Del Piero-Owen, ARMA 1993), the theory has been put in the framework of variational calculus (Choksi-Fonseca, ARMA 1997), thus allowing for solution of problems via energy minimization. Some background, three problems and a discussion on future directions are presented.Comment: 11 pages, 1 figure, 1 diagram. Submitted to the Proceedings volume of the conference CoMFoS1

Corrigendum: quasiconvex elastodynamics: weak‐strong uniqueness for measure‐valued solutions

A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the material is assumed strongly quasiconvex. The proof employs tools from the calculus of variations to establish general convexity-type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics

Methods for calculating nonconcave entropies

Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: i) microcanonical contraction, ii) metastable branches of the free energy, iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, iv) restricted canonical ensemble, and v) inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method.Comment: v1: 22 pages, IOP style, 7 color figures, contribution for the JSTAT special issue on Long-range interacting systems. v2: Open problem and references added, minor typos corrected, close to published versio

Targeting of the Plzf gene in the rat by transcription activator-like effector nuclease results in caudal regression syndrome in spontaneously hypertensive rats

Recently, it has been found that spontaneous mutation Lx (polydactyly-luxate syndrome) in the rat is determined by deletion of a conserved intronic sequence of the Plzf (Promyelocytic leukemia zinc finger protein) gene. In addition, Plzf is a prominent candidate gene for quantitative trait loci (QTLs) associated with cardiac hypertrophy and fibrosis in the spontaneously hypertensive rat (SHR). In the current study, we tested the effects of Plzf gene targeting in the SHR using TALENs (transcription activator-like effector nucleases). SHR ova were microinjected with constructs pTAL438/439 coding for a sequence-specific endonuclease that binds to target sequence in the first coding exon of the Plzf gene. Out of 43 animals born after microinjection, we detected a single male founder. Sequence analysis revealed a deletion of G that resulted in frame shift mutation starting in codon 31 and causing a premature stop codon at position of amino acid 58. The Plzftm1Ipcv allele is semi-lethal since approximately 95% of newborn homozygous animals died perinatally. All homozygous animals exhibited manifestations of a caudal regression syndrome including tail anomalies and serious size reduction and deformities of long bones, and oligo- or polydactyly on the hindlimbs. The heterozygous animals only exhibited the tail anomalies. Impaired development of the urinary tract was also revealed: one homozygous and one heterozygous rat exhibited a vesico-ureteric reflux with enormous dilatation of ureters and renal pelvis. In the homozygote, this was combined with a hypoplastic kidney. These results provide evidence for the important role of Plzf gene during development of the caudal part of a body-column vertebrae, hindlimbs and urinary system in the rat

Global solution to the compressible isothermal multipolar fluid

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