Fractional diffusion-wave problem in cylindrical coordinates

In this Letter, we present analytical and numerical solutions for an axis-symmetric diffusion-wave equation. For problem formulation, the fractional time derivative is described in the sense of Riemann-Liouville. The analytical solution of the problem is determined by using the method of separation of variables. Eigenfunctions whose linear combination constitute the closed form of the solution are obtained. For numerical computation, the fractional derivative is approximated using the Grünwald-Letnikov scheme. Simulation results are given for different values of order of fractional derivative. We indicate the effectiveness of numerical scheme by comparing the numerical and the analytical results for α=1 which represents the order of derivative.     

星模拟器星点能量中心修正方法的研究

对星模光学系统中各种像差对几何中心位置的影响及像差对显示星点能量中心位置造成的偏差进行了分析与综合评估.分析结果表明,视场位置越大的星点产生的像点能量越不均匀,重心偏移越明显,系统中慧差和畸变对于星点能量中心影响较大.根据球面镜组成的共轴光学系统性质可知,能量中心的偏移发生在星点所在极半径方向上,因此提出了一种基于极坐标的星点位置修正方法,只需在星点所在方向对极半径进行修正.该方法简化了基于二维坐标轴分区修正的过程,减少了数据计算量.利用极坐标修正方法对星模拟器修正前后的单星位置误差进行了测试,实验结果表明极坐标修正过程较以往修正方法简单快捷,且修正结果更加准确.     

二维拉格朗日坐标系下气粒混合双向耦合对激波流场影响的计算

喷射颗粒与气体混合是内爆压缩领域的热点和难点. 针对喷射混合中的气粒双向耦合问题, 开展了理论建模、离散算法以及颗粒反馈对激波流场的影响研究. 建立了拉格朗日计算框架下的数学模型; 给出了耦合源项的离散算法; 开展了平面及汇聚构型条件下, 气粒双向耦合的数值模拟研究; 发现了颗粒反馈导致气体激波提速现象以及气区流场物理量分布形态的改变, 初步获得了量化分析结果. 本文建立的数学模型、计算方法和获得的新的物理认识, 为深入理解喷射混合现象、解决相关工程应用问题提供了重要理论支撑.     

Coordinates of principal stresses for elastic plane problem

I.IntroductionInelasticmechanics,thereisakindofproblemsthatcouldbesolveddirectlybyequilibriumequations,i.e.,whenal1oftheboundaryconditionsaretheknownstressesorforcessuchasthestressfunction.Becausestressfunctionsmustsatisfyharmonicequationorbi-harmonicequa…     

正交曲线坐标系下紊流数学模型的曲率修正

考虑弯曲边界曲率效应对水流水力特性的影响,建立了正交曲线坐标系下的素流数学模型。通过计算实例说明,该数学模型能够很好地帷有复杂边界的流线弯曲水流的水力特性。     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy

In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.     

Veiled assonance between geodesics on ellipsoid and billiard in its focal ellipse

We introduce new special ellipsoidal confocal coordinates in ⁿ (n ≥ 3) and apply them to the geodesic problem on a triaxial ellipsoid in ³ as well as the billiard problem in its focal ellipse.

Using such appropriate coordinates we show that these different dynamical systems have the same common analytic first integral. This fact is not evident because there exists a geometrical spatial gap between the geodesic and billiard flows under consideration, and this separating gap just “veils” the resemblance of the two systems.

In short, a geodesic on the ellipsoid and a billiard trajectory inside its focal ellipse are in a “veiled assonance”—under the same initial data they will be tangent to the same confocal hyperboloid. But this assonance is rather incomplete: the dynamical systems in question differ by their intrinsic action angle-variables, thereby the different dynamics arise on the same phase space (i.e. the same phase curves in the same phase space bear quite different rotation numbers).

Some results of this work have been published before in Russian (Tabanov, 1993) and presented to the International Geometrical Colloquium (Moscow, May 10–14, 1993) and the International Symposium on Classical and Quantum Billiards (Ascona, Switzerland, July 25–30, 1994).     

Separation coordinates in Hénon-Heiles systems

In this paper we apply the method of the Kowalewski's Conditions to separate the seven Hénon-Heiles integrable systems. For each of them we provide explicitly the separation coordinates in the form of eigenvalues of a matrix M called Control Matrix. A couple of systems (HH3 KK and HH4 1:12:16) are presented and discussed in a more general form than usually in the literature. We show that the process of separation of coordinates can be reduced, at the end, to the choice of a single function and, eventually, a vector field transversal to the Lagrangian foliation in an extended phase space.