Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition

In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

An Extension Landau-Lifshitz Model in Studying Soft Ferromagnetic Films

In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.     

Journey Making group workshops as a research tool

Problem-structuring group workshops can be used in organizations as a consulting tool and as a research tool. One example of the latter is using a problem-structuring method (PSM) to help a group tackle an organizational issue; meanwhile, researchers collect the participants’ initial views, discussion of divergent views, the negotiated agreement, and the reasoning for outcomes emerging. Technology can help by supporting participants in freely sharing their opinions and by logging data for post-workshop analyses. For example, computers let participants share views anonymously and without being influenced by others (as well as logging those views), and video-cameras can record discussions and intra-group dynamics. This paper evaluates whether technology-supported Journey Making workshops can be effective research tools that can capture quality research data when compared against theoretical performance benchmarks and other qualitative research tools.     

Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.     

多气隙电阻板室抗辐照性能研究

给出了为RHIC-STAR飞行时间探测器设计的多气隙电阻板室(MRPC)的辐照实验结果. 实验采用100mCi⁶⁰Co γ源, 采用不同的剂量率对MRPC进行辐照. 一个室在大剂量率2.87×10^－2Gy/h下辐照了24h后, 其性能如噪声计数率, 暗电流等均大大退化. 另一个室在相对低剂量率5.31×10^－4Gy/h下辐照了530h, 其性能没有见到任何变坏. 实验的目的是为了了解这种探测器在几年的运行中经过大剂量的辐照后的性能变化情况.     

Rheological properties of binary associating polymers

Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G ^′ and G ^″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω _x , and an extremely strong effect of added free stickers (fC) on the dynamics. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.