Bulk viscosity damping for accelerating convergence of low Mach number Euler solvers

In solution of the Euler equations in the steady state external flows, error or residual waves are blamed for decelerating the convergence. These waves may be damped by adding a bulk viscosity term to the momentum equations. We analyse effects of this term on the linearized differential equations, and study its explicit and implicit implementation in one and two space dimensions. Optimum values of the bulk viscosity damping (BVD) are discussed. After generalization to two space dimensions, its performance both alone and in combination with a soft wall boundary condition and residual smoothing in central differencing codes is reviewed. It is shown that BVD is complementary to them, and acts independently of them. Finally, application of BVD in solution of low Mach number flows is considered, to show how it can strongly stabilize and accelerate these low Mach number computations. Copyright © 2003 John Wiley & Sons, Ltd.     

Discontinuous solutions to hyperbolic systems under operator splitting

Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps exactly solves the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to “pseudo acoustic waves” and a nonphysical stationary wave. The implications of these findings for the design of high-resolution computing schemes are discussed.     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

C*-Algebras and Controlled Topology

We describe some aspects of the relationship between the controlled topology and C*-algebra approaches to the Novikov conjecture.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Classical and quantum mechanical systems of Toda-lattice type

Communications in Mathematical Physics - In a previous paper it was shown that certain Schrödinger operatorsH=Δ − V onR ℓ such as the Hamiltonians for the quantized...     

Probing the mechanism of Prins cyclisations and application to the synthesis of 4-hydroxytetrahydropyrans

Trapping intermediates on the Prins cyclisation pathway with carbon-based nucleophiles has given further insight into factors affecting the acid-mediated reactions of homoallylic alcohols with aldehydes, enabling the design of efficient syntheses of 4-hydroxy-2,6-disubstituted tetrahydropyrans.     

Kinetics and mechanism of the N7-hydroxyalkylation of guanosine

The kinetics of the N₇-hydroxyalkylation of guanosine by the equally substituted epoxide, trans-2,3-epoxybutane, and the unequally substituted epoxides, 3-chloro-1,2-epoxypropane, and 1,2-epoxypropane in glacial acetic acid, have been measured by a spectrophotomeric method over the range 20-40°. Activation parameters have been determined. Comparative rates calculated from the ratios of second-order rate constants indicate that 1,2-epoxypropane reacts with guanosine about three times faster than does trans-2,3-epoxybutane and about two times faster than 3-chloro-1,2-epoxypropane. These results coupled with the results of a previous report on the structural analysis of the products from these reactions are consistent with a “push-pull” mechanism in which N₇ of guanosine reacts preferentially at the least substituted carbon of the epoxide with simultaneous transfer of a proton from acetic acid to the oxygen of the epoxide. The lower reactivities of trans-2,3-epoxybutane and 3-chloro-1,2-epoxypropane in comparison to that of 1,2-epoxypropane are discussed in terms of steric factors and electronic factors which determine the stability of the requisite transition state for a “push-pull” mechanism model.