Cauchy fluxes induced by locally summable tensor fields with divergence measure are characterized. The equivalence between integral formulations involving subsets of finite perimeter and much more restricted classes of subsets is proved.
We extend a celebrated identity by P. Pucci and J. Serrin, concerning C 2 solutions of Euler equations of functionals of the calculus of variations, to the case of C 1 solutions under the only additional assumption of strict convexity in the gradient. Some particular cases in which the mere convexity is sufficient are also considered. (2000): 35J65
Mathematics Subject Classification
We demonstrate the existence of a topological disconnection threshold, recently found in Ref.[1], for generic 1 − d anisotropic Heisenberg models interacting with an inter-particle potential R −α when 0 < α < 1 (here R is the distance among spins). We also show that if α is greater than the embedding dimension d then the ratio between the disconnected energy region and the total energy region goes to zero when the number of spins becomes very large. On the other hand, numerical simulations in d = 2, 3 for the long-range case α < d support the conclusion that such a ratio remains finite for large N values. The disconnection threshold can thus be thought as a distinctive property of anisotropic long-range interacting systems.
We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. The three material parameters appearing in the energy are fitted by least square optimization on experimental data, while incompressibility is assumed through a Lagrange multiplier representing the hydrostatic pressure. The activation of the muscle fibers, which is related to the contraction of the sarcomere, is modeled by the so called active strain approach. The loss of performance of an elder muscle is then obtained by lowering of some percentage the active part of the stress. The model is implemented numerically and the obtained results are discussed and graphically represented. arXiv:1701.07823v1 [q-bio.TO]
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