The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics

The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers

Propeller-activated resonances and the fate of short-period cataclysmic variables

We show that the combination of a weak magnetic propeller and accretion disc resonances can effectively halt accretion in short-period cataclysmic variables (CVs) for large fractions of their lifetimes. This may help to explain the discrepancy between the observed and predicted orbital period distributions of CVs at short periods. Orbital resonances cause the disc to become eccentric, allowing material to fall back on to the donor star or out of the system. A weak magnetic field on a rapidly spinning primary star propels disc material outwards, allowing it to access these resonances. Numerical and analytic calculations show that this state can be long lived (∼1011 yr). This is because the magnetic propeller is required only to maintain access to the resonances, and not to push matter out of the Roche lobe, so that the spin-down time-scale is much longer than that for a classical propeller mode

Thermodynamically consistent equilibrium properties of normal-liquid Helium-3

The high-precision data for the specific heat C_{V}(T,V) of normal-liquid Helium-3 obtained by Greywall, taken together with the molar volume V(T_0,P) at one temperature T_0, are shown to contain the complete thermodynamic information about this phase in zero magnetic field. This enables us to calculate the T and P dependence of all equilibrium properties of normal-liquid Helium-3 in a thermodynamically consistent way for a wide range of parameters. The results for the entropy S(T,P), specific heat at constant pressure C_P(T,P), molar volume V(T,P), compressibility kappa(T,P), and thermal expansion coefficient alpha(T,P) are collected in the form of figures and tables. This provides the first complete set of thermodynamically consistent values of the equilibrium quantities of normal-liquid Helium-3. We find, for example, that alpha(T,P) has a surprisingly intricate pressure dependence at low temperatures, and that the curves alpha(T,P) vs T do not cross at one single temperature for all pressures, in contrast to the curves presented in the comprehensive survey of helium by Wilks. Corrected in cond-mat/9906222v3: The sign of the coefficient d_0 was misprinted in Table I of cond-mat/9906222v1 and v2. It now correctly reads d_0=-7.1613436. All results in the paper were obtained with the correct value of d_0. (We would like to thank for E. Collin, H. Godfrin, and Y. Bunkov for finding this misprint.)Comment: 19 pages, 19 figures, 9 tables; published version; note added in proof; v3: misprint correcte

Upper Critical Field in a Spin-Charge Separated Superconductor

It is demonstrated that the spatial decay of the pair propagator in a Luttinger liquid with spin charge separation contains a logarithmic correction relative to the free fermi gas result in a finite interval between the spin and charge thermal lengths. It is argued that similar effects can be expected in higher dimensional systems with spin charge separation and that the temperature dependence of the upper critical field $H_{c2}$ curve is a probe of this effect.Comment: 3 pages, postscript file (compressed and uuencoded

Umklapp scattering from spin fluctuations in Copper-Oxides

The $\mathbf k$-dependent electronic momentum relaxation rate due to Umklapp scattering from antiferromagnetic spin fluctuations is studied within a renormalized mean-field approach to an extended $t-J$ model appropriate to YBa$_2$Cu$_3$O$_{7-x}$ and other cuprates. Transport coefficients are calculated in a relaxation time approximation. We compare these results with those obtained with the phenomenological assumption that all scattering processes dissipate momentum. We show that the latter, which violates momentum conservation, leads to quite different magnitudes and temperature dependences of resistivities and Hall coefficients.Comment: replaced by LaTeX file (due to problems with PostScript

Extended bound states and resonances of two fermions on a periodic lattice

The high-$T_c$ cuprates are possible candidates for d-wave superconductivity, with the Cooper pair wave function belonging to a non-trivial irreducible representation of the lattice point group. We argue that this d-wave symmetry is related to a special form of the fermionic kinetic energy and does not require any novel pairing mechanism. In this context, we present a detailed study of the bound states and resonances formed by two lattice fermions interacting via a non-retarded potential that is attractive for nearest neighbors but repulsive for other relative positions. In the case of strong binding, a pair formed by fermions on adjacent lattice sites can have a small effective mass, thereby implying a high condensation temperature. For a weakly bound state, a pair with non-trivial symmetry tends to be smaller in size than an s-wave pair. These and other findings are discussed in connection with the properties of high-$T_c$ cuprate superconductors.Comment: 21 pages, RevTeX, 4 Postscript figures, arithmetic errors corrected. An abbreviated version (no appendix) appeared in PRB on March 1, 199