We prove global stability results of DiPerna-Lions renormalized solutions to the initial boundary value problem for kinetic equations. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which include the so-called Maxwell boundary condition, and we prove that it is realized (it is not relaxed!). The techniques are illustrated with the Fokker-Planck-Boltzmann equat...

Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardy’s derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and the relation between fractional branes and wrapped branes is investigated for C/Γ orbifolds. The boundary states are generalised to theories with ...

The Sicily Channel Regional Model forecasting system: initial boundary conditions sensitivity and case study evaluation S. Gaberšek, R. Sorgente, S. Natale, A. Ribotti, A. Olita, M. Astraldi, and M. Borghini IMC – International Marine Centre Loc. Sa Mardini, 09170 Oristano, Italy University of Ljubljana, Department of Mathematics and Physics, Jadranska 19, Ljubljana, 1000, Slovenia ISMAR CNR se...

Several aspects of canopy flow are investigated. The problem of steady flow in a horizontally infinite canopy under neutral thermal stratification is treated theoretically. The resulting analytical model is then used as a boundary condition for a nonlinear numerical model designed t o study transition regions near the leading and trailing edges of a canopy. This model shows a wave effect downst...

We report preliminary results obtained from the large eddy simulation of a backward facing step at a Reynolds number of 5100. The numerical platform is based on a high order Legendre spectral element spatial discretization and a least squares time integration scheme. A non-reeective outtow boundary condition is in place to minimize the eeect of downstream innuence. Smagorinsky model with Van Dr...

2 History of the no-slip condition 2 2.1 The previous centuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Traditional situations where slip occurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Newtonian liquids: no-sl...

It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this scheme. The scheme is based on using (1) a horizon locking coordinate which locks the coordinate system to the geometry, and (2) a finite differencing scheme whic...

We study the effect of a periodic roughness on a Neumann boundary condition. We show that, as in the case of a Dirichlet boundary condition, it is possible to approach this condition by a more complex law on a domain without rugosity, called wall law. This approach is however different from that usually used in Dirichlet case. In particular, we show that this wall law can be explicitly written ...

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...