Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

A power system control scheme based on security visualisation in parameter space

Power system real time security assessment is one of the fundamental modules of the electricity markets. Typically, when a contingency occurs, it is required that security assessment and enhancement module shall be ready for action within about 20 minutes’ time to meet the real time requirement. The recent California black out again highlighted the importance of system security. This paper proposed an approach for power system security assessment and enhancement based on the information provided from the pre-defined system parameter space. The proposed scheme opens up an efficient way for real time security assessment and enhancement in a competitive electricity market for single contingency case

Magma Flow Instabilities in a Volcanic Conduit: Implications for Long-Period Seismicity

Silicic volcanic eruptions are typically accompanied by repetitive Long-Period (LP) seismicity that originates from a small region of the upper conduit. These signals have the capability to advance eruption prediction, since they commonly precede a change in the eruption vigour. Shear bands forming along the conduit wall, where the shear stresses are highest, have been linked to providing the seismic trigger. However, existing computational models are unable to generate shear bands at the depths where the LP signals originate using simple magma strength models. Presented here is a model in which the magma strength is determined from a constitutive relationship dependent upon crystallinity and pressure. This results in a depth-dependent magma strength, analogous to planetary lithospheres. Hence, in shallow highly-crystalline regions a macroscopically discontinuous brittle type of deformation will prevail, whilst in deeper crystal-poor regions there will be a macroscopically continuous plastic deformation mechanism. This will result in a depth where the brittle-ductile transition occurs, and here shear bands disconnected from the free-surface may develop. We utilize the Finite Element Method and use axi-symmetric coordinates to model magma flow as a viscoplastic material, simulating quasi-static shear bands along the walls of a volcanic conduit. Model results constrained to the Soufrière Hills Volcano, Montserrat, show the generation of two types of shear bands: upper-conduit shear bands that form between the free-surface to a few 100 metres below it and discrete shear bands that form at the depths where LP seismicity is measured to occur corresponding to the brittle-ductile transition and the plastic shear region. It is beyond the limitation of the model to simulate a seismic event, although the modelled viscosity within the discrete shear bands suggests a failure and healing cycle time that supports the observed LP seismicity repeat times. However, due to the paucity of data and large parameter space available these results can only be considered to be qualitative rather than quantitative at this stage.

Anomalous resonance fluorescence and dressed-state inversion by squeezed light in a Fabry-Perot microcavity

It has been suggested that phased atomic decay in a squeezed vacuum could be detected in the fluorescence spectrum emitted from a driven two-level atom in a cavity. Recently, the existence of other very distinctive features in the fluorescence spectra arising from the nonclassical features of the squeezed vacuum has been reported. In this paper, we investigate the possibility of experimental observation of these spectra. The main obstacle to the experimentalist is ensuring an effective squeezed-vacuum-atom coupling. To overcome this problem we propose the use of a Fabry-Perot microcavity. The analysis involves a consideration of the three-dimensional nature of the electromagnetic held, and the possibility of a mismatch between the squeezed and cavity modes. The problem of squeezing bandwidths is also addressed. We show that under experimentally realistic circumstances many of the spectral anomalies predicted in free space also occur in this environment. In addition, we report large population inversions in the dressed states of the two-level atom. [S1050-2947(98)02301-4].

Two dimensional computational fluid dynamic models for waste stabilisation ponds

Traditional waste stabilisation pond (WSP) models encounter problems predicting pond performance because they cannot account for the influence of pond features, such as inlet structure or pond geometry, on fluid hydrodynamics. In this study, two dimensional (2-D) computational fluid dynamics (CFD) models were compared to experimental residence time distributions (RTD) from literature. In one of the-three geometries simulated, the 2-D CFD model successfully predicted the experimental RTD. However, flow patterns in the other two geometries were not well described due to the difficulty of representing the three dimensional (3-D) experimental inlet in the 2-D CFD model, and the sensitivity of the model results to the assumptions used to characterise the inlet. Neither a velocity similarity nor geometric similarity approach to inlet representation in 2-D gave results correlating with experimental data. However. it was shown that 2-D CFD models were not affected by changes in values of model parameters which are difficult to predict, particularly the turbulent inlet conditions. This work suggests that 2-D CFD models cannot be used a priori to give an adequate description of the hydrodynamic patterns in WSP. (C) 1998 Elsevier Science Ltd. All rights reserved.

Interference in hyperbolic space

The interference in a phase space algorithm of Schleich and Wheeler [Nature 326, 574 (1987)] is extended to the hyperbolic space underlying the group SU(1,1). The extension involves introducing the notion of weighted areas. Analytic expressions for the asymptotic forms for overlaps between the eigenstates of the generators of su(1,1) thus obtained are found to be in excellent agreement with the numerical results.[S1050-2947(98)08602-8].

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Violation of Kohler's rule by the magnetoresistance of a quasi-two-dimensional organic metal

The interlayer magnetoresistance of the quasi-two-dimensional metal alpha-(BEDT-TTF)(2)KHg(SCN)(4) is considered. In the temperature range from 0.5 to 10 K and for fields up to 10 T the magnetoresistance has a stronger temperature dependence than the zero-field resistance. Consequently Kohler's rule is not obeyed for any range of temperatures or fields. This means that the magnetoresistance cannot be described in terms of semiclassical transport on a single Fermi surface with a single scattering time. Possible explanations for the violations of Kohler's rule are considered, both within the framework of semiclassical transport theory and involving incoherent interlayer transport. The issues considered are similar to those raised by the magnetotransport of the cuprate superconductors. [S0163-1829(98)13219-8].

Phase diagram of the one-dimensional Holstein model of spinless fermions

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalization group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the antiadiabatic regime and is consistent with renormalization group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition.