Instabilities in decelerating supersonic flows with applications to cosmic ray shocks

The nature of instabilities in cosmic ray shocks is investigated by using two distinct models for the shock wave. For wavelengths which are short relative to the thickness of the shock wave, the shock is treated as a smoothly decelerating low, and an appropriate JWKB type expansion is used to describe the perturbations to the flow. In this, the short wavelength regime, the presence of squeezing and an effective g renders strong cosmic ray shocks unstable in a way which is similar to instabilities in other supersonic flows, such as in de Laval nozzle flow or a heat conduction dominated shock wave. In the long wavelength limit, where the shock is treated as a discontinuous transition, a stability function is derived which, if negative, corresponds to unstable disturbances growing exponentially in time. In this case, it was found that if the cosmic ray fluid is relativistic (gamma sub c = 4/3) and the background plasma ideal (gamma = 5/3), then strong shocks are unstable

Quantum entanglement and fixed-point bifurcations

How does the classical phase space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.Comment: v2: Structure of the paper changed for clarity, reduced length, now 9 pages with 6 figure

The variety generated by order algebras

Every ordered set can be considered as an algebra in a natural way. We investigate the variety generated by order algebras. We prove, among other things, that this variety is not finitely based and, although locally finite, it is not contained in any finitely generated variety; we describe the bottom of the lattice of its subvarieties

Comparison of the phase diagram of the half-filled layered organic superconductors with the phase diagram of the RVB theory of the Hubbard-Heisenberg model

We present an resonating valence bond (RVB) theory of superconductivity for the Hubbard--Heisenberg model on an anisotropic triangular lattice. We show that these calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta', kappa and lambda phases of (BEDT-TTF)_2X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)_2X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d_{x^2-y^2} superconductor with a small superfluid stiffness and a pseudogap with d_{x^2-y^2} symmetry. The Mott--Hubbard transition can be driven either by increasing the on-site Coulomb repulsion, U, or by changing the anisotropy of the two hopping integrals, t'/t. Our results suggest that the ratio t'/t plays an important role in determining the phase diagram of the organic superconductors.Comment: 4 pages, 3 figur

Studies of auroral X-ray imaging from high altitude spacecraft

Results of a study of techniques for imaging the aurora from a high altitude satellite at X-ray wavelengths are summarized. The X-ray observations allow the straightforward derivation of the primary auroral X-ray spectrum and can be made at all local times, day and night. Five candidate imaging systems are identified: X-ray telescope, multiple pinhole camera, coded aperture, rastered collimator, and imaging collimator. Examples of each are specified, subject to common weight and size limits which allow them to be intercompared. The imaging ability of each system is tested using a wide variety of sample spectra which are based on previous satellite observations. The study shows that the pinhole camera and coded aperture are both good auroral imaging systems. The two collimated detectors are significantly less sensitive. The X-ray telescope provides better image quality than the other systems in almost all cases, but a limitation to energies below about 4 keV prevents this system from providing the spectra data essential to deriving electron spectra, energy input to the atmosphere, and atmospheric densities and conductivities. The orbit selection requires a tradeoff between spatial resolution and duty cycle

Temperature Dependence of the Magnetic Susceptibility for Triangular-Lattice Antiferromagnets with spatially anisotropic exchange constants

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular-lattices, using high temperature series expansions. We consider a model with two exchange constants, $J_1$ and $J_2$ on a lattice that interpolates between the limits of a square-lattice ($J_1=0$), a triangular-lattice ($J_2=J_1$), and decoupled linear chains ($J_2=0$). In all cases, the susceptibility which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature, $T_p$. Scaling the exchange constants to get the same peak temperature, shows that the susceptibilities for the square-lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$ and to a number of organic molecular crystals. We find that the former (Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.Comment: 10 pages, 9 figures and 1 table, revised versio