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

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

Generic stability of dissipative non-relativistic and relativistic fluids

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the nonnegativity of the transport coefficients.Comment: 22 page

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

Cardioprotective Regimen of Adaptation to Chronic Hypoxia Diversely Alters Myocardial Gene Expression in SHR and SHR-mtBN Conplastic Rat Strains

Adaptation to continuous normobaric hypoxia (CNH) protects the heart against acute ischemia/reperfusion injury. Recently, we have demonstrated the infarct size-limiting effect of CNH also in hearts of spontaneously hypertensive rats (SHR) and in conplastic SHR-mtBN strain characterized by the selective replacement of the mitochondrial genome of SHR with that of more ischemia-resistant Brown Norway rats. Importantly, cardioprotective effect of CNH was more pronounced in SHR-mtBN than in SHR. Thus, here we aimed to identify candidate genes which may contribute to this difference between the strains. Rats were adapted to CNH (FiO2 0.1) for 3 weeks or kept at room air as normoxic controls. Screening of 45 transcripts was performed in left ventricles using Biomark Chip. Significant differences between the groups were analyzed by univariate analysis (ANOVA) and the genes contributing to the differences between the strains unmasked by CNH were identified by multivariate analyses (PCA, SOM). ANOVA with Bonferroni correction revealed that transcripts differently affected by CNH in SHR and SHR-mtBN belong predominantly to lipid metabolism and antioxidant defense. PCA divided four experimental groups into two main clusters corresponding to chronically hypoxic and normoxic groups, and differences between the strains were more pronounced after CNH. Subsequently, the following 14 candidate transcripts were selected by PCA, and confirmed by SOM analyses, that can contribute to the strain differences in cardioprotective phenotype afforded by CNH: Alkaline ceramidase 2 (Acer2), Fatty acid translocase (Cd36), Aconitase 1 (Aco1), Peroxisome proliferator activated receptor gamma (Pparg), Hemoxygenase 2 (Hmox2), Phospholipase A2 group IIA (Ppla2g2a), Dynamin-related protein (Drp), Protein kinase C epsilon (Pkce), Hexokinase 2 (Hk2), Sphingomyelin synthase 2 (Sgms2), Caspase 3 (Casp3), Mitofussin 1 (Mfn1), Phospholipase A2 group V (Pla2g5), and Catalase (Cat). Our data suggest that the stronger cardioprotective phenotype of conplastic SHR-mtBN strain afforded by CNH is associated with either preventing the drop or increasing the expression of transcripts related to energy metabolism, antioxidant response and mitochondrial dynamics