[show abstract][hide abstract] ABSTRACT: We discuss the reflection of light by a rheoscopic fluid (a suspension of
microscopic rod-like crystals) in a steady two-dimensional flow. This is
determined by an order parameter which is a non-oriented vector, obtained by
averaging solutions of a nonlinear equation containing the strain rate of the
fluid flow. Exact solutions of this equation are obtained from solutions of a
linear equation which are analogous to Bloch bands for a one-dimensional
Schrodinger equation with a periodic potential. On some contours of the stream
function, the order parameter approaches a limit, and on others it depends
increasingly sensitively upon position. However, in the long-time limit a local
average of the order parameter is a smooth function of position in both cases.
We analyse the topology of the order parameter and the structure of the generic
zeros of the order parameter field.
Journal of Fluid Mechanics 10/2009; · 2.18 Impact Factor
[show abstract][hide abstract] ABSTRACT: We consider the patterns formed by small rod-like objects advected by a random flow in two dimensions. An exact solution indicates that their direction field is non-singular. However, we find from simulations that the direction field of the rods does appear to exhibit singularities. First, ` scar lines' emerge where the rods abruptly change direction by $\pi$. Later, these scar lines become so narrow that they ` heal over' and disappear, but their ends remain as point singularities, which are of the same type as those seen in fingerprints. We give a theoretical explanation for these observations.
[show abstract][hide abstract] ABSTRACT: We discuss the difficulties faced by the conventional theory of planet formation, which involves aggregation of microscopic dust particles. We describe an alternative hypothesis, termed 'concurrent collapse', in which planets form by gravitational collapse at the same time as the star about which they orbit. This mechanism avoids theoretical difficulties associated with the conventional model and suggests satisfying explanations for various poorly understood phenomena. We introduce new explanations for FU Orionis outbursts seen in young stars, the discovery of exoplanets with eccentric orbits and the existence of small rocky objects such as chondrules in the solar system.
[show abstract][hide abstract] ABSTRACT: We discuss relative velocities and the collision rate of small particles suspended in a highly turbulent fluid. In the limit where the viscous damping is very weak, we estimate the relative velocities using the Kolmogorov cascade principle. Comment: 5 pages, no figures, v2 contains additional results
[show abstract][hide abstract] ABSTRACT: We determine the probability distribution of the breaking strength for chains of N links, which have been produced by repeatedly breaking a very long chain. Comment: 4 pages, 1 figure
Journal of Statistical Physics 08/2006; · 1.40 Impact Factor
[show abstract][hide abstract] ABSTRACT: We show quantitatively how the collision rate of droplets of visible moisture in turbulent air increases very abruptly as the intensity of the turbulence passes a threshold, due to the formation of fold caustics in their velocity field. The formation of caustics is an activated process, in which a measure of the intensity of the turbulence, termed the Stokes number St, is analogous to temperature in a chemical reaction: the rate of collision contains a factor exp(-C/St). Our results are relevant to the long-standing problem of explaining the rapid onset of rainfall from convecting clouds. Our theory does not involve spatial clustering of particles.
[show abstract][hide abstract] ABSTRACT: We discuss the response of a quantum system to a time-dependent perturbation with spectrum \Phi(\omega). This is characterised by a rate constant D describing the diffusion of occupation probability between levels. We calculate the transition rates by first-order perturbation theory, so that multiplying \Phi(\omega) by a constant \lambda changes the diffusion constant to \lambda D. However, we discuss circumstances where this linearity does notextend to the function space of intensities, so that if intensities \Phi_i(\omega) yield diffusion constants D_i, then the intensity \sum_i \Phi_i(\omega) does not result in a diffusion constant \sum_i D_i. This `semilinear' response can occur in the absorption of radiation by small metal particles.
[show abstract][hide abstract] ABSTRACT: We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Padé-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterize two distinct clustering effects which occur in that limit.
[show abstract][hide abstract] ABSTRACT: We analyze the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and noncoagulating phases. We show that the phase transition is related to a Kramers problem, and we use this to determine the phase diagram in two dimensions, as a function of the dimensionless inertia of the particles, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We find that the phase line is described by a function which is nonanalytic at epsilon=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realizations of this phase transition.
[show abstract][hide abstract] ABSTRACT: . We present a semiclassical analysis for the electric dipole absorption of electromagnetic radiation by small metallic particles, in the case where the electron motion is diffusive. We find that there are two contributions to the one-body effective potential: the `static' potential makes a dominant contribution to the absorption coefficient below the frequency # c = D/a 2 , and the `dynamic' potential is dominant for frequencies # # # c (here D is the diffusion constant, and a the size of the particle). Remarkably, these two contributions sum to give exactly the classical absorption coefficient for all frequencies. 1. Introduction The absorption of electromagnetic radiation by a dilute dispersion of small metallic particles can be analysed using classical electrodynamics by using an effective-medium theory to evaluate the imaginary part of the dielectric constant [1--3]. The corresponding quantum theory, reviewed in [4--6], has attracted considerable interest, largely stimulate...
Journal of Physics Condensed Matter 07/1999; · 2.36 Impact Factor