The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in $L^{2}$ Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes. Accepted for publication in Nonlinearit

An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Transitional Care for Patients with Congenital Colorectal Diseases: An EUPSA Network Office, ERNICA, and eUROGEN Joint Venture

Background: Transition of care (TOC; from childhood into adulthood) of patients with anorectal malformations (ARM) and Hirschsprung disease (HD) ensures continuation of care for these patients. The aim of this international study was to assess the current status of TOC and adult care (AC) programs for patients with ARM and HD. Methods: A survey was developed by members of EUPSA, ERN eUROGEN, and ERNICA, including patient representatives (ePAGs), comprising of four domains: general information, general questions about transition to adulthood, and disease-specific questions regarding TOC and AC programs. Recruitment of centres was done by the ERNs and EUPSA, using mailing lists and social media accounts. Only descriptive statistics were reported. Results: In total, 82 centres from 21 different countries entered the survey. Approximately half of them were ERN network members. Seventy-two centres (87.8%) had a self-reported area of expertise for both ARM and HD. Specific TOC programs were installed in 44% of the centres and AC programs in 31% of these centres. When comparing centres, wide variation was observed in the content of the programs. Conclusion: Despite the awareness of the importance of TOC and AC programs, these programs were installed in less than 50% of the participating centres. Various transition and AC programs were applied, with considerable heterogeneity in implementation, content and responsible caregivers involved. Sharing best practice examples and taking into account local and National Health Care Programs might lead to a better continuation of care in the future. Level of Evidence: III