Apollonian packings as physical fractals

The Apollonian packings (APs) of spheres are fractals that result from a space-filling procedure. We discuss the finite size effects for finite intervals s?∈?[s _min,?s _max] between the largest and the smallest sizes of the filling spheres. We derive a simple analytical generalization of the scale-free laws, which allows a quantitative study of such physical fractals. To test our result, a new efficient space-filling algorithm has been developed which generates random APs of spheres with a finite range of diameters: the correct asymptotic limit s _min/s _max?→?0 and the known APs' fractal dimensions are recovered and an excellent agreement with the generalized analytic laws is proved within the overall range of sizes.     

Permeability of mixed soft and hard granular material: Hydrogels as drainage modifiers

We measure the flow of water through mixed packings of glass spheres and soft swellable hydrogel grains, at constant sample volume. Permeability values are obtained at constant sample volume and at porosities smaller than random close packing, for different glass bead diameters D and for variable gel grain diameter d, as controlled by the salinity of the water. The gel content is also varied. We find that the permeability decays exponentially in n(D/d ) ^b , where n = N _gel/N _glass is the gel to glass bead number ratio and b is approximately 3. Therefore, flow properties are determined by the volume fraction of gel beads. A simple model based on the porosity of overlapping spheres is used to account for these observations.     

Transport coefficients of hard sphere fluids

New calculations have been made of the self-diffusion coefficient D, the shear viscosity η_s, the bulk viscosity η_b and thermal conductivity λ of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (～0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial N dependence for N < 500 at equilibrium fluid densities (ε 0.494). D increased with N, especially at intermediate densities in the range ε ～ 0.3–0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys., 62, 509 was shown to fit these data well for N ～ 500 particle systems. We found that the packing fraction ε dependence of the two viscosities and thermal conductivity, generically denoted by X, were represented well by the simple formula X/X ₀ = 1/[1 ? (ε/ε₁)]^m within the equilibrium fluid range 0 > ε > 0.493. This formula has two disposable parameters, ε and m, and X ₀ is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972, Adv. Colloid. Interface Sci., 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X _o was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ε = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for η_s/η_o ?30–40, suggesting that the ‘crowding’ effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D_o/D ～ 11 at the same packing fraction, possibly indicating the contribution from ‘hydrodynamic enhancement’ of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.     

Statistical Analysis of Simulated Random Packings of Spheres

This paper describes two algorithms for the generation of random packings of spheres with arbitrary diameter distribution. The first algorithm is the force‐biased algorithm of Mościński and Bargieł. It produces isotropic packings of very high density. The second algorithm is the Jodrey‐Tory sedimentation algorithm, which simulates successive packing of a container with spheres following gravitation. It yields packings of a lower density and of weak anisotropy. The results obtained with these algorithms for the cases of log‐normal and two‐point sphere diameter distributions are analysed statistically, i. e. standard characteristics of spatial statistics such as porosity (or volume fraction), pair correlation function of the system of sphere centres and spherical contact distribution function of the set‐theoretical union of all spheres are determined. Furthermore, the mean coordination numbers are analysed. These results are compared for both algorithms and with data from the literature based on other numerical simulations or from experiments with real spheres.     

Simulation of random packing of spherical particles with different size distributions

A numerical model for a loose packing process of spherical particles is presented. The simulation model starts with randomly choosing a sphere according to a pregenerated continuous particle-size distribution, and then dropping the sphere into a dimension-specified box, and obtaining its final position by using dropping and rolling rules which are derived from a similar physical process of spheres dropping in the gravitational field to minimize its gravity potential. Effects of three different particle-size distributions on the packing structure were investigated. Analysis on the physical background of the powder-based manufacturing process is additionally applied to produce optimal packing parameters of bimodal and Gaussian distributions to improve the quality of the fabricated parts. The results showed that higher packing density can be obtained using bimodal size distribution with a particle-size ratio from 1.5 to 2.0 and the mixture composition around n ₂:n ₁=6:4. For particle size with a Gaussian distribution, the particle radii should be limited in a narrow range around 0.67 to 1.5.     

Study of the influence of the injection section on the stability of a high-current relativistic electron beam propagating through the gaseous medium of a plasmochemical reactor

Results are presented from experimental study of the influence of the injection section on the stability of a high-current relativistic electron beam (REB) propagating through the gaseous medium of a plasmochemical reactor (PR). An REB with the electron energy E _e =1 MeV, beam current I _b =10–22 kA, and pulse duration t=60 ns was generated by the Tonus accelerator and, then, injected into a 0.1-m-diameter PR filled with air. The PR consisted of two sections with lengths L ₁= 0.3–1.0 m and L ₂=1.1–2.5 m; the total length of the system was no longer than 3.5 m. The first section was filled with air at a pressure of P ₁=0.8–1.5 torr, and the pressure in the second section was varied within the range P ₂=0.1–760 torr. The current I _b of an REB passed through both sections of the PR was measured with the help of a sectioned vacuum Faraday cup. The transportation efficiency of the beam was determined as the ratio I _b /I _inj, where I _inj is the beam current measured at the point of injection into the PR. It is shown that, for the optimal dimensions of the first PR section, it has a stabilizing action on the REB with a current density of up to 3 kA/cm², which makes it possible to increase the effective length of the second (working) PR section, which is filled with a gas at various pressures, to L ₂=(25–35)L _bet, where L _bet is the beam betatron length.     

直径任意分布球填充的数值模拟

提出球填充数值算法的新分类方法.改进原有的松弛算法,使其能够模拟直径任意分布的球填充问题,采用可变循环周期使不同球数情形下的填充率基本保持不变.算例数据表明,该算法的填充率和配位数均高于原算法.由于采用背景网格搜索和双向链表组数据结构,使得邻接球搜索效率有相当大的提高,算法的时间复杂度为O(N)(N为球数).在一台AMD Athlon 3200+PC上,对于10000个等径球的随机密排列,只需217s,填充率即可达到0.64.     

Two triple points in the H2O–H2 system

Using a volumetric technique, phase transitions in the H₂O–H₂ system were investigated in the vicinity of two points of an invariant equilibrium, L+I _h+sII and L+sII+C ₁, located at 1.07 kbar and?10 °C and at 3.6 kbar and 1 °C, respectively. Liquid water (L), low-pressure hexagonal ice (I _h) and high-pressure cubic (sII) and rhombohedral (C ₁) clathrate hydrates were in equilibrium with gaseous hydrogen taken in excess.     

Numerical Simulation of Random Close Packing with Tetrahedra

The densest packing of tetrahedra is still an unsolved problem. Numerical simulations of random close packing of tetrahedra are carried out with a sphere assembly model and improved relaxation algorithm. The packing density and average contact number obtained for random close packing of regular tetrahedra is 0.6817 and 7.21 respectively, while the values of spheres are 0.6435 and 5.95. The simulation demonstrates that tetrahedra can be randomly packed denser than spheres. Random close packings of tetrahedra with a range of height are simulated as well. We find that the regular tetrahedron might be the optimal shape which gives the highest packing density of tetrahedra.     

Electromagnetic properties of random material

Abstract

This work addresses the relationship between grain properties and the permeability and permittivity spectra of non-crystalline materials or aerosols.

The scattered multipolar fields about a single sphere are related to the polarizability of a random collection of such spheres. Using the Clausius–Mossotti relation the effective permeability and permittivity spectra of an amorphous material is determined for arbitrary permittivity and permeability of the individual spheres, packing density, and sphere size. Although the author considers the spectra over a range where the product of the external wavevector and sphere radius is kept small, typically less than one-tenth, the product of the internal wavevector and sphere radius is unconstrained and seen to have a large effect on predicted spectra.

The result is a variety of possible spectral types which include resonances, relaxations and certain complex. conglomerate spectra that have been measured and far which no direct explanation is otherwise available.     

System Ni-Ti. Crystallogeometrical features

The work deals with a search for general crystallogeometrical regularities in binary alloys in a Ni-Ti system. The histograms of the B2, B19, D0₂₄ and E9₃ structure distributions are constructed in binary systems as a function of the space filling coefficient and superstructure compression. It is shown that the packing density and phase formation enthalpy in the Ni-Ti system increase concurrently. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 7–17, March, 2008.     

Mean-field cage theory for the random close packed state of a metastable hard-sphere glass

In 2005, we developed a mean-field cage theory for the freezing of a stable hard-sphere fluid using the character of a stable hard-sphere fluid, some observations and the mean-configuration approximation [X.Z. Wang, J. Chem. Phys. 122 (2005) 044515]. It was found that near the freezing point, a thermal fluctuation of a cage causes the hard sphere in this cage to exchange positions with one of its nearest neighbors. In this paper, we extend the theory to the random close packed state of a metastable hard-sphere glass. It is found that near the random close packing point, a thermal fluctuation of a cage sets three of the hard spheres in this cage and its nearest cages into the local circulatory motion, resulting in indirect position exchanges among these three hard spheres. We obtain an analytical formula for the random close packing density. The predicted values are in good agreement with the experimental and simulation results for spatial dimensions d=2–7$d=2\text{–}7$.     

光谱开关与多色光场的奇点光学效应

推导出多色高斯光束和高斯-谢尔模型光束通过杨氏实验双缝传输的谱强度公式.对完全空间相干光和部分空间相干光照明杨氏实验装置出现的光谱开关作了详细研究,并判断其是否属于奇点光学效应. 结果表明：多色场奇点光学效应的判据应当是光谱开关出现时的谱强度极小值S_min=0,而不是总光强极小值I_min=0. 当用多色高斯-谢尔模型光束照明杨氏实验装置时,在近场和远场产生的光谱开关都不属于奇点光学效应. 当用多色高斯光束照明杨氏实验装置时,只有远场产 关键词： 光谱开关 奇点光学效应 完全相干和部分相干 多色光场     

Excitation energy dependence of Raman bands in multiwalled carbon nanotubes

Vertically aligned multiwalled carbon nanotubes (MWCNTs) were grown on 1‐ and 3‐nm cobalt (Co) films, at various growth times by microwave plasma enhanced chemical vapor deposition technique and their microstructural properties were analyzed with the help of Raman spectra that were obtained from different sources of laser excitation energies (E_L: 2.41, 1.96 and 1.58 eV). The variation of D and G band positions in MWCNTs grown on 1‐ and 3‐nm Co films follows a similar behavior, and an anomalous behavior was observed in the E_L dependence of the D′‐band wavenumber. In the second‐order spectra, the G′ band varied strongly according to structure with the laser excitation energy (E_L). The I_D/I_G ratio decreased with the increase of E_L for all MWCNTs; however, for a fixed E_L, the I_D/I_G dispersion is higher at lower E_L. The crystallite sizes were estimated using I_DI_G and E_L. We have shown that, for all MWCNTs, I_D/I_G ratio is inversely proportional to . Copyright © 2010 John Wiley & Sons, Ltd.     

Emission and percolation of excitons in dense sensembles of quantum dots on the spherical surface

We study core/shell heterostructures in which a core (SiO₂) is overcoated with a shell of ZnO quantum dots, randomly distributed on the sphere surface with the surface filling factor P∼0.45. Due to the high surface energy of SiO₂ spheres, ZnO quantum dots have the shape of disks in which, in spite of the large radii, quantum size effects of excitons are retained. The height of ZnO disks estimated by the effective mass approximation is comparable with the exciton diameter in bulk ZnO. Analysis of optical spectra has shown that, at the given density of ZnO quantum dots, the exciton system is above the percolation threshold. The quantitative parameters characterizing such phenomenon are obtained using the elements of percolation theory and the topology of the samples.     

Simulation of output power and optical gain characteristics of self-assembled quantum-dot lasers: Effects of homogeneous and inhomogeneous broadening,quantum dot coverage and phonon bottleneck

The effects of temperature (homogeneous broadening (HB)) on output power, gain spectrum, and light–current (L–I) characteristics of self-assembled quantum-dot lasers (SAQDLs) are investigated. We also analyze the effects of inhomogeneous broadening (IHB) and QD coverage on L–I characteristics and the effects of carrier relaxation and recombination lifetimes on L–I and optical gain–current characteristics. We propose the possibility of single mode lasing for every HB that is comparable, near, or equal to IHB and for every lasing injected current. We also show that peak optical gain does not change with variations of temperature (HB) and injected current. Simulation of L–I characteristics shows that L–I curves become nonlinear as HB elevates up to near IHB. Exceeding HB from IHB and elevating IHB result in degradation of L–I characteristics. Threshold current grows as temperature (HB) enhances. It is, therefore, concluded that the SAQDL has the best L–I characteristics when HB is equal to IHB. It is also shown that there is a threshold and an optimum QD coverage. We reveal that the phonon bottleneck degrades L–I characteristics and that the maximum output power decreases significantly with enhancement of IHB. Finally, we show that the phonon bottleneck, low wetting layer and QD crystal quality reduce the differential gain, relaxation oscillation frequency and modulation bandwidth.     

Crystal structure of ethyl (2Z)-2-(3-methoxy-4-acetyloxy benzylidene)-7-methyl-3-oxo-5-phenyl-2,3-dihydro-5H-[1,3]thiazolo[3,2-a]pyrimidine-6-carboxylate

The title compound, C₂₆H₂₄N₂O₆S, (I), crystallizes in the monoclinic space group, P2₁/c, with cell parameters a = 16.248(1), b = 7.927(1), c = 19.371(4) ?, β = 105.295(2)°, Z = 4. The central pyrimidine ring in the compound (I) is significantly puckered, assuming a screw-boat conformation. The C11–C16 benzene ring stands vertical while thiazole and C18–C23 benzene rings are coplanar to the mean plane of pyrimidine ring having dihedral angles of 87.48(12), 3.63(11) and 0.94(12)°, respectively. In the absence of potential hydrogen bonding interaction, the crystal packing is influenced by intramolecular C-H…S interaction and intermolecular C-H…π interactions.     

A characterization of dilatation analytic integral kernels

We characterize integral operators belonging to B(L ² (ℝ³))which are dilatation analytic in the Cartesian product of two sectors S _a ⊂ ℂ as analytic functions from S _a×S_a into B(L ²(Ω)), the space of bounded operators on square integrable functions on the unit sphere Ω, which satisfy certain norm estimates uniformly on every subsector.     

Positron annihilation response and broadband dielectric spectroscopy: Salol

A phenomenological analysis of the ortho-positronium (o-Ps) annihilation from positron annihilation lifetime spectroscopy (PALS) and the dynamics from broadband dielectric spectroscopy (BDS) are reported on a small molecular glass former of intermediate H-bonding and fragility: salol. The dielectric spectra extend over a very broad frequency range of about 2 × 10⁻²−3.5 × 10¹¹ Hz, providing information on the α-relaxation, the secondary relaxation giving rise to the excess wing, and the shallow high-frequency minimum in the micro- to milli-meter wave range. A number of empirical correlations between the o-Ps lifetime, τ ₃(T), and the various spectral and relaxation features have been observed. Thus, the phenomenological evaluation of the τ ₃(T) dependence of the PALS response of the amorphous sample reveals three characteristic PALS temperatures: T _g ^PALS, T _b1 ^L = 1.15T _g ^PALS and T _b2 ^L = 1.25T _g ^PALS, which are discussed in relation to similar findings for some typical small molecular vdW- and H-bonded glass formers. A slighter change of the slope at T _b1 ^L appears to be related to the transition from excess wing to the primary α-process-dominated behavior, with the secondary process dominating in the deeply supercooled liquid state below T _b1 ^L . The high-temperature plateau effect in the τ ₃(T) plot occurs at T _b2 ^L and agrees with the characteristic Stickel temperature, T _B ^ST, marking a qualitative change of the primary α process, but it does not follow the relation T _b2 ^L < T _α [τ ₃(T _b2) < τ _α ]. Both effects at T _b1 ^L and T _b2 ^L correlate with two crossovers in the spectral shape and related non-exponentiality parameter of the structural relaxation, β _KWW. Finally, the application of the two-order parameter (TOP) model to the structural relaxation as represented by the primary α relaxation times from BDS leads to the characteristic TOP temperature, T _m ^c , close to T _b1 from PALS. Within this model the phenomenological interpretation is offered based on changes in the probability of occurrence of solid-like and liquid-like domains to explain the dynamic as well as PALS responses. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in small molecule glass formers.     

Assessing the Exact Muffin-Tin Orbitals method for the Bain path of metals

Abstract

We scrutinise the muffin-tin approximation and the screening within the framework of the Exact Muffin-Tin Orbitals method in the case of cubic and tetragonal crystal symmetries. Systematic total energy calculations are carried out for the Bain path including the body-centred cubic and face-centred cubic structures for a set of simple and transition metals. The present converged results in terms of potential sphere radius (S) and hard sphere radius (b) are in good agreement with previous theoretical calculations. We demonstrate that for all structures considered here, potential sphere radii around and slightly larger than the average Wigner–Seitz radius (w) yield accurate total energy results whereas S values smaller than w give large errors. It is shown that for converged total energies hard spheres with radii b = 0.7–0.8w should be used for an efficient screening within real space clusters consisting typically of 70–90 lattice sites. The less efficient convergence of the total energy in the case of small hard spheres is ascribed to the delocalisation of the screened spherical waves, which leads to inaccurate interstitial overlap matrix. The above conclusions are not significantly affected by the volume of the system.