9,735 research outputs found
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, and on a lattice that
interpolates between the limits of a square-lattice (), a
triangular-lattice (), and decoupled linear chains (). In all
cases, the susceptibility which has a Curie-Weiss behavior at high
temperatures, rolls over and begins to decrease below a peak temperature,
. 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 CsCuCl and CsCuBr and to a
number of organic molecular crystals. We find that the former (CsCuCl
and CsCuBr) 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
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