Topology, vorticity, and limit cycle in a stabilized Kuramoto-Sivashinsky equation.

A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which interconnect them.

2D Colloidal Crystals with Anisotropic Impurities.

We report a study of 2D colloidal crystals with anisotropic ellipsoid impurities using video microscopy. It is found that at low impurity densities, the impurity particles behave like floating disorder with which the quasi-long-range orientational order survives and the elasticity of the system is actually enhanced. There is a critical impurity density above which the 2D crystal loses the quasi-long-range orientational order.

Dynamics of noise-induced wave-number selection in the stabilized Kuramoto-Sivashinsky equation.

We revisit the question of wave-number selection in pattern-forming systems by studying the one-dimensional stabilized Kuramoto-Sivashinsky equation with additive noise. In earlier work, we found that a particular periodic state is more probable than all others at very long times, establishing the critical role of noise in the selection process. However, the detailed mechanism by which the noise picked out the selected wave number was not understood.

Global potential, topology, and pattern selection in a noisy stabilized Kuramoto-Sivashinsky equation.

We formulate a general method to extend the decomposition of stochastic dynamics developed by Ao et al. [ 37, L25-L30 (2004)] to nonlinear partial differential equations which are nonvariational in nature and construct the global potential or Lyapunov functional for a noisy stabilized Kuramoto-Sivashinsky equation. For values of the control parameter where singly periodic stationary solutions exist, we find a topological network of a web of saddle points of stationary states interconnected by unstable eigenmodes flowing between them.

Wave-number selection in pattern-forming systems.

Wave-number selection in pattern-forming systems remains a long-standing puzzle in physics. Previous studies have shown that external noise is a possible mechanism for wave-number selection. We conduct an extensive numerical study of the noisy stabilized Kuramoto-Sivashinsky equation.

Consistent Hydrodynamics for Phase Field Crystals.

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.

Kosterlitz-Thouless physics: a review of key issues.

This article reviews, from a very personal point of view, the origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the experimental verifications of the theory and some numerical simulations.

State selection in the noisy stabilized Kuramoto-Sivashinsky equation.

In this work, we study the one-dimensional stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states.

2-(3-Methyl-3H-diaziren-3-yl)ethyl 1-(1-phenylethyl)-1H-imidazole-5-carboxylate: a derivative of the stereoselective general anesthetic etomidate for photolabeling ligand-gated ion channels.

To locate general anesthetic binding sites on ligand-gated ion channels, a diazirine derivative of the potent intravenous anesthetic, R-(+)-etomidate (2-ethyl 1-(1-phenylethyl)-1H-imidazole-5-carboxylate), has been synthesized and characterized. R-(+)-Azietomidate [2-(3-methyl-3H-diaziren-3-yl)ethyl 1-(1-phenylethyl)-1H-imidazole-5-carboxylate] anesthetizes tadpoles with an EC(50) of 2.2 microM, identical to that of R-(+)-etomidate.

Sharp interface limits of phase-field models.

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena that includes order-disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the "sharp-interface limit" from phase-field models which have interfaces that are diffuse on a length scale xi. In particular, phase-field equations are mapped onto sharp-interface equations in the limits xi(kappa)<<1 and xi(v)/D<<1, where kappa and v are, respectively, the interface curvature and velocity and D is the diffusion constant in the bulk.

Phase-field modeling of eutectic growth.

A phase-field model of eutectic growth is proposed in terms of a free energy F, which is a functional of a liquid-solid order parameter psi, and a conserved concentration field c. The model is shown to recover the important features of a eutectic phase diagram and to reduce to the standard sharp-interface formulation of nonequilibrium growth. It is successfully applied to the study of directional solidification when the solid phase is a single or two phase state.

Income security. Do it yourself.

Washington--and Americans--are at a crossroads between the collective approach to social security and medicare and the corporate trend toward self-reliance. Workers may become more prudent consumers as they assume responsibility for retirement and health care costs, but the disadvantaged may find it difficult to provide for their own needs.

Stern measures.

Andy Stern, new head of the Service Employees International Union, has set his sights on the nation's health care industry, linking workers' rights with consumer protection. The union's strategy is on display in California, where managed care has made dramatic inroads and financially pinched hospitals are shedding workers.

Unmanaged care?

Changes in the health care marketplace have outpaced many of the laws and regulations that were intended to protect patients. Consumer advocates want new safeguards, but employers and the managed care industry warn that could raise the cost of coverage.

The second wave.

The interest groups that helped defeat health care reform aren't uncorking the champagne yet. Some fear a new push for regulation and cost cutting in Washington and in state capitals. And some want to salvage pieces of the President's reform plan that would have benefited them.

The spoils of reform.

The nation's most prestigious medical schools and teaching hospitals like the idea of comprehensive health care reform. And little wonder: Thanks to aggressive lobbying and some powerful friends, they seem to have gotten just about everything on their wish list--and then some--in the leading reform plans now under consideration on Capitol Hill.