Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Nine classes of integrable boundary conditions for the eight-state supersymmetric fermion model

Nine classes of integrable boundary conditions for the eight-state supersymmetric model of strongly correlated fermions are presented. The boundary systems are solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations for all nine cases are given.

Calculating current densities and fields due to shielded bi-planar radio-frequency coils

A method for the accurate computation of the current densities produced in a wide-runged bi-planar radio-frequency coil is presented. The device has applications in magnetic resonance imaging. There is a set of opposing primary rungs, symmetrically placed on parallel planes and a similar arrangement of rungs on two parallel planes surrounding the primary serves as a shield. Current densities induced in these primary and shielding rungs are calculated to a high degree of accuracy using an integral-equation approach, combined with the inverse finite Hilbert transform. Once these densities are known, accurate electrical and magnetic fields are then computed without difficulty. Some test results are shown. The method is so rapid that it can be incorporated into optimization software. Some preliminary fields produced from optimized coils are presented.

Thickness and stability of adsorbed film in cylindrical mesopores

The adsorbed film in small cylindrical mesopores is studied by using MCM-41 samples of uniform cylindrical channels as model systems. It is found that at a given relative pressure, the smaller the pore radius, the thicker the adsorbed film is, as postulated by Broekhoff and De Beer. Thermodynamics analysis established that the stability of the adsorbed film is determined by interface curvature and the potential of interaction between adsorbate and adsorbent. A semiempirical equation is proposed to describe the state of stable adsorbed films in cylindrical mesopores. It is also shown to be useful in calculations of pore size distributions of mesoporous solids.

Epidermal iontophoresis: I. Development of the ionic mobility-pore model

Purpose, An integrated ionic mobility-pore model for epidermal iontophoresis is developed from theoretical considerations using both the free volume and pore restriction forms of the model for a range of solute radii (r(j)) approaching the pore radii (r(p)) as well as approximation of the pore restriction form for r(j)/r(p) < 0.4. In this model, we defined the determinants for iontophoresis as solute size (defined by MV, MW or radius), solute mobility, solute shape, solute charge, the Debye layer thickness, total current applied, solute concentration, fraction ionized, presence of extraneous ions (defined by solvent conductivity), epidermal permselectivity, partitioning rates to account for interaction of unionized and ionized lipophilic solutes with the wall of the pore and electroosmosis. Methods, The ionic mobility-pore model was developed from theoretical considerations to include each of the determinants of iontophoretic transport. The model was then used to reexamine iontophoretic flux conductivity and iontophoretic flux-fraction ionized literature data on the determinants of iontophoretic flux. Results. The ionic mobility-pore model was found to be consistent with existing experimental data and determinants defining iontophoretic transport. However, the predicted effects of solute size on iontophoresis are more consistent with the pore-restriction than free volume form of the model. A reanalysis of iontophoretic flux-conductivity data confirmed the model's prediction that, in the absence of significant electroosmosis, the reciprocal of flux is linearly related to either donor or receptor solution conductivity. Significant interaction with the pore walls, as described by the model, accounted for the reported pH dependence of the iontophoretic transport for a range of ionizable solutes. Conclusions. The ionic mobility-pore iontophoretic model developed enables a range of determinants of iontophoresis to be described in a single unifying equation which recognises a range of determinants of iontophoretic flux.

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Thermal diffusion in molecular dynamics simulations of thin film diamond deposition

Molecular dynamics simulations of carbon atom depositions are used to investigate energy diffusion from the impact zone. A modified Stillinger-Weber potential models the carbon interactions for both sp2 and sp3 bonding. Simulations were performed on 50 eV carbon atom depositions onto the (111) surface of a 3.8 x 3.4 x 1.0 nm diamond slab containing 2816 atoms in 11 layers of 256 atoms each. The bottom layer was thermostated to 300 K. At every 100th simulation time step (27 fs), the average local kinetic energy, and hence local temperature, is calculated. To do this the substrate is divided into a set of 15 concentric hemispherical zones, each of thickness one atomic diameter (0.14 nm) and centered on the impact point. A 50-eV incident atom heats the local impact zone above 10 000 K. After the initial large transient (200 fs) the impact zone has cooled below 3000 K, then near 1000 K by 1 ps. Thereafter the temperature profile decays approximately as described by diffusion theory, perturbed by atomic scale fluctuations. A continuum model of classical energy transfer is provided by the traditional thermal diffusion equation. The results show that continuum diffusion theory describes well energy diffusion in low energy atomic deposition processes, at distance and time scales larger than 1.5 nm and 1-2 ps, beyond which the energy decays essentially exponentially. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

On uniquely determining cell-wall material properties with the compression experiment

A finite element model (FEM) of the cell-compression experiment has been developed in dimensionless form to extract the fundamental cell-wall-material properties (i.e. the constitutive equation and its parameters) from experiment force-displacement data. The FEM simulates the compression of a thin-walled, liquid-filled sphere between two flat surfaces. The cell-wall was taken to be permeable and the FEM therefore accounts for volume loss during compression. Previous models assume an impermeable wall and hence a conserved cell volume during compression. A parametric study was conducted for structural parameters representative of yeast. It was shown that the common approach of assuming reasonable values for unmeasured parameters (e.g. cell-wall thickness, initial radial stretch) can give rise to nonunique solutions for both the form and constants in the cell-wall constitutive relationship. Similarly, measurement errors can also lead to an incorrectly defined cell-wall constitutive relationship. Unique determination of the fundamental wall properties by cell compression requires accurate and precise measurement of a minimum set of parameters (initial cell radius, initial cell-wall thickness, and the volume loss during compression). In the absence of such measurements the derived constitutive relationship may be in considerable error, and should be evaluated against its ability to predict the outcome of other mechanical experiments. (C) 1998 Elsevier Science Ltd. All rights reserved.

The cost of life expectancy and the implicit social valuation of life

A new method of estimating the economic value of life is proposed. Using cross-country data, an equation is estimated to explain life expectancy as a function of real consumption of goods and services. The associated cost function for life expectancy in terms of the prices of specific goods and services is used to estimate the cost of a reduction in age-specific mortality rates sufficient to save the life of one person. The cost of saving a life in OECD countries is as much as 1000 times that in the poorest countries. Ethical implications are discussed.

Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

Effects of coping strategies, social support and work-nonwork conflict on shift worker's health

Objectives This study examines the direct and mediated effects of shift workers' coping strategies and social support on structural work-nonwork conflict and subjective health. Methods The participants were 172 registered female nurses, aged 21 to 40 years. They all worked full-time, on rapidly rotating, 8-hour shifts in metropolitan general hospitals. All the respondents completed a self-administered questionnaire requesting demographic information and data on sources of social support, work-nonwork conflict, and coping strategies. Results A path model with good fit (chi(2)=28.88, df=23, P>.23, CFI=0.97) demonstrated complex effects of social support and coping on structural work-nonwork conflict and health. Conclusions Structural work-nonwork conflict mediated the effects of social support from supervisors and emotionally expressive coping on psychological symptoms. Control of shifts mediated the effect of social support from supervisors on structural work-nonwork conflict. Disengagement coping had direct and mediated effects on psychological and physical health. However, it also had mediated effects, with the effect on psychological health being mediated by support from co-workers and the effect on physical symptoms being mediated by family support. Go-worker support mediated the effect of social support from supervisors on psychological symptoms. Overall, these findings support previous research and clarify the process by which coping strategies and social support affect structural work-nonwork conflict and health in shift work.

Integrability of a t - J model with impurities

A t - J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1).

Tidal effects on sea water intrusion in unconfined aquifers

A variable-density groundwater model is used to analyse the effects of tidal fluctuations on sea-water intrusion in an unconfined aquifer. It is shown that the tidal activity forces the sea-water to intrude further inland and it also creates a thicker interface than would occur without tidal effects. Moreover, the configuration of the interface is radically changed when the tidal fluctuations are included. This is because of the dramatic changes in the flow pattern and velocity of the groundwater near the shoreline. For aquifer depths much larger than tidal amplitudes, the tidal fluctuation does not have much effect on how far the sea-water intrudes into the aquifer; nevertheless, a significant change in the configuration of concentration contours because of the effect of tidal fluctuations is observed. This change is more noticeable at the top of the aquifer, near the water table, than at the bottom of the aquifer, and is caused by the infiltration of salt water into the top of the aquifer at higher tidal levels. A flatter beach slope, therefore, intensifies this phenomenon. The interface configurations do not change noticeably over the course of a tidal cycle. Neglecting tidal fluctuation effects results in an inaccurate evaluation of the water table elevation at the land end of the aquifer, although no distinguishable difference is seen between the water tables near the shoreline. Where the landward boundary condition is a constant head, the effects of tidal fluctuations on sea-water intrusion are more pronounced than for cases where the landward boundary condition is a specified flux. Also it is shown that the effects of tidal fluctuations are more significant for a sloping beach than for a vertical shoreline and the salt water intrudes further inland for the sloping case. (C) 1999 Elsevier Science B.V. All rights reserved.