Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben II

Summary In a recent paper [11], two of the authors investigated a fast reduction method for solving difference equations which approximate certain boundary value problems for Poisson's equation. In this second paper, we prove the numerical stability of the reduction method, and also report on further developments of the method. For the general case, the provided bounds for the numerical errors behave roughly like the condition numberO(n ²) of the linear system; for more realistic model problems estimates of order less thanO(n) are obtained (n ^–1=h=mesh width). The number of operations required for the reduction method isO(n ² ), for the usual five-point difference formula, as well as for the common nine-point formula with discretization error of orderh ⁴.     

On the Dynamics of the Classical Transverse Field Ising Chain

We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions.     

Development and validation of a new LBM-MRT hybrid model with enthalpy formulation for melting with natural convection

This article presents a new model to simulate melting with natural convection of a phase change material. For the phase change problem, the enthalpy formulation is used. Energy equation is solved by a finite difference method, whereas the fluid flow is solved by the multiple relaxation time (MRT) lattice Boltzmann method. The model is first verified and validated using the data from the literature. Then, the model is applied to a tall brick filled with a fatty acid eutectic mixture and the results are presented. The main results are (1) the spatial convergence rate is of second order, (2) the new model is validated against data from the literature and (3) the natural convection plays an important role in the melting process of the fatty acid mixture considered in our work.     

Properties of silver halide core-clad fibers and the use of fiber bundle for thermal imaging

Abstract

Optical infrared (IR) fibers with core-clad structure are of great importance because they have better qualities than unclad fibers for most IR fiber applications, especially in CO₂ laser power delivery and radiometry. We have fabricated core-clad polycrystalline silver halide optical fibers with different compositions and core diameters, and although their loss is still higher than that of unclad fibers, they already have many advantages and new capabilities. The behavior of the scattering loss along these fibers and other optical properties was measured and compared with that of unclad silver halide fibers. We show that the higher loss of clad fibers results mainly from excessive scattering. The improvement in the process of fabricating clad fibers enabled the production of new elements such as single-mode fibers (SMFs) and fiber bundles for thermal imaging.     

Properties of gravitationally bound dark compact ultra dense objects

We consider compact astrophysical objects formed from dark matter fermions of mass 250 GeV to 100 TeV or from massless fermions hidden by vacuum structure of similar energy scale. These objects have maximum stable masses of sub-planetary scale and radii of micron to centimeter scale. We describe the surface gravity and tidal forces near these compact ultra dense objects, as pertinent to signatures of their collisions with visible matter objects.     

Ansa macrolides as molecular workbenches for stereoselective additions to achiral (E) olefins

Highly stereocontrolled additions to achiral acyclic (E) olefins are achieved via incorporation into an ansa macrolide with a non-racemic stilbene diol (molecular workbench approach).     

Crystal Structure and Packing of Isocyclosporin A

The crystal structure of isocyclosporin A ( 1 ), a rearrangement product of the immunosuppressant drug cyclosporin A, has been determined at 193 (2) K. Crystals are orthorhombic with cell dimensions a = 26.684 (7), b = 26.936 (3) Å, c = 28.549 (7) Å, space group C222₁. The structure was solved by direct methods and refined by full-matrix least-squares methods to a conventional R value of 0.110. In contrast to the structure of cyclosprin A in solution and in the crystal, isocyclosporin A ( 1 ) has no regular secondary structural elements. The backbone adopts an open, irregular conformation with cis amide bonds between residue 2 and 3, and 3 and 4, respectively. All the other amide bonds and the ester linkage are trans. Contrary to crystal structures of cyclosporin derivatives, this crystal structure is stabilized by two transannular and four intermolecular H-bonds.