We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of Þxed or free boundary curves in R, S and H. The algorithm makes no restriction on the genus and can handle singular triangulations. For a discrete harmonic map a conjugation process is presented leading in case of minimal surfaces additionally to instable solutions of the free boundary value problem fo...

Under two boundary conditions: the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary.

We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete primary fields are given in terms of SU(2) rotation coefficients while boundary amplitudes involving discrete boundary fields are independent of the boundary in...

This paper discusses about the detection of clause boundaries using a hybrid approach. The Conditional Random fields (CRFs), which have linguistic rules as features, identifies the boundaries initially. The boundary marked is checked for false boundary marking using Error Pattern Analyser. The false boundary markings are re-analysed using linguistic rules. The experiments done with our approach...

We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Hölder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetr...

We study a nematic crystal model appearing in [Liu et al.,2007] modeling stretching effects depending on the different shape of microscopic molecules of the material, under periodic boundary conditions. The aim of the present article is twofold: to extend the results given in [Sun & Liu, 2009], to a model with more complete stretching terms and to obtain some stability and asymptotic stability ...

We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure loss coefficient enables us to establish a relation on the pressure and to thus formulate an equivalent problem.

Fast Algorithms with Applications to PDEs

*Correspondence: [email protected] Department of Applied Mechanics, Chalmers University of Technology, Hörsalsvägen 7, 412 96 Göteborg, Sweden Abstract Background: Seepage in porous media is modeled as a Stokes flow in an open pore system contained in a rigid, impermeable and spatially periodic matrix. By homogenization, the problem is turned into a two-scale problem consisting of a Da...