格点量子Zakharov方程组紧致核截面的存在性与熵的估计

讨论一类非自治带量子纠正的修正Zakharov方程组在无穷格点上解的渐近行为,应用截断函数的技巧证明该格点方程组紧致核截面的存在性,并给出核截面的Kolmogorov-ε熵的上界估计.     

Efficient Lagrangian scalar tracking method for reactive local mass transport simulation through porous media

Mass transfer in the presence of chemical reactions for flows through porous media is of interest to many disciplines. The Lattice Boltzmann method (LBM) is particularly attractive in such cases due to the ease with which it handles complicated boundary conditions. However, useful Lagrangian information (such as solute survival distance, effective diffusivity, collision frequency) is challenging to obtain from the LBM. In this paper, we present a straightforward and efficient Lagrangian methodology (Lagrangian scalar tracking, LST) for performing solute transport simulations in the presence of heterogeneous, first‐order, irreversible reactions, based on a velocity field obtained from LBM. The hybrid LST/LBM technique tracks passive mass markers that have two contributions to their movement: convective (obtained through interpolation of a previously obtained velocity field) and Brownian. Various Schmidt number solutes and different solute release modes can be modeled with a single solvent flow field using this method. Moreover, the mass markers can have a range of reaction rate coefficients. This allows for the exploration of the whole spectrum of first‐order heterogeneous reaction rates with just a single simulation. In order to show the applicability of the LST/LBM scheme, results from a case study are presented in which the consumption of oxygen and/or nutrients within a porous bone tissue engineering scaffold is modeled under flow perfusion culturing conditions. Although the reactive LST methodology described in this paper compliments the LBM, it can also be used with any other flow simulation that can generate the velocity field. Copyright © 2010 John Wiley & Sons, Ltd.     

Counting and ordering periodic stationary solutions of lattice Nagumo equations

We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs we are able to divide these periodic solutions into equivalence classes that can be partially ordered and counted. In order to accomplish this, we use combinatorial concepts such as necklaces, bracelets and Lyndon words.     

一阶格点系统的不变测度与Liouville型方程

该文讨论一阶格点系统的解在相空间中的概率分布问题.作者先证明该格点系统的解算子生成的过程存在拉回吸引子,然后证明拉回吸引子上存在唯一的Borel不变概率测度,且该不变测度满足Liouville型方程.     

Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar–Gross–Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.     

The predicted compressive strength of a pyramidal lattice made from case hardened steel tubes

A sandwich panel with a core made from solid pyramidal struts is a promising candidate for multifunctional application such as combined structural and heat-exchange function. This study explores the performance enhancement by making use of hollow struts, and examines the elevation in the plastic buckling strength by either strain hardening or case hardening. Finite element simulations are performed to quantify these enhancements. Also, the sensitivity of competing collapse modes to tube geometry and to the depth of case hardening is determined. A comparison with other lattice materials reveals that the pyramidal lattice made from case hardened steel tubes outperforms lattices made from solid struts of aluminium or titanium and has a comparable strength to a core made from carbon fibre reinforced polymers.     

Asymptotics of Selberg-like integrals by lattice path counting

We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to the Selberg and Selberg-like multidimensional integrals. Our method of solution is combinatorial: it consists in the enumeration of certain classes of lattice paths associated to the solution of recurrence relations.