Chord length distributions in binary stochastic media in two and three dimensions

Simple models for transport through stochastic media usually assume that the chord lengths of materials are distributed exponentially. Theory predicts that, in a medium consisting of disks/spheres that can interpenetrate, chord lengths in the background material (between the disks/spheres) should exactly follow an exponential. In a medium with impenetrable (non-overlapping) disks/spheres, the distribution is only approximately exponential. This paper demonstrates, through direct numerical simulations, that for randomly distributed disks in 2D and spheres in 3D, with distributions of radii, chord lengths in the background material (between the disks/spheres) are accurately described by exponentials over five orders of magnitude when the material is dilute. The chord lengths inside the disks and spheres are not exponentially distributed, but those distributions can be calculated. A scaling relationship between the mean chord lengths in the two materials is presented for an infinite medium. By knowing the mean properties of the disks/spheres in a medium, this relationship allows one to accurately describe the statistical properties of the background material. The stochastic simulations are validated by this infinite medium relationship. When the fraction of space occupied by the disks or spheres becomes large, the distributions are no longer accurately described by an exponential.     

Photorefractive BaTiO(3) spheres and spherical disks

We have produced single-crystal spheres and spherical disks of photorefractive barium titanate (BaTiO(3)) . The spheres and disks allow direct fiber-to-fiber two-beam coupling without additional optical elements. We also investigate the spontaneous oscillation of triangles and other whispering-gallery modes in these spherical structures.     

球型和棒状金纳米粒子的光谱性质比较

柠檬酸钠还原和诱导晶种生长法合成了球型和棒状金纳米粒子。金纳米粒子的吸收光谱表明,表面等离子体共振(SPR)强烈依赖于金属粒子的形状,球型粒子表现为单-SPR谱峰,而棒状粒子则具有横向和纵向SPR谱峰,且纵向SPR峰位和强度取决于棒状粒子的径横比。棒状金纳米粒子对吸附的对巯基苯甲酸分子的拉曼散射比球型金纳米粒子具有更强的表面增强性能,归因于棒状粒子高能晶面上的吸附可能导致的更强的化学增强效应。     

Intersecting disks (and spheres) and statistical mechanics. I. Mathematical basis

The calculations of a previous paper on intersecting disks are completed. Further quantities of interest in connection with intersecting disks and spheres are defined. The above considerations are extended to spherical boundary conditions. Then two applications are stated: The penetrable-sphere model of Widom and Rowlinson, and the hard-sphere system. Finally, the generalization toD-dimensional spheres is outlined.     

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.     

The statistical mechanics of granular systems composed of spheres and elongated grains

In this paper we will apply a statistical mechanical theory of granular materials to a system composed of a mixture of elongated rods and spheres (both mono- and polydisperse). We will show for a system of rods and spheres that the system's constituents do not completely phase segregate even at minimum close packing. The generalisation of this to packings of rods and bi-disperse spheres produces a similar result except that the two species of sphere do phase segregate at some particular packing.     

A simple GUI for modeling the optical properties of single metal nanoparticles

We present a graphical user interface, based on the modified long-wavelength approximation, to compute the optical properties of single metal nanoparticles of ellipsoidal geometry (spheres, rods, and disks). The user-friendly interface allows one to readily gauge the accuracy of results obtained using the modified long-wavelength approximation. For spherical particles, up to 10-nm diameter, we confirm that our approach yields an exact correspondence with Mie theory, and gives an approximation error of less than 15% for gold (silver) particles with diameters approaching 40 nm (26 nm). Results are shown to be sensitive to the source data for the optical constants for a given material. The modular nature of the simulation platform provides a quick and intuitive guide for optical characterization experiments.     

Self-diffusion and sedimentation of tracer spheres in (semi)dilute dispersions of rigid colloidal rods

Long-time self-diffusion and sedimentation of fluorescent tracer spheres in electrostatically stabilized dispersions of rigid colloidal host rods have been measured in situ with fluorescence recovery after photobleaching, and gravitational and ultracentrifugal sedimentation. The dynamics of silica tracer spheres of 39 and 370 nm radius was monitored in dispersions of host rods with aspect ratios 9.6 and 25.7 at various rod volume fractions. The translational and rotational diffusion coefficient of the host rods was obtained independently with dynamic light scattering and birefringence decay measurements. Our results indicate that sedimentation and long-time self-diffusion are determined by the same friction factor. Furthermore we find that, as long as the host rods are relatively mobile, tracer sphere sedimentation and long-time self-diffusion are governed by the macroscopic solution viscosity, regardless of the tracer and host rod size. However, when the host rods are immobilized, due to rod entanglements at higher volume fractions, tracer sphere dynamics depends strongly on the tracer size relative to the pore size of the host rod network. The large tracers are completely trapped in the network whereas the small tracer spheres remain mobile. Current models for tracer sphere motion in rod assemblies do not satisfactorily explain the complete dynamic regime covered by our experimental model system because the effect of host rod mobility is not properly taken into account.     

Variational approach to hard sphere segregation under gravity

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known "Brazil nut" fashion, i.e., with the larger particles rising to the top, but also in reverse "Brazil nut" fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.     

Molecular Fluids at High Dimensionality

We extend the analysis of orientational first-order phase transitions in anisotropic molecular fluids at high spatial dimensionality to hard-disk fluids, and then to mixture of hard disks and hard spheres. The effect of hard-sphere admixture depends sensitively on the relative sizes of the two geometrical objects, and large spheres completely quench the disk transition. An introductory study is made of spatially ordered states.     

Some comments on the electrostatic forces between circular electrodes

We study the force between two circular electrodes in different configurations. A formula analogous to Kelvin's formula for the spheres is given in the case of equal disks held at the same potential and when one plate is earthed. An expression for the force at short distance between two arbitrarily charged disks is found: the generic case shows a logarithmic repulsive force, also for disks carrying charges of opposite sign. Some numerical computations support the results. A classification for the possible behaviors of the force is proposed on the basis of a decomposition of the capacitance matrix. It is shown that the forces depend strongly on the dimensionality of the contact zone between the conductors. The analysis is supported by a numerical computation carried for the case of two disks of different radii.     

The acoustic basis for target discrimination by FM echolocating bats

Past experiments show that echolocating bats of the species Myotis lucifugus and Eptesicus fuscus can discriminate among airborne sonar targets presented in the context of pursuit maneuvers for the interception of prey. These bats distinguish between edible mealworms and inedible spheres of various sizes. Myotis can distinguish between disks and mealworms similar enough in size that the bat's performance requires the ability to perceive the acoustic equivalent of target shape. Previously observed small differences in the spectrum of echoes from mealworms and disks appear insufficient to distinguish these targets at the performance levels achieved by bats. We measured the acoustic properties of the targets by broadcasting ultrasonic impulses at mealworms, spheres, and disks and recording their echoes, displaying the results in terms of impulse echo waveforms and the frequency response of targets derived from the target transfer function. The echoes from disks and mealworms at various orientations convey the range-axis profile of the target (number and spacing of reflecting points or glints distributed at different ranges) in terms of the impulse structure of their waveforms and in terms of the locations and spacing of notches or nulls in their spectra. For targets that bats can discriminate and that reflect echoes which do not clearly differ in overall amplitude, the targets appear distinguishable from the acoustic representation of their range profile, which is a feature of targets that bats can perceive with great acuity.     

Colloidal Silica Rods: Material Properties and Fluorescent Labeling

In this paper, the characterization and fluorescent labeling of silica rods are reported. These rods are synthesized following a recently reported method. Material properties of the silica rods measured with NMR, elemental analysis, TGA, and porosimetry are compared with those of well‐established Stöber silica spheres. Additionally, silica rods are made suitable for quantitative real‐space studies by confocal microscopy. Several methods of fluorescent labeling to prepare rods with different fluorescent patterning, ranging from uniform fluorescence levels to gradients from one rod‐end to the other, and even patterns of several colors are presented and discussed.     

Segregation in binary mixtures under gravity

We employ kinetic theory for a binary mixture to study segregation by size and/or mass in a gravitational field. Simple segregation criteria are obtained for spheres and disks that are supported by numerical simulations.     

Limiting polytope geometry for rigid rods,disks, and spheres

The available configuration space for finite systems of rigid particles separates into equivalent disconnected regions if those systems are highly compressed. This paper presents a study of the geometric properties of the limiting high-compression regions (polytopes) for rods, disks, and spheres. The molecular distribution functions represent cross sections through the convex polytopes, and for that reason they are obliged to exhibit single-peak behavior by the Brünn-Minkowski inequality. We demonstrate that increasing system dimensionality implies tendency toward nearest-neighbor particle-pair localization away from contact. The relation between the generalized Euler theorem for the limiting polytopes and cooperative jamming of groups of particles is explored. A connection is obtained between the moments of inertia of the polytopes (regarded as solid homogeneous bodies) and crystal elastic properties. Finally, we provide a list of unsolved problems in this geometrical many-body theory.     

A new graph expansion of virial coefficients

It is well known that the virial coefficients of the pressure of thermodynamic systems can be represented in terms of graphs. The existing graph expansions are compared with a new one, the overlap graph expansion. The merits of overlap graphs in general and especially for hard disks and spheres are discussed.     

Visualizations of the transitional flow patterns at the mid-span between shrouded co-rotating disks

Transitional air flow patterns at the mid-plane of gap between co-rotating disks in a stationary cylindrical enclosure are visualized under the acceleration condition of disks. The flow visualization is performed using olive oil particles with a laser sheet and CCD camera. On disk spinning-up, the transition flow patterns are clearly observed. The affect of magnitude of acceleration on the onset of transition and the relations of the number of vortex cells in fully turbulent regime of the flow in an outer region of the flow field to the rotating speed are also investigated. The centrifugal effect of particle is evaluated from the comparison with visualization results using hollow glass spheres.     

A method of solution of the ornstein-zernike equation in one and three dimensions

An elegant analytic method is presented to derive a modified form of the Ornstein-Zernike equation which not only solves the statistical mechanical problem for hard rods and spheres but can be used to find solutions for arbitrary non-vanishing direct correlation functions.     

Vortex patterns in a superconducting-ferromagnetic rod

A superconducting rod with a magnetic moment on top develops vortices obtained here through 3D calculations of the Ginzburg–Landau theory. The inhomogeneity of the applied field brings new properties to the vortex patterns that vary according to the rod thickness. We find that for thin rods (disks) the vortex patterns are similar to those obtained in presence of a homogeneous magnetic field instead because they consist of giant vortex states. For thick rods novel patterns are obtained as vortices are curve lines in space that exit through the lateral surface.     

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the τ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for τ, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the τ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts τ ∼ d ³. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the τ parameter should be of order unity as d tends to infinity.