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- Henrik Shahgholian, Nina Uraltseva, Georg S. Weiss
- 2006

For the two-phase membrane problem ∆u = λ + χ {u>0} − λ − χ {u<0} , where λ + and λ − are positive Lipschitz functions, we prove in higher dimensions that the free boundary is in a neighborhood of each " branch point " the union of two C 1-graphs. The result is optimal in the sense that these graphs are in general not of class C 1,Dini , as shown by a… (More)

In structurally disordered solids, some atoms or small groups of atoms are able to quantum mechanically tunnel between two nearly equivalent sites. These atomic tunneling systems have been identified as the cause of various low-temperature anomalies of bulk glasses and as a source of decoherence of superconducting qubits where they are sparsely present in… (More)

Parasitic two-level tunnelling systems originating from structural material defects affect the functionality of various microfabricated devices by acting as a source of noise. In particular, superconducting quantum bits may be sensitive to even single defects when these reside in the tunnel barrier of the qubit's Josephson junctions, and this can be… (More)

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a… (More)

- Sagun Chanillo, Georg S. Weiss
- 2012

a r t i c l e i n f o a b s t r a c t MSC: primary 35R35 secondary 35J60 Keywords: Free boundary Star Singular point In this paper we classify the free boundary associated to equilibrium configurations of compressible, self-gravitating fluid masses, rotating with constant angular velocity. The equilibrium configurations are all critical points of an… (More)

We consider the singular perturbation problem ∆u ǫ = β ǫ (u ǫ), where β ǫ (s) = 1 ǫ β(s ǫ), β is a Lipschitz continuous function such that β > 0 in (0, 1), β ≡ 0 outside (0, 1) and 1 0 β(s) ds = 1 2. We construct an example exhibiting a degenerate singularity as ǫ k ց 0. More precisely, there is a sequence of solutions u ǫ k → u as k → ∞, and there exists x… (More)

We derive the precise limit of SHS in the high activation energy scaling suggested by B. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term. In the first part of our paper… (More)

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