Search results for "spheres"

Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory …

2015

The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force dis…

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

2018

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersatura…

Electromagnetic energy within dielectric spheres

1987

We present exact and approximate analytic expressions for the time-averaged electromagnetic energy within dielectric spheres on the basis of rigorous Mie theory. Such information is of importance for the study of photochemical reactions within atmospheric water spheres. Numerical results show that on the average the energy inside a cloud droplet is enlarged by a factor exceeding 2 compared with that of a sphere of the same radius of the surrounding medium. In regions of resonance peaks the electromagnetic energy may be increased by more than 2 orders of magnitude.

Exact results for the homogeneous cooling state of an inelastic hard-sphere gas

1998

The infinite set of moments of the two-particle distribution function is found exactly for the uniform cooling state of a hard-sphere gas with inelastic collisions. Their form shows that velocity correlations cannot be neglected, and consequently the 'molecular chaos' hypothesis leading to the inelastic Boltzmann and Enskog kinetic equations must be questioned. © 1998 Cambridge University Press.

Feynman-diagramme als vektorsysteme invariantentheoretisch behandelt (compton-streuung, elektron-positron-vernichtung

1985

Employing a special contact transformation devised by S. Lie, which takes spheres into lines, we interpret the Feynman diagrams of photon electron scattering in terms of vector systems. This gives a nice kinematic model of Compton scattering. We further compute in detail the transition probabilities of the Compton scattering process by making use of the calculus of chains of complexes from classical invariant theory rather than applying the usual Dirac-matrix technique. In the final paragraph of this paper an application of our calculations to the treatment of myon decay is indicated.

Electrokinetic Phenomena Revisited: A Lattice—Boltzmann Approach

2003

The Lattice-Boltzmann method (LBM) is an efficient tool to solve the Navier-Stokes equations. Based on this method we have developed a scheme to investigate electrokinetic phenomena in charged colloidal suspensions. The equations of motion that are solved are the so-called electrokinetic equations, i.e. a set of partial differential equations that couple the gradient of the electrostatic potential to the hydrodynamic flow by means of a mean field theory. These equations have been extensively used to study electroviscous phenomena for the limit of a weakly charged sphere in an unbounded electrolyte. We demonstrate that our method can be applied beyond these limit. As an example we discuss th…

Autoradiographic technique to assess distribution of blood flow within organs

1969

A method is described for assessing the distribution of blood flow within organs. Microspheres, 5–50 μ in diameter, labelled with a beta-emitting isotope were injected into the left ventricle of experimental animals. The distribution of the indicator within the tissues, which is assumed to represent the regional distribution of flow, was visualized and measured quantitatively by autoradiography. Local flow rates in areas of about 1,2 mm in diameter could be determined. Application of the technique for the study of regional myocardial and renal circulation is demonstrated.

1997

We have determined by forced Rayleigh scattering the diffusion coefficients of photo-labeled polystyrene micronetwork spheres (radii ≤ 10 nm) in melts of linear polyvinylmethylether (M W ≤ 40000 g/mol) at temperatures of 20-80°C. An expected slippage of the spheres through the meshes of the entanglement network appears possible but is still within the experimental uncertainty of our results.

Diffusion in concentrated colloidal suspensions and glasses

1998

The well established analogy between colloidal suspensions and atomic fluids has been extended to the glass transition problem in the past few years. Colloids have become the ideal test case for checking glass transition theories; this was due to the possibility of modeling hard spheres with colloidal dispersions. Significant progress has also been made in instrumentation, especially in the development of light-scattering techniques allowing moderately turbid and nonergodic samples to be analyzed. Mode coupling theory has become a paradigm not only for the glass transition, but also for the understanding of dynamics in highly concentrated colloidal dispersions where crystallization is suppr…

Statistical Characterization of Self-Assembled Colloidal Crystals by Single-Step Vertical Deposition

2014

Abstract We have statistically characterized the self-assembly of multi-layer polystyrene colloidal crystals, using the technique of vertical deposition, with parameters chosen to produce thick layers of self-assembled crystals in one deposition step. The size distribution of domains produced with this technique was seen to follow a log-normal distribution, hinting that aggregation or fragmentation phenomena play a role. In addition, using a lithographically directed self-assembly method, we have shown that the size of multi-layer, continuous crack-free domains in lithographically defined areas can be many times larger than in the surrounding areas. In a single deposition step, we have prod…