Aggregation of Filler Particles in Polymer Composites. An Analysis within the Framework of Irreversible Aggregation Models

Based on the model of irreversible cluster-cluster aggregation, a principal possibility of predicting and simulating the degree of aggregation of filler particles, mathematically expressed by the size distribution of aggregates, is shown. For a practical application of this method, it is necessary to determine the correlation relationship between the model parameters and processing characteristics of the composites.     

Two-Dimensional Artin Groups with CAT(0) Dimension Three

We exhibit 3-generator Artin groups which have finite two-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a two-dimensional CAT(0) complex. We prove that infinitely many of these groups are the fundamental groups of compact, non-positively curved 3-complexes. These examples show that the geometric dimension of a CAT(0) group may be strictly less than its CAT(0) dimension.     

Gravitational field of spherical domain wall in higher dimension

An exact solution of Einstein’s equations is found describing the gravitational field of a spherical domain wall with nonvanishing stress component in the direction perpendicular to the plane of the wall. Also we have studied the motion of test particle around the domain wall.     

一维弹道修正弹飞行稳定性研究

为分析一维弹道修正弹阻力片不同修正能力下,其打开后对弹丸飞行稳定性的影响大小,以某型100mm一维弹道修正弹为研究对象,运用Simulink软件建立了6自由度刚体弹道模型,通过设置不同仿真条件,利用阻力片打开后弹丸攻角变化、陀螺稳定性判据、动态稳定性判据判断弹丸飞行稳定性。求出了在阻力片分别产生原来弹丸阻力系数3倍、4倍、5倍阻力下,为保证弹丸飞行稳定应控制阻力片打开后产生的新的静力矩的极限值应分别小于原弹丸静力矩的3倍、3.5倍、4倍。通过研究阻力片打开时间对弹丸飞行稳定性的影响,结果表明,阻力片打开时间越晚其对弹丸飞行稳定性的影响越大;分析了阻力片一定修正能力下,以不同射角射击时为保证阻力片打开后弹丸飞行稳定性,阻力片最晚打开时间。     

Extra dimensions and phase experiments

In modern Kaluza‐Klein theories which successfully unify gravity, electromagnetism and a scalar field, null geodesics in five dimensions lead to simplified expressions for phase shifts in four‐dimensional spacetime. It might be possible to test for an extra dimension by experiments such as those where neutron interferometry is used to measure the Aharonov‐Bohm effect.

     

Characterization of floc size and structure under different monomer and polymer coagulants on microfiltration membrane fouling

The characteristic of aggregates pre-coagulated by inorganic monomer alum, polymer aluminium chlorohydrate(ACH) and polyaluminium chloride(PACl) coagulants impose major impact on the removal of humic acids (HAs) and the reduction of microfiltration (MF) membrane fouling. The fractal dimension of flocs formed by ACH and PACl is higher than that by monomer alum, indicating Keggin structure produced by polymer coagulants is much more compact compared with hexameric ring structure of alum hydrolysis species. Correspondingly, cake layer specific resistance is far higher and the MF membrane flux deteriorates much more severely when pre-coagulated by ACH and PACl than by alum. Moreover, the higher basicity contains in PACls, the cake layer fouling is more serious for producing more proportion of dense hydrolysis species Al₁₃. Thus, the polymer coagulant ACH and PACl seems not adapt to the pre-coagulation–MF process for cake layer resistance increase two to three times although they save 60–70% dose in comparison with alum for HAs removal. Additionally, for three Al-based coagulants under sweep coagulation condition, insufficient dose result in lower HAs removal and produce more small particles caused higher cake layer specific resistance according to Carman–Kozeny relationship. On the other hand, coagulant hydrolysis species as direct contaminant loading aggravated cake resistance on the MF membrane when overdosed. The optimum dose should keep the minimum to provide better HAs removal efficiency, and produce lower cake layer specific resistance and higher membrane filterability for pre-coagulation–MF hybrid process.     

The mystery of perpendicular fivefold axes and the fourth dimension in intermetallic structures

The structures of eight related known intermetallic structure types are the impetus to this paper: Li21Si5, Mg44Rh7, Zn13(Fe,Ni)2, Mg6Pd, Na6Tl, Zn91Ir11, Li13Na29Ba19, and Al69Ta39. All belong to the F43m space group, have roughly 400 atoms in their cubic unit cells, are built up at least partially from the gamma-brass structure, and exhibit pseudo-tenfold symmetric diffraction patterns. These pseudo-tenfold axes lie in the {110} directions, and thus present a paradox. The {110} set is comprised of three pairs of perpendicular directions. Yet no 3D point group contains a single pair of perpendicular fivefold axes (by Friedel's Law, a fivefold axis leads to a tenfold diffraction pattern). The current work seeks to resolve this paradox. Its resolution is based on the largest of all 4D Platonic solids, the 600-cell. We first review the 600-cell, building an intuition discussing 4D polyhedroids (4D polytopes). We then show that the positions of common atoms in the F43m structures lie close to the positions of vertices in a 3D projection of the 600-cell. For this purpose, we develop a projection method that we call intermediate projection. The introduction of the 600-cell resolves the above paradox. This 4D Platonic solid contains numerous orthogonal fivefold rotations. The six fivefold directions that are best preserved after projection prove to lie along the {110} directions of the F43m structures. Finally, this paper shows that at certain ideal projected cluster sizes related to one another by the golden mean (tau=(1+ radical 5)/2), constructive interference leading to tenfold diffraction patterns is optimized. It is these optimal values that predominate in actual F43m structures. Explicit comparison of experimental cluster sizes and theoretically derived cluster sizes shows a clear correspondence, both for isolated and crystalline pairs of projected 600-cells.     

A sharp estimate and change on the dimension of the attractor for singular semilinear parabolic equations

We consider the semilinear reaction diffusion equation

Eden-Staudacher and Beisert-Eden-Staudacher equations in the $$\mathcal{N} = 4$$ supersymmetric gauge theory

We investigate the Eden-Staudacher and Beisert-Eden-Staudacher equations for the anomalous dimension of twist-2 operators at a large spin s in the supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions ζ(k) having the maximum transcendentality property. We also show that at a large coupling, the “singular” solution of the Beisert-Eden-Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT correspondence. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 117–129, April, 2008.