Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and mu is unscaled. We give explicit examples for the complex, real, and imaginary eigenvalue densities including Nf=2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of mu. On the mathematical side our new results include an analytical formula for the spectral density of real Wishart eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.Comment: 45 pages, 31 figures; references added, as published in JHE

Thermal expansion of the spin-1/2 Heisenberg-chain compound Cu(C4_4H4_4N2_2)(NO3_3)2_2

Compounds containing magnetic subsystems representing simple model spin systems with weak magnetic coupling constants are ideal candidates to test theoretical predictions for the generic behavior close to quantum phase transitions. We present measurements of the thermal expansion and magnetostriction of the spin-1/2-chain compound copper pyrazine dinitrate Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$. Of particular interest is the low-temperature thermal expansion close to the saturation field $H_c \simeq 13.9 \mathrm{T}$, which defines a quantum phase transition from the gapless Luttinger liquid state to the fully saturated state with a finite excitation gap. We observe a sign change of the thermal expansion for the different ground states, and at the quantum critical point $H_c$ the low-temperature expansion approaches a $1/\sqrt{T}$ divergence. Thus, our data agree very well with the expected quantum critical behaviour.Comment: 4 pages, 3 figures; to appear in the proceedings of the ICM 09 held in Karlsruhe, German

A finite difference scheme for the equilibrium equations of elastic bodies

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques

A survey of nearby galaxies for CO

We have made a survey of the nuclei of 81 galaxies for the 1-) line of CO. 38 of the galaxies are from a complete sample with recession velocity ≦400 km s-1 and 21-cm line strength ≧10-27 Wm-2, and the remainder represent nearby galaxies with weaker or no HI, early-type galaxies (E/SO/Sa) with detected HI and active/infrared galaxies. Galaxies with strong CO lines like M82, NGC253 and IC342 are exceedingly rare: all the galaxies we observed are weaker than 0/2K except the irregular galaxy DDO133 with T*A=0.22K. We have new, confirmed detections of two other irregular galaxies, IC10 and Pegasus, at a weaker level, and unconfirmed detections of the irregular NGC3109 and the nearest Type I Seyfert galaxy NGC4051. We have confirmed the existence of CO in the nucleus of NGC6946 and obtained spectra of new positions in M82 and NGC253

A compact finite difference scheme for div(Rho grad u) - q2u = 0

A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented

EUVE/XTE orbit decay study

The Explorer Platform (EP) program currently comprises two missions, the Extreme Ultraviolet Explorer (EUVE) and the X-ray Timing Explorer (XTE), each of which consists of a scientific payload mounted to the EP. The EP has no orbit maintenance capability. The EP with the EUVE payload will be launched first. At the end of the EUVE mission, the spacecraft will be serviced by the Space Transportation System (STS), and the EUVE instrument will be exchanged for the XTE. The XTE mission will continue until reentry or reservicing by the STS. Because the missions will be using the EP sequentially, the orbit requirements are unusually constrained by orbit decay rates. The initial altitude must be selected so that, by the end of the EUVE mission (2.5 years), the spacecraft will have decayed to an altitude within the STS capabilities. In addition, the payload exchange must occur at an altitude that ensures meeting the minimum XTE mission lifetime (3 years) because no STS reboost will be available. Studies were performed using the Goddard Mission Analysis System to estimate the effects of mass, cross-sectional area, and solar flux on the fulfillment of mission requirements. In addition to results from these studies, conclusions are presented as to the accuracy of the Marshall Space Flight Center solar flux predictions

System Design for a Nuclear Electric Spacecraft Utilizing Out-of-core Thermionic Conversion

Basic guidelines are presented for a nuclear space power system which utilizes heat pipes to transport thermal power from a fast nuclear reactor to an out of core thermionic converter array. Design parameters are discussed for the nuclear reactor, heat pipes, thermionic converters, shields (neutron and gamma), waste heat rejection systems, and the electrical bus bar-cable system required to transport the high current/low voltage power to the processing equipment. Dimensions are compatible with shuttle payload bay constraints

Low-noise 1 THz niobium superconducting tunnel junction mixer with a normal metal tuning circuit

We describe a 1 THz quasioptical SIS mixer which uses a twin-slot antenna, an antireflection-coated silicon hyperhemispherical lens, Nb/Al-oxide/Nb tunnel junctions, and an aluminum normal-metal tuning circuit in a two-junction configuration. Since the mixer operates substantially above the gap frequency of niobium (nu >~ 2 Delta/h ~ 700 GHz), a normal metal is used in the tuning circuit in place of niobium to reduce the Ohmic loss. The frequency response of the device was measured using a Fourier transform spectrometer and agrees reasonably well with the theoretical prediction. At 1042 GHz, the uncorrected double-sideband receiver noise temperature is 840 K when the physical temperature of the mixer is 2.5 K. This is the first SIS mixer which outperforms GaAs Schottky diode mixers by a large margin at 1 THz

Structural Optimisation: Biomechanics of the Femur

A preliminary iterative 3D meso-scale structural model of the femur was developed, in which bar and shell elements were used to represent trabecular and cortical bone respectively. The cross-sectional areas of the bar elements and the thickness values of the shell elements were adjusted over successive iterations of the model based on a target strain stimulus, resulting in an optimised construct. The predicted trabecular architecture, and cortical thickness distribution showed good agreement with clinical observations, based on the application of a single leg stance load case during gait. The benefit of using a meso-scale structural approach in comparison to micro or macro-scale continuum approaches to predictive bone modelling was achievement of the symbiotic goals of computational efficiency and structural description of the femur.Comment: Accepted by Engineering and Computational Mechanics (Proceedings of the ICE