Related papers: Integrable boundary interaction in 3D target space…
Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive-zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in…
In this work we consider the free boundary inverse equilibrium problem for 3D ideal MHD. We review boundary conditions for both fixed and free boundary solutions and under what circumstances a sheet current may exist at the plasma-vacuum…
We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the…
We examine the solutions of world-volume action for a D3-brane being put near other D3-brane which is replaced by the background configuration of bulk space. It is shown that the BPS solutions are not affected by the D3-brane background,…
D-branes in curved backgrounds can be treated with techniques of boundary conformal field theory. We discuss the influence of scalar condensates on such branes, i.e. perturbations of boundary conditions by marginal boundary operators. A…
The class of 2-dimensional non-integrable flat dynamical systems has a rather extensive literature with many deep results, but the methods developed for this type of problems, both the traditional approach via Teichm\"{u}ller geometry and…
Interactions of relatively rotated Dp-branes in 1, 2, 3 and 4 angles in M(atrix) model are calculated and it is found to be in agreement with string theory calculations. In 4 angles case the agreement is achieved after subtracting the…
Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection…
We present the effective field equations obtained from a generalized gravity action with Euler-Poincare term and a cosmological constant in a $D$ dimensional bulk space-time. A class of plane-symmetric solutions that describe a 3-brane…
We present an approach for analyzing initial-boundary value problems which is formulated on the finite interval ($0\le x\le L$, where $L$ is a positive constant) for integrable equations whose Lax pairs involve $3\times 3$ matrices.…
In order to simulate the mechanical behavior of large structures assembled from thin composite panels, we propose a coupling technique which substitutes local 3D models for the global plate model in the critical zones where plate modeling…
We use the reduced relaxed micromorphic model (RRMM) to capture the effective "bulk" dynamical response of finite size metamaterial specimens made out of a Labyrinthine unit cell. We show that for small finite-size specimens, boundary…
We study boundary conditions and defects in a three-dimensional topological sigma-model with a complex symplectic target space X (the Rozansky-Witten model). We show that boundary conditions correspond to complex Lagrangian submanifolds in…
In this paper, we study the Dirichlet problem for the minimal surface equation in $\rm Sol_3$ with possible infinite boundary data, where $\rm Sol_3$ is the non-abelian solvable $3$-dimensional Lie group equipped with its usual…
A generic surface in Euclidean 3-space is determined uniquely by its metric and curvature. Classification of all special surfaces where this is not the case, i.e. of surfaces possessing isometries which preserve the mean curvature, is known…
WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time they have a sigma model description of closed string propagation on group manifolds which,…
This article addresses the solvability of the multi-dimensional divergence-curl problem with a no-slip boundary condition. A solvability criterion is derived as an orthogonality condition of the vorticity function to pseudo-harmonic fields.…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…
We construct explicitly time-dependent exact solutions to the field equations of 6D gauged chiral supergravity, compactified to 4D in the presence of up to two 3-branes situated within the extra dimensions. The solutions we find are scaling…
If our (3+1) dimensional universe is a brane or domain wall embedded in a higher dimensional space, then a phenomenon that may be designated as "Clash of Symmetries" provides a new method of breaking continuous symmetries. The paper…