水中受激布里渊散射脉冲的反常压缩

受激布里渊散射(SBS)具有脉冲压缩的特性,受激布里渊散射的脉冲宽度随着抽运能量的增大而变小,在水中可以达到几百皮秒的量级.本文在实验上观察到一种受激布里渊散射的脉冲宽度随抽运能量增大而变大的现象,这里称之为反常压缩.SBS的脉冲反常压缩和脉冲压缩与抽运光的强弱会聚情况有关.利用数值模拟,模拟了强弱会聚情况下抽运光在水中的传输规律,强弱会聚情况的抽运光对受激布里渊散射形成的有效增益长度不同:抽运光强会聚时有效增益长度短,形成SBS脉冲宽度的反常压缩;弱会聚时有效增益长度长,也就是正常的SBS脉冲压缩.     

Spaces N ∪ R and their dimensions

About spaces N∪$\text{R}$ (see [2, Exercise 5I]), the following are proved: (1) dim $\text{N∪}\text{R}\text{= dim β(N∪}\text{R}\text{)?N∪}\text{R}\text{,(2)if|β(N∪}\text{R}\text{)?N∪}\text{R}\text{|<2}{}^{\mathrm{?}}{}^{\mathrm{o}}$, then no real-valued continuous fu ction on N∪$\text{R}$ is onto (and hence, dim $\text{N∪}\text{R}\text{=0}$), (3) any compact metric space without isolated points is homeomorphic to some $\text{β(N∪}\text{R}\text{)?N∪}\text{R}$ and (4)there are spaces X,X₁ and X₂ of the form N∪$\text{R}$ such that X=X₁∪X₂,X₂andX₂ are zero sets of X, and dim X=n, dimX₁=dimX₂=0, where n=1,2,… or ∞.     

On problems of optimal design of shallow shell with double curvature on elastic foundation

The present paper discusses a method of optimal design of the shallow shell with double curvature on the elastic foundation Substantially we take the initial flexural function as the control function or design variable which will be found and the potential energy of the external loads as the criterion of quality of the optimal design of the shallow shell with double curvature, therefore the functional of the potential energy will be aim function. The optimal conditions and the isoperimetric conditions belong to the constrained conditions. thus we obtain the necessary conditions of the optimal design for the given problems, at the same time the conjugate function is introduced, then the problems are reduced to the solutions of two boundary value problems for the differential equation of conjugate function and the initial flexual function.     

Unconditionally Converging Multilinear Operators

We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems to be new also in the linear case), which allow to considerably simplify the work with this kind of operators.     

收敛柱激波在粉尘气体中的传播

取稀颗粒群气固两相耦合的双流体简化模型，采用高解数值方法研究了收敛柱激波在粉尘气体中的传播和波后流场特性。通过与纯气体情况比较，揭示了固体颗粒出现对收敛柱激波传播特性的影响。     

球面波的相奇异分布区域特征

从波动方程出发，在基尔霍夫边界条件下，根据积分的物理意义，简明地研究了发散和汇聚球面波的相奇异区域分布。结果表明，除了汇聚的球面波焦点区域存在相奇异现象外，焦点以外的区域及对发散的球面波同样存在相奇异现象。发散球面波的相奇异区位于入射空间，在相奇异区域的不同部分相奇异规律不同，源点是相奇异区里的一个特殊点。汇聚的球面波的相奇异区域存在于像空间，结构简单，焦点是相奇异区域里的一个特殊点。     

Fast and reliable reconstruction of phylogenetic trees with indistinguishable edges

Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree from short input sequences, assuming common stochastic models of evolution. The fast converging reconstruction algorithms introduced in the last decade dramatically reduced the sequence length required to guarantee accurate reconstruction of the entire tree. However, if the tree in question contains even few edges which cannot be reliably reconstructed from the input sequences, then known fast converging algorithms may fail to reliably reconstruct all or most of the other edges. This calls for an adaptive approach suggested in this paper, called adaptive fast convergence, in which the set of edges which can be reliably reconstructed gradually increases with the amount of information (length of input sequences) available to the algorithm. This paper presents an adaptive fast converging algorithm which returns a partially resolved topology containing no false edges: edges that cannot be reliably reconstructed are contracted into high degree vertices. We also present an upper bound on the weights of those contracted edges, which is determined by the length of input sequences and the depth of the tree. As such, the reconstruction guarantee provided by our algorithm for individual edges is significantly stronger than any previously published edge reconstruction guarantee. This fact, together with the optimal complexity of our algorithm (linear space and quadratic‐time), makes it appealing for practical use. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 350–384, 2011     

Noh's constant-velocity shock problem revisited

We present the solutions to Noh's shock tube problem in planar, cylindrical, and spherical geometry. This problem has the well-deserved reputation of being challenging to numerical methods. Since the gas is initially cold there are infinitely many reflections of the shock between the fixed wall and the piston as the piston moves with constant velocity towards the wall. An implicit adaptive grid algorithm allows us, for the first time, to generate the complete solutions in these three geometries. We discuss them in detail, in particular follow the shock over many reflections, and perform numerical consistency checks. For the planar case the exact analytical solution is derived, and the numerical error in all physical quantities is found to be less than 1% on a 100 grid-point computational domain. For the converging geometries an approximate analytical theory is presented, and the deviations between the theory and the numerical results are found to be less than 10% on the same domain. A substantial part of this total error is due to errors in the approximate analytical results. We discuss the physics of the shock reflection in the three geometries, and analyze in particular the finite amount of entropy that is produced after the the first shock reflection. In an appendix we present some details of our code and demonstrate that the adaptive grid permits us to carry out computations of extreme precision. The reliability of our solutions in all three geometries allows them to become demanding tests for 2D and 3D codes. Received 16 April 1996 / Accepted 15 August 1996     

Numerical study of the spontaneous nucleation of self-rotational moist gas in a converging–diverging nozzle

Spontaneous nucleation is the primary way of droplet formation in the supersonic gas separation technology, and the converging–diverging nozzle is the condensation and separation unit of supersonic gas separation devices. A three-dimensional geometrical model for the generation of self-rotational transonic gas flow is set up, based on which, the spontaneous nucleation of self-rotational transonic moist gas in the converging–diverging nozzle is carried out using an Eulerian multi-fluid model. The simulated results of the main flow and nucleation parameters indicate that the spontaneous nucleation can occur in the diverging part of the nozzle. However, different from the nucleation flow without self-rotation, the distributions of these parameters are unsymmetrical about the nozzle axis due to the irregular flow form caused by the self-rotation of gas flow. The nucleation region is located on the position where gas flows with intense rotation and the self-rotation impacts much on the nucleation process. Stronger rotation delays the onset of spontaneous nucleation and yields lower nucleation rate and narrow nucleation region. In addition, influences of other factors such as inlet total pressure p ₀, inlet total temperature T ₀, the nozzle-expanding ratio ? and the inlet relative humidity ф ₀ on the nucleation of self-rotational moist gas flow in the nozzle are also discussed.     

Experimental studies of an unstable confocal resonator alexandrite laser

The effects of excited converging wave in an unstable confocal resonator onthe properties of an alexandrite laser are investigated experimentally.The results show thatexciting the converging wave inside the resonator is an effective method to reduce the diver-gence of the laser beam for low gain laser medium.