Abstract. We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula. These functionals, based on submodular interactions, arise in discrete optimization and are known as a large class of problems which can be solved in polynomial time. In particular, some of them can be solved very efficiently by maximal flow algorithms and are quite popular in the image processing community. We study the limit in the continuum of these functionals, show that they always converge to some "crystalline" perimeter/total variation, and provide an almost explicit formula for the limiting functional.Mathematics Subject Classification. 49Q20, 65K10.
We analyze a 1-d ring structure composed of many two-levels systems, in the limit where only one excitation is present. The two-levels systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior. Moreover, each two-levels system is coupled to another independent environment, modeled by a classical white noise, simulating a dephasing bath and described by the Haken-Strobl master equation. Single exciton Superradiance, an example of cooperative quantum coherent effect, is destroyed at a critical dephasing strength proportional to the system size, showing robustness of cooperativity to the action of the dephasing environment. We also show that the coupling to a common decay channel contrasts the action of dephasing, driving the entanglement decay to slow down on increasing the system size. Moreover, after a projective measurement which finds the excitation in the system, the entanglement reaches a stationary value, independent of the initial conditions.
this data shows that suprarenal clamping, which is necessary for the radical treatment of juxtarenal aortic aneurysms, can be performed with a low risk.
We prove the existence of a quasistatic evolution for a model in strain gradient plasticity proposed by Gurtin and Anand concerning isotropic, plastically irrotational materials under small deformations. This is done by means of the energetic approach to rate-independent evolution problems. Finally we study the asymptotic behavior of the evolution as the strain gradient length scales tend to zero recovering in the limit a quasistatic evolution in perfect plasticity.
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