14 research outputs found
Strong Phase Separation in a Model of Sedimenting Lattices
We study the steady state resulting from instabilities in crystals driven
through a dissipative medium, for instance, a colloidal crystal which is
steadily sedimenting through a viscous fluid. The problem involves two coupled
fields, the density and the tilt; the latter describes the orientation of the
mass tensor with respect to the driving field. We map the problem to a 1-d
lattice model with two coupled species of spins evolving through conserved
dynamics. In the steady state of this model each of the two species shows
macroscopic phase separation. This phase separation is robust and survives at
all temperatures or noise levels--- hence the term Strong Phase Separation.
This sort of phase separation can be understood in terms of barriers to
remixing which grow with system size and result in a logarithmically slow
approach to the steady state. In a particular symmetric limit, it is shown that
the condition of detailed balance holds with a Hamiltonian which has
infinite-ranged interactions, even though the initial model has only local
dynamics. The long-ranged character of the interactions is responsible for
phase separation, and for the fact that it persists at all temperatures.
Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses
epsf, three ps figure
Are Steadily Moving Crystals Unstable?
We study the dynamics of small fluctuations about the uniform state of a
crystal moving through a dissipative medium, e.g. a sedimenting colloidal
crystal or a moving flux lattice, using a set of continuum equations for the
displacement fields, and a one-dimensional driven lattice-gas model for the
coupled concentration and tilt fields. For the colloidal crystal we predict a
continuous nonequilibrium phase transition to a clumped state above a critical
Peclet number.Comment: 4 pages, revtex, 2 .eps figures, uses epsf.sty; To be published in
Phys. Rev. Lett. This version is substantially rewritten but the essential
content is the same as befor
Nonequilibrium phase transitions in sheared colloids
Colloidal crystals under steady shear flow are known to melt by a first order transition. At high shear rates, molecular dynamics simulations show a reentrant transition by which the system orders back into a flowing crystalline phase. We describe here a simple two variable model which captures both these phase transitions. In doing so we propose a prescription for identifying the stable phase in nonequilibrium steady states which should apply to a variety of other problems
Brownian motion in a classical ideal gas:A microscopic approach to Langevin's equation
We present an insightful `derivation' of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton's law of motion (mxx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force (F) oc -x x and (2) the correlation function of the fluctuating force rl = F - (F) is related to the strength of the average force