We prove an h-principle with boundary condition for a certain class of sheaves Ψ: Emb d −→ Top. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper we recover the homotopy equivalence BCk,d ≃ Ω d−1Th(γ⊥ k,d) of [2] and [3].

This paper begins with an overview of the boundary condition capturing approach to solving problems with interfaces. Although, the authors’ original motivation was to extend the ghost fluid method from compressible to incompressible flow, the elliptic nature of incompressible flow quickly quenched the idea that ghost cells could be defined and used in the usual manner. Instead the boundary cond...

The boundary conditions for a multicomponent effective wave function are obtained in the eight-band Kane model. The relations are established between boundary-condition matrix elements and the Kane Hamiltonian parameters in constitutive semiconductors. In general, these relations are incompatible with component-bycomponent continuity of the effective wave function, traditionally employed in mul...

We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov’s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville ...

have uniformly dense range! In terms of uniform algebras, it becomes_a question of necessary and sufficient conditions for thejuniform algebra H(D) of uniform limits o£ functions holomorphic near D Jo coincide with the uniform algebra A(D) of all continuous functions on D which are holomorphic on D. A necessary condition obviously is that the respective collections of complex homomorphisms, A//...

This paper offers a simple macroscopic approach to the question of the slip boundary condition to be imposed upon the tangential component of the fluid velocity at a solid boundary. Plausible reasons are advanced for believing that it is the energy equation rather than the momentum equation that determines the correct fluid-mechanical boundary condition. The scheme resulting therefrom furnishes...

We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov’s non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville ...

a lattice boltzmann method is applied to demonstrate the comparison results of simulating natural convection in an open end cavity using different hydrodynamic and thermal boundary conditions. the prandtl number in the present simulation is 0.71, rayleigh numbers are 104,105 and 106 and viscosities are selected 0.02 and 0.05. on-grid bounce-back method with first-order accuracy and non-slip met...

We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some...