Analysis of steady state polydisperse counterflow spray diffusion flames in the large Stokes number limit

A new mathematical analysis is presented of certain aspects of the behavior of opposed flow polydisperse spray diffusion flames within the framework of a model in which large slip is permitted between the droplets and their host surroundings. The sectional approach is used to model the polydisperse spray. Operating conditions are identified under which the inverses of sectional Stokes numbers are small spray-related parameters to be used in a perturbation analysis of the liquid phase governing equations. The steady state equations and their solutions are similar in form to the equivalent equations considered in previous work of the authors in which dynamical equilibrium of the droplets with the carrier phase was assumed. However, here there is much more mathematical complexity involved in the spray equations solution. A hybrid Eulerian–Lagrangian approach is also suggested to get an insight into the phenomenon of reversal in the motion of the droplets that has been reported in independent experimental and computational research. Computed results based on the analytical solutions up to the 1st order of approximation reveal the influence of large droplet slip on the droplets velocity field and on the spray diffusion flame’s thermal field, for which appreciable heterogeneous combustion can occur under the operating conditions considered.     

The feature study on the <Emphasis Type="Italic">π</Emphasis> and proton rapidity distributions at AGS,SPS and RHIC

The features of nuclear stopping power and multi-hadron production systematically are studied by making an analysis of rapidity distributions of pion and proton at AGS, SPS and RHIC in this work. It is found that nuclear stopping power increases linearly with project rapidity y _p at AGS and SPS, but that is not liner at RHIC. It is argued that the average rapidity loss is saturated at central rapidity region at RHIC. For pion distribution, it is found that the phase space of pion distribution distributes uniformly in the longitudinal direction, and a linear relationship of 〈βγ〉_L with log√s is given at AGS and SPS. Non-uniform flow model may explain the features of the distribution at AGS and SPS, but may not explain those of at RHIC. Supported by the Excellent Youth Foundation of Hubei Scientific Committee (Grant No. 2006ABB036), the Educational Commission of Hubei Province of China (Grant No. Z20081302), and the Natural Science Foundation of China Three Gorges University (Grant No. 2003C02)     

Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.     

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

In this paper, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved analytically by using the homotopy analysis method (HAM). Graphical results are presented to investigate the influence of the nondimensional wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.      

Minimizing multi-homogeneous Bézout numbers by a local search method

Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous Bézout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous Bézout number. As with any other local search method, it may give a local minimum rather than the minimum over all possible homogenizations. Numerical examples show the efficiency of this local search method.

     

求数列极限的两个定理

本文给出关于数列极限的两个定理 .     

Canonical splittings of groups and 3-manifolds

We introduce the notion of a `canonical' splitting over or for a finitely generated group . We show that when happens to be the fundamental group of an orientable Haken manifold with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of . This leads to a new proof of Johannson's Deformation Theorem.

     

An addition theorem for the color number

There is a close relation between the color number of a continuous map without fixed points and the topological dimension. If  is an involution, the color number is also related to the co-index. An addition theorem for the color number is established thus underscoring the interrelations between color number, dimension and co-index.

     

The Forcing Convexity Number of a Graph

For two vertices u and v of a connected graph G, the set I(u,v) consists of all those vertices lying on a u-v geodesic in G. For a set S of vertices of G, the union of all sets I(u,v) for u, v S is denoted by I(S). A set S is a convex set if I(S) = S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. A convex set S in G with |S| = con(G) is called a maximum convex set. A subset T of a maximum convex set S of a connected graph G is called a forcing subset for S if S is the unique maximum convex set containing T. The forcing convexity number f(S, con) of S is the minimum cardinality among the forcing subsets for S, and the forcing convexity number f(G, con) of G is the minimum forcing convexity number among all maximum convex sets of G. The forcing convexity numbers of several classes of graphs are presented, including complete bipartite graphs, trees, and cycles. For every graph G, f(G, con) con(G). It is shown that every pair a, b of integers with 0 a b and b is realizable as the forcing convexity number and convexity number, respectively, of some connected graph. The forcing convexity number of the Cartesian product of H × K ₂ for a nontrivial connected graph H is studied.     

Another Note on the Greatest Prime Factors of Fermat Numbers

For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if F_m = 2^2m + 1 is the mth Fermat number, then P(F_m) 2^m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(F_a,m), where F_a,m = a^2m + 1 whenever a is even and m a¹⁸.AMS Subject Classification (1991) 11A51 11J86