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Research examines the superfluidity phenomenon in liquid helium near the lambda transition temperature with a flux of heat passing through it. The entire liquid helium sample exhibits a uniform reduced temperature. Data on the heat capacity of the helium and implications of this research in space exploration experiments are discussed.

The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged correlations between the magnetic and velocity fields. This is quite different from the results of previous variational treatments, which relied on a local product ansatz for the thermodynamic Gibbs distribution. The equilibria display the same type of coherent structures, such as compact eddies and zonal jets, previously found in pure fluid equilibria. Possible consequences of this for recent simulations of the solar tachocline are discussed. [ABSTRACT FROM AUTHOR]

We show that rotating shallow water dynamics possesses an approximate (adiabatic-type) positive quadratic invariant, which exists not only at midlatitudes (where its analog in the quasigeostrophic equation has been previously investigated), but near the equator as well (where the quasigeostrophic equation is inapplicable). When deriving the extra invariant we find two kinds of small denominators: (i) those due to the triad resonances (as in the case of the quasigeostrophic equation) and (ii) those due to the equatorial limit, when the Rossby radius of deformation becomes infinite. We show that both kinds of small denominators can be canceled. The presence of the extra invariant can lead to the generation of zonal jets. We find that this tendency should be especially pronounced near the equator. A similar invariant occurs in magnetically confined fusion plasmas and can lead to the emergence of zonal flows. [ABSTRACT FROM AUTHOR]

It is shown that previous arguments, leading to the equality z=d for the dynamical exponent describing the Bose glass to superfluid transition in d dimensions, may break down, as apparently seen in recent simulations. The key observation is that the major contribution to the compressibility, which remains finite through the transition and was predicted to scale as kappa approximately |delta|((d-z)nu) (where delta is the deviation from criticality and nu is the correlation length exponent) comes from the analytic, not the singular part of the free energy, and is not restricted by any conventional scaling hypothesis.

A theory of active sonar (or radar) pulse wave form design, for optimal target detection in cluttered environments, is presented. The received target signal is maximized via a cost function L that incorporates both the signal-to-noise ratio and a generalization of the Heisenberg uncertainty principle, which is used to balance bandwidth (or range resolution) against signal gain. The optimal pulse wave form is the ground state solution to a one-dimensional Schrödinger-type equation in frequency space, with an effective potential energy that tends to concentrate pulse energy in frequency bands where the target reflectivity dominates the clutter reflectivity.

An experiment is proposed to test a previously developed theory of the hydrodynamics of a nonequilibrium heat current-induced superfluid-normal interface. It is shown that the interfacial "trapped" second-sound mode predicted by the theory leads to a sharp resonant dip in the reflected signal from an external second-sound pulse propagated toward the interface when its horizontal phase speed matches that of the interface mode. The influence of the interface on thermal fluctuations in the bulk superfluid is shown to lead to slow power dependence of the order parameter, and other quantities, on distance from it.

The problem of coherent vortex and zonal jet formation in a system of oceanic or planetary nonlinear Rossby waves is considered from the point of view of the late time steady state achieved by free decay of a given initial state. Statistical equilibrium equations respecting all conservation laws are constructed for a broad class of models, generalizing those derived previously for two-dimensional inviscid Euler flow. Jetlike solutions are ubiquitous, with large coherent vortices existing only when there is a background flow whose velocity locally cancels the beta effect.

Doppler shift corrections to ocean acoustic signals are complicated by the multi-spatial-scale structure of the ocean medium, resulting in a multi-time-scale structure of the acoustic Green function. Repeated reflections and refractions lead in general to an infinite number of acoustic paths or modes, with different times of flight, connecting source and receiver. The rate of change of these flight times with source or receiver motion gives rise to Doppler shift corrections, and each acoustic path or mode has a different correction. A clean Doppler correction (in the sense of an observable coherent motion-induced frequency shift for each path or mode) is shown to emerge only when the medium is homogeneous along the direction of source or receiver motion, even when it is highly inhomogeneous in directions orthogonal to the motion. A very general quantitative theory for this correction is developed, encompassing earlier results in the literature, and presented in a form amenable to efficient numerical implementation in data processing.

It was recently demonstrated [Phys. Rev. Lett. 91, 143908 (2003)] that the scattered electric field from highly conducting targets following a rapidly terminated electromagnetic pulse displays a universal t(-1/2) power law divergence at early time. It is now shown that for strongly permeable targets, micro(c)/micro(b)>>1, where micro(b) is the background magnetic permeability, the early-time regime separates into two distinct power law regimes, with the early-early time t(-1/2) behavior crossing over to t(-3/2) at late-early time, reflecting a spectrum of magnetic surface modes. The latter is confirmed by data from ferrous targets where micro(c)/micro(b)=O(10(2)), and for which the early-early-time regime is invisibly narrow.

We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.

The time-domain response of highly conducting targets following a rapidly terminated electromagnetic pulse displays three distinct regimes: early, intermediate, and late time. The intermediate and late times are characterized by a superposition of exponentially decaying eigenmodes. At early time an ever increasing number of rapidly decaying modes contribute, with the result that the scattered electric field displays a universal t(-1/2) power law which emerges from the diffusive decay of a pattern of surface currents induced by the pulse. The power law amplitude reflects the surface geometry of the target, a property that may prove useful in buried target classification in geophysical remote sensing applications.