相关论文: Tangential Touch between Free and Fixed Boundaries…
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…
Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically…
We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.
In a bounded domain, we consider a variable range nonlocal operator, which is maximally isotropic in the sense that its radius of interaction equals the distance to the boundary. We establish $C^{1,\alpha}$ boundary regularity and existence…
In this paper, we consider the properties of a special free boundary point in the following obstacle problem: The Laplacian of u equals f(x) multiplied by the characteristic function of the set where u is positive within the two-dimensional…
We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an…
We study the regularity of the "free surface" in boundary obstacle problems. We show that near a non-degenerate point the free boundary is a $C^{1,\alpha}$ $(n-2)$-dimensional surface in $\real^{n-1}$.
We develop a phenomenological model of superconductivity near a domain wall in a ferromagnet. In addition to the electromagnetic interaction of the order parameter with the ferromagnetic magnetization, we take into account the possibility…
The conductance through a semi-infinite one-dimensional wire, partly embedded in a superconducting bulk electrode, is studied. When the electron-electron interactions within the wire are strongly repulsive, the wire effectively decouples…
The purpose of this article is to discuss a view concerning key datasets of the properties of grain boundaries in high-Tc superconductors that was recently expressed in Ref. 1. The reference also criticizes our research. Using examples I…
We study a linear problem that arises in the study of dynamic boundaries, in particular in free boundary problems in connection with fluid dynamics. The equations are also very natural and of interest on their own.
Grain boundaries play a critical role in applications of superconducting Nb$_3$Sn: in dc applications, grain boundaries preserve the material's inherently high critical current density by pinning flux, while in ac applications grain…
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…
We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime.…
This paper considers the conductance through a dirty junction between a normal conductor and a superconductor with an insulating barrier. It is shown that for large barrier resistances there is a relative enhancement of the conductance near…
In this paper we establish the exact growth of the solution of the singular quasilinear p-parabolic obstacle problem near the free boundary from which we deduce its porosity.
We study the regularity and well-posedness of physical solutions to the supercooled Stefan problem. Assuming only that the initial temperature is integrable, we prove that the free boundary, known to have jump discontinuities as a function…
In this paper, we are concerned with the two-dimensional steady supersonic combustion flows with a contact discontinuity moving through a nozzle of finite length. Mathematically, it can be formulated as a free boundary value problem…
We investigate the electronic structure of twin boundaries in orthorhombically distorted high-T$_c$ materials using the quasiclassical theory of superconductivity. At low temperatures we find a local instability to a time-reversal symmetry…
We study $s$-wave superconductivity in hyperbolic spaces using the Bogoliubov-de Gennes theory for discrete hyperbolic lattices and the Ginzburg-Landau theory for the continuous hyperbolic plane. Hyperbolic lattices maintain a finite…