Surface Effects in Superconductors with Corners

准脆性材料和摩擦材料的屈服准则：对有角曲面的推广

Yield criteria for quasibrittle and frictional materials: a generalization to surfaces with corners

屈服函数（或相变函数）的凸性及其与相应屈服表面（或相变表面）的凸性的关系对于新屈服（或相变）标准的发明、定义和与实验的比较是必不可少的。这个问题以前只在表面光滑的假设下得到解决，但是具有拐角的屈服面（例如Hill，Tresca或Coulomb-Mohr屈服准则）在塑性理论中具有根本的重要性。本文将函数及相应曲面的凸性与非光滑屈服面和相变面的凸性相联系的一个命题加以推广，并推广了非光滑弹性势函数的一个定理。虽然前者的这些概括是至关重要的屈服和相变条件，后者可能会发现应用的势能函数描述相变材料，或材料与不连续锁定在张力，或接触的一个身体与离散的弹性/摩擦支持。

Water waves problem with surface tension in a corner domain I: A priori estimates with constrained contact angle

We study the two dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact point. Moreover, when the contact angle is less than $π/6$, no singularity appears in our settings. Using elliptic estimates in corner domains and a geometric approach, we prove an a priori estimate for the water waves problem.

Effects of Corners in Surface Superconductivity

We study the Ginzburg-Landau functional describing an extreme type-II superconductor wire with cross section with finitely many corners at the boundary. We derive the ground state energy asymptotics up to $ o(1) $ errors in the surface superconductivity regime, i.e., between the second and third critical fields. We show that, compared to the case of smooth domains, each corner provides an additional contribution of order $ \mathcal{O}(1) $ depending on the corner opening angle. The corner energy is in turn obtained from an implicit model problem in an infinite wedge-like domain with fixed magn…

有角的表面超导电性

Surface Superconductivity in Presence of Corners

我们考虑具有非光滑截面的极端II型超导导线，即，在金兹伯格-朗道理论的框架中，在边界处有一个或多个角。我们证明了存在的一个区间的值的应用领域，超导性是均匀分布沿边界的样品。更确切地说，能量不受角点的存在和Ginzburg-Landau极小化的模的主导阶沿横向方向近似恒定。界定这种表面超导制度的临界场与没有边界奇点的临界场一致。

Two-Dimensional Yang-Mills Theory on Surfaces With Corners in Batalin-Vilkovisky Formalism

In this paper we recover the non-perturbative partition function of 2D~Yang-Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D~Yang-Mills theory on surfaces with boundaries and corners in the Batalin-Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting -- the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces -- building blocks -- and choosing a convenient gauge-fixing on the pieces, and assembli…

Bulk, surface and corner free energies of the anisotropic triangular Ising model: series expansions and critical behaviour

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman's spinor method to calculate low-temperature series expansions for the partition function to high order. From these we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk free energy. For the isotropic case, they also agree with Vernier and Jacobsen's conjecture for the $60^{\circ}$ corners, and with Cardy and Peschel's conform…