A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

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.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential that is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak-coupling Gross-Pitaevskii regime to the strong-coupling, fermionic Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Phase-dependent fluorescence linewidth narrowing in a three-level atom damped by a finite-bandwidth squeezed vacuum

We examine subnatural phase-dependent linewidths in the fluorescence spectrum of a three-level atom damped by a narrow-bandwidth squeezed vacuum in a cavity. Using the dressed-atom model approach of a strongly driven three-level cascade system, we derive the master equation of the system from which we obtain simple analytical expressions for the fluorescence spectrum. We show that the phase effects depend on the bandwidths of the squeezed vacuum and the cavity relative to the Rabi frequency of the driving fields. When the squeezing bandwidth is much larger than the Rabi frequency, the spectrum consists of five lines with only the central and outer sidebands dependent on the phase. For a squeezing bandwidth much smaller than the Rabi frequency the number of lines in the spectrum and their phase properties depend on the frequency at which the squeezing and cavity modes are centered. When the squeezing and cavity modes are centered on the inner Rabi sidebands, the spectrum exhibits five lines that are completely independent of the squeezing phase with only the inner Rabi sidebands dependent on the squeezing correlations. Matching the squeezing and cavity modes to the outer Rabi sidebands leads to the disappearance of the inner Rabi sidebands and a strong phase dependence of the central line and the outer Rabi sidebands. We find that in this case the system behaves as an individual two-level system that reveals exactly the noise distribution in the input squeezed vacuum. [S1050-2947(97)00111-X].

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.