稠密气固流动中颗粒聚集的定量评价

本文提出了定量评价稠密两相流动中颗粒聚集现象的参数和方法:用碰撞频率的大小估计颗粒聚集的强弱;用颗粒体积分数的标准偏差评价流场中颗粒分布的不均匀程度;用颗粒分布的相关系数衡量流动的相似性;用颗粒体积分数的概率分布和颗粒分布曲线描述流场细节;用高密集区域颗粒数目比例和稀疏区域面积比例来反映流场的特征部分。     

概率空间上一类集合的分形维数

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On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations

Hydraulic permeability is studied in porous media consisting of randomly distributed monodisperse spheres by means of computational fluid dynamics (CFD) simulations. The packing of spheres is generated by inserting a certain number of nonoverlapping spherical particles inside a cubic box at both low and high packing fractions using proper algorithms. Fluid flow simulations are performed within the interparticulate porous space by solving Navier-Stokes equations in a low-Reynolds laminar flow regime. The hydraulic permeability is calculated from the Darcy equation once the mean values of velocity and pressure gradient are calculated across the particle packing. The simulation results for the pressure drop across the packing are verified by the Ergun equation for the lower range of porosities (<0.75), and the Stokes equation for higher porosities (∼1). Using the results of simulations, the effects of porosity and particle diameters on the hydraulic permeability are investigated. Simulations precisely specified the range of applicability of empirical or semi-empirical correlations for hydraulic permeability, namely the Carman-Kozeny, Rumpf-Gupte, and Howells-Hinch formulas. The number of spheres in the model is gradually decreased from 2000 to 20 to discover the finite-size effect of pores on the hydraulic permeability of spherical packing, which has not been clearly addressed in the literature. In addition, the scale dependence of hydraulic permeability is studied via simulations of the packing of spheres shrunk to lower scales. The results of this work not only reveal the validity range of the aforementioned correlations, but also show the finite-size effect of pores and the scale-independence of direct CFD simulations for hydraulic permeability.     

On a posterior evaluation of a simple greedy method for set packing

We consider an approach for ex post evaluation of approximate solutions obtained by a well known simple greedy method for set packing. A performance bound is derived that is a function of the highest average reward per item over subsets as well as the number of allocated subsets and ground items. This a posterior bound can enable much revelation of optimality when the solution is near optimal. One of the advantages of the ex post analysis is that it does not require computing the optimal solution to the LP relaxation. The ex post bound will not be guaranteed to reveal substantial levels of optimality for all problem instances but can be a useful tool that is complementary to other traditional methods for ex post evaluation for the set packing problem.     

Prevalence and Significance of Approximate Symmetry in Organic Pc Structures

A survey has been made of the well determined (R≤0.050) organic crystal structures that have only a single glide plane (e. g., are in space group Pc) and that have more than one crystallographically independent formula unit (Z′>1); the goal was to discover what fraction have additional approximate symmetry. Of the 377 unique structures examined 8 % should almost certainly been refined in a higher-symmetry unit cell; 86 % of the remaining 347 have approximate symmetry that is periodic in at least one dimension. While these percentages are similar to those found for P1 structures (C. P. Brock, Acta Crystallogr., Sect. B 2022 , 78, 576–588), the types of approximate symmetry differ because 89 % of the P1, Z′>1 structures were composed of enantiopure material. The 347 reliable Pc structures include 118 that are slightly distorted or mimicked Cc and P2₁/c structures, 15 of which were reported as having been determined at room temperature. The distortions in another 72 are so large that the approximate symmetry must be seen as periodic in two dimensions only. These results suggest that symmetry lowering may accompany transformation of a crystal nucleus to a macroscopic crystal.     

Structural property and function of D-erythro asymmetric chain sphingomyelins as studied by microcalorimetry and electron microscopy

D-erythro sphingomyelines (SM) having a defined acyl chain were synthesized with sphingosylphosphorylcholine as a starting material, and both a structural property and its relating phase transition phenomenon were compared between a symmetric chain length SM (palmitoyl-SM: C16-SM) and asymmetric chain length SMs (behenoyl-SM: C22-SM, lignoceryl-SM: C24-SM). Furthermore, effect of increasing a content of asymmetric chain SMs in the mixture systems of C22-SM/C16-SM, and C24-SM/C16-SM was investigated. The present calorimetric and electron microscopic studies revealed that (1) The main transition enthalpy is smaller for the asymmetric chain SMs than for the symmetric chain SM by about 3 kJ mol⁻¹, although the acyl chain length is longer for the former than for latter; (2) Relatively small size vesicles (100∼200 nm diameters) surrounded by one or more lamellae are observed for the asymmetric chain SMs, in contrast to large multilamellar vesicles (1500∼2500 nm diameters) having at least fifteen stained lamellae for the symmetric chain SM and (3) The coexisting asymmetric chain SMs cause the decrease in size and multiplicity for the MLV of the symmetric chain SM, simultaneously with a decrease in the main transition enthalpy.     

An asymptotic approximation scheme for the concave cost bin packing problem

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant ?, there exists a polynomial-time approximation algorithm with an asymptotic worst-case performance ratio of no more than 1 + ?.     

Random-order bin packing

The average-case analysis of algorithms usually assumes independent, identical distributions for the inputs. In [C. Kenyon, Best-fit bin-packing with random order, in: Proc. of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 1996, pp. 359–364] Kenyon introduced the random-order ratio, a new average-case performance metric for bin packing heuristics, and gave upper and lower bounds for it for the Best Fit heuristics. We introduce an alternative definition of the random-order ratio and show that the two definitions give the same result for Next Fit. We also show that the random-order ratio of Next Fit equals to its asymptotic worst-case, i.e., it is 2.     

Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

We show that three important topics in nonlinear analysis and optimization are intimately related: the theory of perturbations, the notion of well-posedness and variational principles in the sense of Ekeland, Borwein–Preiss and Deville–Godefroy–Zizler. The concept of genericity and the new notion of flexible perturbation play a key role in these connections. This notion enables one to consider topologies on spaces of functions which have been introduced recently. A link between the Asplund and Ekeland–Lebourg methods and the Palais–Smale condition, another important topic in nonlinear analysis, is pointed out.     

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.