A Performance Analysis of Appel's Algorithm for Performing Pairwise Calculations in a Many Particle System

Appel's algorithm for efficiently performing pairwise potential energy calculations is analyzed with regard to both computing time required and error incurred. Four factors are identified which determine the practical value of Appel's method: the total number of particles in the system, the tolerance for error in the calculations, the complexity of the pairwise energy calculation, and the spacial distribution of the particles.     

On small homotopies of loops

Two natural questions are answered in the negative:

• “If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic?”

• “Can adding arcs to a space cause an essential curve to become nulhomotopic?”

The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and π₁-shape injective.

单壁碳纳米管储氢研究

摘要 利用Gaussian03程序计算出C-H键的键能是1.88eV，键长是0.113nm。已知H-H键能是4.748eV，键长是0.074nm。显然， H-H键能大于C-H键的键能，所以在常温常压下碳纳米管储氢时，以物理吸附H2分子为主，化学形式的C-H键吸附为辅。另外，利用LJ势能函数，计算了H2分子在碳纳米管中C原子所成的六边形中心正上方、C原子正上方以及相邻两C原子中间正上方时H2分子与碳纳米管之间的势能。得到无论管内、管外或者两端，都是H2分子在C原子所成的六边形中心正上方时能量最低。且在管内时H2分子距离管壁的距离是0.320nm，在管外时距离管壁的距离是0.309nm；在两端的管内时距离管壁的距离是0.324nm，在两端的管外时距离管壁的距离是0.313nm。     

INTERFACIAL FREE ENERGIES,ZETA POTENTIALS AND THROMBORESI STANCE IN BOVINE AND OVINE CAROTID ARTERIES

The physical properties of the intimal surfaces of both natural and artificial arteries are important In the prevention of thrombosis and clotting. It Is expected thati a) the interface between the blood plasma and the intima should be highly negatively charged, to repel negatively charged platelets and other blood constituents, and b) the interfacial free energy at the plasma-intima interface should be as low as possible, to prevent adhesion If the charge barrier is breached. Few measurements of either the zeta potential or the interfacial free energy at the intimal surface can be found in the literature. Zeta potentials of natural and cross-linked bovine carotid intima, and of an expanded Teflon prosthesis were determined by a streaming potential method in 0.9% (w/v) NaC1. Interfacial free energies of both bovine and ovine carotid intima, and of an expanded Teflon prosthesis were also determined by a contact-angle method using water immiscible liquid drops on the intimal surface Immersed in 0.9% (w/v) NaC1.     

Integral Self-affiine Tiles of Bandt＇s Model

Integral self-affine tiling of Bandt＇s model is a generalization of the integral self-affine tiling. Using ergodic theory, we show that the Lebesgue measure of the tile is a rational number where the denominator equals to the order of the associate symmetry group. We apply the result to the study of the Levy Dragon.     

On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the “embeddings of Banach spaces” point of view.     

Mechanical properties and deformation morphologies of covalently bridged multi-walled carbon nanotubes: Multiscale modeling

We formulate a multiscale modeling framework to investigate the deformation morphologies and energetics of covalently bridged multi-walled carbon nanotubes (MWCNTs). The formulation involves extending a previously established quasi-continuum model by incorporating the inter-wall bridging energy density function into the constitutive relations via message passing from fully atomistic simulations. Using the extended numerical model, we studied the mechanical responses of the 10-walled MWCNT with varying inter-wall bridge densities under torsion, bending, and uniaxial compression. Our simulation results show that the presence of inter-wall covalent bridges not only enhances the post-buckling rigidities of the MWCNTs, but also modifies the deformation morphologies and morphology pathways. For bending and uniaxial compression, we constructed in the space of bridge density and applied strain the deformation morphology phase diagram, where three phases, uniformly deformed phase, rippling pattern, and diamond-shaped pattern, are identified and separated by linear phase boundaries. We attribute the deformation phase transitions to the interplay of inter-wall and intra-wall interaction energies. The multiple shape transitions of MWCNTs and the elastic nature of the deformation suggest that MWCNTs can be designed as shape-memory nanodevices with tunable stabilities.     

跳过程存在成功耦合的充要条件

本文研究了一般状态跳过程的ｈ骨架的不变σ代数，尾σ－代数之间的关系，并由此证明具有正则ｑ对的非常返跳过程存在成功耦合的充要条件是跳过程的所有有界调和函数都是常数。