Validation of Pore-Scale Simulations of Hydrodynamic Dispersion in Random Sphere Packings

We employ the lattice Boltzmann method and random walk particle tracking to simulate the time evolution of hydrodynamic dispersion in bulk,random,monodisperse,hard-sphere packings with bed porosities(interparticle void volume fractions)between the random-close and the random-loose packing limit.Using JodreyTory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings,whose microstructures differ in their degree of heterogeneity(DoH).Because the DoH quantifies the heterogeneity of the void space distribution in a packing,the asymptotic longitudinal dispersion coefficient calculated for the packings increases with the packings’DoH.We investigate the influence of packing length(up to 150 d_(p),where d_(p) is the sphere diameter)and grid resolution(up to 90 nodes per d_(p))on the simulated hydrodynamic dispersion coefficient,and demonstrate that the chosen packing dimensions of 10 d_(p)×10 d_(p)×70 d_(p) and the employed grid resolution of 60 nodes per d_(p) are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects.Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.

一类基于Weil和的少重量二元线性码

近年来,通过定义集构造有限域上少重量线性码得到了广泛的关注。部分少重量线性码已经被应用于密钥分享方案,强正则图、认证码和关联方案。本文中研究一类线性码的参数和重量分布,得到二重或四重的二元线性码,并确定它们对偶码的参数。特别地,部分对偶码是关于Sphere packing界距离最优的。

A fast and practical method to pack spheres for mesh generation

Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.

Rectangular Body-centered Cuboid Packing Lattices and Their Possible Applications

We first introduce several sphere packing ways such as simple cubic packing(SC),face-centered cubic packing(FCC),body-centered cubic packing(BCC),and rectangular body-centered cuboid packing(recBCC),where the rectangular body-centered cuboid packing means the packing method based on a rectangular cuboid whose base is square and whose height is times the length of one side of its square base such that the congruent spheres are centered at the 8 vertices and the centroid of the cuboid.The corresponding lattices are denoted as SCL,FCCL,BCCL,and recBCCL,respectively.Then we consider properties of those lattices,and show that FCCL and recBCCL are the same.Finally we point out some possible applications of the recBCC lattices.

A Class of New Optimal Ternary Cyclic Codes over F3m with Minimum Distance 4

As a branch of applied mathematics, coding theory plays an important role. Among them, cyclic codes have attracted much attention because of their good algebraic structure and easy analysis performance. In this paper, we will study one class of cyclic codes over F3. Given the length and dimension, we show that it is optimal by proving its minimum distance is equal to 4, according to the Sphere Packing bound.

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,

一类新的最优三元循环码

循环码是线性码的一个重要子类,由于代数结构清晰、编译码简单且易于实现,被广泛地应用于数据存储系统和通信系统中。本文研究了一类三元循环码,通过分析某些方程在三元域上的解,确定了此类三元循环码的参数,由Sphere Packing界证明了该码具有最优性。

Optimized Filling of a Given Cuboid with Spherical Powders for Additive Manufacturing

In additive manufacturing(also known as 3D printing),a layer-by-layer buildup process is used for manufacturing parts.Modern laser 3D printers can work with various materials including metal powders.In particular,mixing various-sized spherical powders of titanium alloys is considered most promising for the aerospace industry.To achieve desired mechanical properties of the final product,it is necessary to maintain a certain proportional ratio between different powder fractions.In this paper,a modeling approach for filling up a rectangular 3D volume by unequal spheres in a layer-by-layer manner is proposed.A relative number of spheres of a given radius(relative frequency)are known and have to be fulfilled in the final packing.A fast heuristic has been developed to solve this special packing problem.Numerical results are compared with experimental findings for titanium alloy spherical powders.The relative frequencies obtained by using the imposed algorithm are very close to those obtained by the experiment.This provides an opportunity for using a cheap numerical modeling instead of expensive experimental study.

Subfield Codes of Linear Codes from Perfect Nonlinear Functions and Their Duals

Let F_(p)^(m) be a finite field with p^(m) elements,where p is an odd prime and m is a positive integer.Recently,[17]and[35]determined the weight distributions of subfield codes with the form C f={((T r(a f(x)+b x)+c)_(x∈F_(p)^(m)),T r(a)):a,b∈F_(p)^(m),c∈F_(p)}for f(x)=x^(2) and f(x)=x p k+1,respectively,where Tr(⋅)is the trace function from F_(p)^(m) to F_(p),and k is a nonnegative integer.In this paper,we further investigate the subfield code C f for f(x)being a known perfect nonlinear function over F_(p)^(m) and generalize some results in[17,35].The weight distributions of the constructed codes are determined by applying the theory of quadratic forms and the properties of perfect nonlinear functions over finite fields.In addition,the parameters of the duals of these codes are also determined.Several examples show that some of our codes and their duals have the best known parameters according to the code tables in[16].The duals of some proposed codes are optimal according to the Sphere Packing bound if p≥5.