Magnetic field effect on the superconducting magnetic gap of Nd1.85Ce0.15CuO4

Inelastic neutron-scattering measurements on the archetypical electron-doped material Nd1.85Ce0.15CuO4 up to a high relative magnetic-field strength, H/H(c2) approximately 50%, reveal a simple linear magnetic-field effect on the superconducting magnetic gap and the absence of field-induced in-gap states. The extrapolated gap-closing field value is consistent with the upper critical field H(c2), and the high-field response resembles that of the paramagnetic normal state.     

Dynamo theory,vorticity generation,and exponential stretching

A discussion is given of the analogy between the dynamo equation for the generation of a magnetic field by the motion of an electrically conducting fluid and the equation for the evolution of vorticity of a viscous fluid. In both cases exponential stretching is an important feature of the underlying instability problem. For the "fast" dynamo problem, the existence of exponential stretching (i.e., the positivity of the Lyapunov exponent) somewhere in the flow is a necessary condition when the flow is smooth. An example is presented of a flow with exponential stretching (an Anosov flow) that supports fast dynamo action. A parallel treatment is described for the linearized Navier-Stokes equations for the motion of a viscous fluid. In this problem the analogous necessary condition for "fast vorticity generation" is the existence of some instability in the corresponding Euler (i.e., inviscid) equation. Dynamo theory methods give a second related result, namely a universal geometric estimate from below on the growth rate of a small perturbation in an inviscid fluid. This bound gives an effective sufficient condition for local instability for Eulers equations. In particular, it is proved that a steady flow with a hyperbolic stagnation point is unstable. The growth rate of an infinitesimal perturbation in a metric with derivatives depends on this metric. This dependence is completely described.     

Attractors of Navier-Stokes systems and of parabolic equations,and estimates for their dimensions

One investigates the problem of the existence of an attractor α of the semi-group S_t, generated by the solutions of the nonlinear nonstationary equations $$\frac{{\partial u}}{{\partial t}} = A(u), u|_{t = 0} = u_0 (x); S_t u_0 \equiv u(t)$$ . One proves a very general theorem on the existence of an attractor α of the semigroup S_t for t→∞. One gives examples of differential equations having attractors: a second-order quasilinear parabolic equation, a two-dimensional Navier—Stokes system, a monotone parabolic equation of any order. One proves a theorem on the finiteness of the Hausdorff dimension of the attractor α. One gives an estimate for the Hausdorff dimension of the attractor α for a two-dimensional Navier—Stokes system.     

Incompressible Flows of an Ideal Fluid¶with Unbounded Vorticity

In this paper we study solutions to the Euler equations of an ideal incompressible fluid in R ⁿ singular at the origin with a finite symmetry group. For an “admissible” class of finite groups we prove a local existence and uniqueness theorem. In even dimensions this theorem covers some symmetric flows with essentially unbounded vorticity. In arbitrary dimension (including n=3) we construct local in time solutions with vorticity that behaves, e.g., like a function of homogeneous degree zero near the origin. The symmetry condition provides necessary additional cancellations and is preserved by the evolution due to uniqueness. Received: 31 March 1999 / Accepted: 10 July 2000     

Are Corals Colorful?

Using in situ spectrometry data and visual system modeling, we investigate whether the colors conferred to the reef-building corals by GFP-like proteins would look colorful not only to humans, but also to fish occupying different ecological niches on the reef. Some GFP-like proteins, most notably fluorescent greens and nonfluorescent chromoproteins, indeed generate intense color signals. An unexpected finding was that fluorescent proteins might also make corals appear less colorful to fish, counterbalancing the effect of absorption by the photosynthetic pigments of the endosymbiotic algae, which might be a form of protection against herbivores. We conclude that GFP-determined coloration of corals may be an important factor in visual ecology of the reef fishes.