Comparative study of symmetric and asymmetric cylindrical MRI gradient Y-coils in terms of induced eddy currents

We have recently introduced the concept of whole-body asymmetric MRI systems [1]. In this theoretical study, we investigate the PNS characteristics of whole-body asymmetric gradient systems as compared to conventional symmetric systems. Recent experimental evidence [2] supports the hypothesis of transverse gradients being the largest contributor of PNS due to induced electric currents. Asymmetric head gradient coils have demonstrated benefits in the past [3]. The numerical results are based on an anatomically-accurate 2mm-human voxel-phantom NORMAN [4]. The results of this study can facilitate the optimization of whole-body asymmetric gradients in terms of patient comfort/safety (less PNS), while prospering the use of asymmetric MRI systems for in-vivo medical interventions.

Mutation analysis to verify feature matrices for isolating errors in simulation models

Software simulation models are computer programs that need to be verified and debugged like any other software. In previous work, a method for error isolation in simulation models has been proposed. The method relies on a set of feature matrices that can be used to determine which part of the model implementation is responsible for deviations in the output of the model. Currrently these feature matrices have to be generated by hand from the model implementation, which is a tedious and error-prone task. In this paper, a method based on mutation analysis, as well as prototype tool support for the verification of the manually generated feature matrices is presented. The application of the method and tool to a model for wastewater treatment shows that the feature matrices can be verified effectively using a minimal number of mutants.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

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.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions, We illustrate how this general formalism applier; to construct multiparametric versions of the supersymmetric t-J and Li models.

Integrable eight-state supersymmetric U model with boundary terms and its Bethe ansatz solution

A class of integrable boundary terms for the eight-state supersymmetric U model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1998 Elsevier Science B.V.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

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.