1,721,059 research outputs found
L-infinity energies on discontinuous functions
No full textWe study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f(u') V sup ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.
Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint
No full textWe provide a variational description of nearest-neighbours and next-to-nearest neighbours binary lattice systems. By studying the Gamma-limit of proper scaling of the energies of the systems, we highlight phase and antiphase boundary phenomena and show how they depend on the geometry of the lattice
T regulatory cell therapy in preclinical and clinical pancreatic islet transplantation
No full textCell therapy with regulatory T cells (Tregs) is a promising immunomodulatory approach to promote transplant tolerance in patients with type 1 diabetes (T1D) undergoing pancreatic islet transplantation. While several clinical trials with Tregs are ongoing in the clinical setting of hematopoietic stem cell transplantation (HSCT), T1D, renal and kidney transplantation, only one Treg immunotherapy phase I clinical trial is currently active in the setting of allogeneic pancreatic islet transplantation. In this chapter, we summarize available preclinical Treg cell therapy data conducted in the setting of experimental pancreatic islet transplantation and discuss potential challenges, for example, compatibility with immunosuppression, safety and efficacy for Treg cell therapies not yet in the clinic. We also summarize available clinical data from Treg cell therapies conducted in the liver, kidney transplantation, and T1D
Variational description of bulk energies for bounded and unbounded spin systems
No full textWe study the asymptotic behaviour, as the mesh size tends to zero, of a class of discrete energies under very general assumptions that cover the case of bounded and unbounded spin systems, leading to variational limits of integral type. The cases of homogenization and of non-pairwise interacting systems (e.g. multiple-exchange spin systems) are also discussed
A classical S2 spin system with discrete out-of-plane anisotropy: Variational analysis at surface and vortex scalings
No full textWe consider a classical Heisenberg system of S2 spins on a square lattice of spacing ɛ. We introduce a magnetic anisotropy by constraining the out-of-plane component of each spin to take only finitely many values. Computing the Gamma-limit of a suitable scaling of the energy functional as eps to 0 we prove that, in the continuum description, the system concentrates energy at the boundary of sets in which the out-of-plane component of the spin is constant. In a second step we analyze a different scaling of the energy and we prove that, in each of such phases, the energy can further concentrate on finitely many points corresponding to vortex-like singularities of the in-plane components of the spins
The Gibbs–Thomson relation for non homogeneous anisotropic phase transitions
No full textIn this paper we prove the Gibbs-Thomson relation between the coarse grained chemical potential and the non homogeneous and anisotropic mean curvature of a phase interface within the gradient theory of phase transitions thus proving a generalization of a conjecture stated by Gurtin and proved by Luckhaus and Modica in the homogeneous and isotropic case
Crystalline Motion of Interfaces Between Patterns
No full textWe consider the dynamical problem of an antiferromagnetic spin system on a two-dimensional square lattice with nearest-neighbour and next-to-nearest neighbour interactions. The key features of the model include the interaction between spatial scale and time scale , and the incorporation of interfacial boundaries separating regions with microstructures. By employing a discrete-time variational scheme, a limit continuous-time evolution is obtained for a crystal in which evolves according to some motion by crystalline curvatures. In the case of anti-phase boundaries between striped patterns, a striking phenomenon is the appearance of some "non-local" curvature dependence velocity law reflecting the creation of some defect structure on the interface at the discrete level
Interfaces, Modulated Phases and Textures in Lattice Systems
Full text linkWe introduce a class of n-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be described by a phase-transition energy which we compute by means of variational techniques. Degeneracies due to frustration are also discussed
Q-tensor continuum energies as limits of head-to-tail symmetric spin systems
No full textWe consider a class of spin-type discrete systems and analyze their continuum limit as the lattice spacing goes to zero. Under standard coerciveness and growth assumptions together with an additional head-to-tail symmetry condition, we observe that this limit can be conveniently written as a functional in the space of Q-tensors. We further characterize the limit energy density in several cases (both in two and three dimensions). In the planar case we also develop a second-order theory and we derive gradient or concentration-type models according to the chosen scaling
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