Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as ∼D ^-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk. Received 26 October 2001 and Received in final form 14 December 2001     

Stability of self-gravitating astrophysical disks

Criteria which guarantee the stability of self-gravitating gaseous and stellar disks toward any localized small perturbations are obtained. These criteria are formulated as inequalities of the form Q>Q _c (separately for gas and stars). The latter should be satisfied by the “stability parameter” Q, which is equal, by definition, to unity on the stability boundary of radial perturbations. The critical value of the stability parameter Q _c is appreciably greater than (although of the order of) unity, attesting to the great instability of nonaxially symmetric perturbations. It is shown that the stability criterion derived for gaseous disks is valid for disks rotating within a spheroidal component (as in spiral galaxies) or in the field of a central mass (planetary rings and accretion disks). Stellar disks are stabilized with significantly greater difficulty. This is attributable mainly to the anisotropy of the velocity distribution inherent to them, which is favorable for instability. Zh. éksp. Teor. Fiz. 112, 771–795 (September 1997)     

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.     

Growth, percolation, and correlations in disordered fiber networks

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameterp which controls the degree of clustering. Forp=1 the deposited network is uniformly random, while forp=0 only a single connected cluster can grow. Forp=0 we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. Forp>0 we carry out extensive simulations on fibers, and also needles and disks, to study the dependence of the percolation threshold onp. We also derive a mean-field theory for the threshold nearp=0 andp=1 and find good qualitative agreement with the simulations. The fiber networks produced by the model display nontrivial density correlations forp<1. We study these by deriving an approximate expression for the pair distribution function of the model that reduces to the exactly known case of a uniformly random network. We also show that the two-point mass density correlation function of the model has a nontrivial form, and discuss our results in view of recent experimental data on mss density correlations in paper sheets.     

Percolation of randomly distributed growing clusters: the low initial density regime

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, p. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low values of p we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a spanning cluster to occur, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.     

Jamming patterns in a two-dimensional hopper

We report experimental studies of jamming phenomenon of monodisperse metal disks falling through a two-dimensional hopper when the hopper opening is larger than three times the size of the disks. For each jamming event, the configuration of the arch formed at the hopper opening is studied. The cumulative distribution functionsf _d (X) for hoppers of opening sized are measured. (HereX is the horizontal component of the arch vector, which is defined as the displacement vector from the center of the first disk to the center of the last disk in the arch.) We found that the distribution off _d (X) can be collasped into a master curveG(X) = f _d (X)μ(d) that decays exponentially forX > 4. The scaling factorμ(d) is a decreasing function ofd and is approximately proportional to the jamming probability.     

Photo-elastic properties of the wing imaginal disc of Drosophila

In the study of developmental biology, the physical properties and constraints of the developing tissues are of great importance. In spite of this, not much is known about the elastic properties of biologically relevant tissues that are studied in biology labs. Here, we characterize properties of the wing imaginal disc of Drosophila, which is a precursor organ intensely studied in the framework of growth control and cell polarity. In order to determine the possibility of measuring mechanical stresses inside the tissue during development, we quantify the photo-elastic properties of the tissue by direct mechanical manipulation. We obtain a photo-elastic constant of 2×10^-10 Pa^-1\ensuremath 2\times10^{-10}{\,\mbox{Pa}}^{-1} .     

Mesoscopic superconducting disks

Using the nonlinear Ginzburg–Landau (GL) equations, type I superconducting disks of finite radius (R) and thickness (d) are studied in a perpendicular magnetic field. Depending on R and d, first- or second-order phase transitions are found for the normal to superconducting state. For sufficiently large R, several transitions in the superconducting phase are found corresponding to different angular momentum giant vortex states. In an increasing magnetic field the superconductor is in its ground state, while in a field down sweep it is possible to drive the system into metastable states. We also present a quantitative analysis of the relation between the detector output and the sample magnetization. The latter, and the incorporation of the finite thicknesses of the disks, are essential in order to obtain quantitative agreement with experiment.     

Dynamics of wing cracks and nanoscale damage in glass

We investigate initiation, growth, and healing of wing cracks in confined silica glass by molecular dynamics simulations. Under dynamic compression, frictional sliding of precrack surfaces nucleates nanovoids which evolve into nanocrack columns at the precrack tip. Nanocrack columns merge to form a wing crack, which grows via coalescence with nanovoids in the direction of maximum compression. Lateral confinement arrests the growth and partially heals the wing crack. Growth and arrest of the wing crack occur repeatedly, as observed in dynamic compression experiments on brittle solids under lateral confinement.     

硅油基底表面铁薄膜的生长机理及表面有序结构

利用直流溅射方法在液体基底(硅油)表面成功制备出金属铁薄膜系统，研究了其生长机理及特征的表面有序结构.实验发现铁薄膜的生长过程与液相基底表面非磁性金属薄膜的情况类似，基本服从二阶段生长模型.连续铁薄膜中可观测到尺寸巨大的圆盘形有序结构，其生长演化与溅射功率、沉积时间和真空环境中的生长时间等实验条件密切相关.实验证明，此类有序结构是在薄膜内应力作用下，铁原子及原子团簇在液体表面自由扩散迁移，并最终在硅油基底表面某些区域成核凝聚所致.在较大溅射功率和沉积时间条件下，圆盘外部区域的铁薄膜中形成周期分布的波纹褶皱，其波长约为10 μm，波峰基本与圆盘的边界平行.进一步研究表明：在沉积过程中，由于沉积铁原子的局域能量作用，导致硅油的表面层结构发生改变而形成一聚合物层；在随后的冷却过程中，聚合物层的强烈收缩使铁薄膜处于很大的压应力场中，促使薄膜起皱形成波纹结构. 关键词： 液体基底 铁薄膜 生长机理 有序结构     

A solution for galactic disks with Yukawian gravitational potential

We present a new solution for the rotation curves of galactic disks with gravitational potential of the Yukawa type. We follow the technique employed by Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new solution allows an easy comparison between the Newtonian solution and the Yukawian one. Therefore, constraints on the parameters of theories of gravitation can be imposed, which in the weak field limit reduce to Yukawian potentials. We then apply our formulae to the study of rotation curves for a zero-thickness exponential disk and compare it with the Newtonian case studied by Freeman in 1970. As an application of the mathematical tool developed here, we show that in any theory of gravity with a massive graviton (this means a gravitational potential of the Yukawa type), a strong limit can be imposed on the mass (m _g) of this particle. For example, in order to obtain a galactic disk with a scale length of b∼ 10 kpc, we should have a massive graviton of m _g ≪ 10⁻⁵⁹g. This result is much more restrictive than those inferred from solar system observations.     

Multiple scaled disorder in the photonic structure of Morpho rhetenor butterfly

The iridescence of Morpho rhetenor butterfly is known to result from a photonic structure on wing scales, where multilayer interference and grating diffraction occur simultaneously. We characterize the disorder at the photonic structure length scale and at the butterfly scale. We measure the scattering pattern of the wing. Through RCWA and 1st Born approximation models, we link the different disorders to different features in the scattering patterns.     

Patterns of broken symmetry in the impurity-perturbed rigid-disk crystal

As a new example of spontaneous pattern formation in many-body systems, we examine the collective means by which a close-packed disk crystal reacts to the presence of a single oversized impurity disk. Computer simulation has been used for this purpose; it creates the jammed impurity-containing packings by a kinetic particle-growth algorithm. Hexagonal primitive cells with periodic boundary conditions were employed, and the natural number 3n ² of disks (including the impurity) ranged upt to 10,800. For impurity diameter 1.2 times that of the other disks, the patterns of observed crystal perturbation displayed several remarkable features. Particle displacements relative to the unperturbed triangular crystal possess local irregularity but long-range coherence. The symmetry of the coherent patterns preserved that of the hexagonal cell for rapid growth, but was lower for slower growth. The final jammed packings contain rattler disks of the sort known to apper in random disk packings. Finally, the area increase induced by the presence of a fixed-size impurity appears to grow without bound as the system size (i.e., 3n ²) itself increases.     

Disks around young stellar objects

By 1939, when Chandrasekhar’s classic monograph on the theory of Stellar Structure was published, although the need for recent star formation was fully acknowledged, no one had yet recognized an object that could be called a star in the process of being born. Young stellar objects (YSOs), as pre-main-sequence stars, were discovered in the 1940s and 1950s. Infrared excess emission and intrinsic polarization observed in these objects in the 1960s and 1970s indicated that they are surrounded by flattened disks. The YSO disks were seen in direct imaging only in the 1980s. Since then, high-resolution optical imaging with HST, near-infrared adaptive optics on large ground-based telescopes, mm and radiowave interferometry have been used to image disks around a large number of YSOs revealing disk structure with ever-increasing detail and variety. The disks around YSOs are believed to be the sites of planet formation and a few such associations have now been confirmed. The observed properties of the disk structure and their evolution, that have very important consequences for the theory of star and planet formation, are discussed.     

Transport coefficients and mechanical response in hard-disk colloidal suspensions

We investigate the transport properties and mechanical response of glassy hard disks using nonlinear Langevin equation theory.We derive expressions for the elastic shear modulus and viscosity in two dimensions on the basis of thermalactivated barrier-hopping dynamics and mechanically accelerated motion.Dense hard disks exhibit phenomena such as softening elasticity,shear-thinning of viscosity,and yielding upon deformation,which are qualitatively similar to dense hard-sphere colloidal suspensions in three dimensions.These phenomena can be ascribed to stress-induced "landscape tilting".Quantitative comparisons of these phenomena between hard disks and hard spheres are presented.Interestingly,we find that the density dependence of yield stress in hard disks is much more significant than in hard spheres.Our work provides a foundation for further generalizing the nonlinear Langevin equation theory to address slow dynamics and rheological behavior in binary or polydisperse mixtures of hard or soft disks.     

Geometric properties of random disk packings

Random packings ofN2000 rigid disks in the plane, subject to periodic boundary conditions on a square primitive cell, have been generated by a concurrent construction which treats all disks on an equal footing, as opposed to previously investigated sequential constructions. The particles start with random positions and velocities, and as they move about they grow uniformly in size, from points to jammed disks. The collection of packings displays several striking geometric features. These include (for largeN) typically polycrystalline textures with irregular grain boundaries and linear shear fractures. The packings occasionally contain monovacancies and trapped but unjammed rattler disks. The latter appear to be confined to the grain boundaries. The linear shear fractures preserve bond orientational order, but disrupt translational order, within the crystalline grains. A new efficient event-driven simulation algorithm is employed to generate the histories of colliding and jamming disks. On a computer which can process one million floating-point instructions per second the algorithm processes more than one million pairwise collisions per hour.     

Front Propagation Techniques to Calculate the Largest Lyapunov Exponent of Dilute Hard Disk Gases

A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear flow. We derive a generalized Boltzmann equation for an extended one-particle distribution that includes deviations from the reference phase space point. The equation is valid for very low densities n, and requires an unusual expansion in powers of 1/|ln n|. It reproduces and extends results from the earlier, more heuristic clock model and may be interpreted as describing a front propagating into an unstable state. The asymptotic speed of propagation of the front is proportional to the largest Lyapunov exponent of the system. Its value may be found by applying the standard front speed selection mechanism for pulled fronts to the case at hand. For the equilibrium case, an explicit expression for the largest Lyapunov exponent is given and for sheared systems we give explicit expressions that may be evaluated numerically to obtain the shear rate dependence of the largest Lyapunov exponent.     

Entropy and irreversibility in a dilute gas of hard disks

The partition of the canonical entropy (invariant of motion) into a thermodynamic part 5th and a nonthermodynamic oneS _nonth, respectively increasing and decreasing functions of time for a system approaching equilibrium, was proposed by Prigogine and co-workers. This viewpoint is critically examined in the special case of an initially uncorrelated gas of hard disks. BothSth and the leading term ofS _nonth are evaluated for finite assemblies of 400,1600, and 6400 disks, by the method of molecular dynamics. There is good evidence that, in the limit of an infinite system, the Prigogine scheme is verified.On leave of absence from the University of Brussels, Belgium.     

Micro-disks embedded microring for optical filter

We propose a novel ultra compact structure of micro-disks embedded microring filter (MDEMR) and several parameters which impact the performance of MDEMR are analyzed. The filter is shown to exhibit much smaller size and better spectrum than traditional microring one. The number and radius of the inner disks are found to mainly influence the resonance frequency of the micro-disks, and the valley of transmittivity. The resonance between microring and micro-disks is decrease with increasing the gap between microring and micro-disks, which also leads to the extinction ratio improved significantly. The Q factor is found to be improved from 300 to 3000 with the gap increased from 0.2 μm to 0.4 μm, while the transmission peak affected slightly.     

Population inversion on vibrational transitions of molecules under nonresonant optical excitation

The possibility of obtaining a population inversion on vibrational transitions of molecules through nonlinear effects when the pump radiation is absorbed in the wings of spectral lines is investigated theoretically. We show that a population inversion can be produced in molecules on vibrational transitions when intense pump radiation is absorbed in the blue wing of the R branch of the vibrational-rotational molecular spectrum. This effect is related to inequality of the probabilities of the absorption and stimulated emission of radiation and is attributable to collisional transitions between rotational levels. We have ascertained that the larger the rotational constant of the molecule and the higher the pump radiation intensity, the higher the effective frequency of the collisions that give rise to a population inversion. Using the carbon monoxide (CO) molecule as an example, we show that when intense (∼1010 W cm⁻²) pump radiation is absorbed in the blue wing of the R branch, a noticeable population inversion can be produced and the gain at the center of the R and P branches of the molecular spectrum can reach 0.011 and 0.250 cm⁻¹ at temperatures T = 300 and 100 K, respectively.