Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Efficient group communication for large-scale parallel clustering

Global communication requirements and load imbalance of some parallel data mining algorithms are the major obstacles to exploit the computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication cost in iterative parallel data mining algorithms. In particular, the analysis focuses on one of the most influential and popular data mining methods, the k-means algorithm for cluster analysis. The straightforward parallel formulation of the k-means algorithm requires a global reduction operation at each iteration step, which hinders its scalability. This work studies a different parallel formulation of the algorithm where the requirement of global communication can be relaxed while still providing the exact solution of the centralised k-means algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real world distributed applications or can be induced by means of multi-dimensional binary search trees. The approach can also be extended to accommodate an approximation error which allows a further reduction of the communication costs.

Precise analysis of array usage in scientific programs

The automatic transformation of sequential programs for efficient execution on parallel computers involves a number of analyses and restructurings of the input. Some of these analyses are based on computing array sections, a compact description of a range of array elements. Array sections describe the set of array elements that are either read or written by program statements. These sections can be compactly represented using shape descriptors such as regular sections, simple sections, or generalized convex regions. However, binary operations such as Union performed on these representations do not satisfy a straightforward closure property, e.g., if the operands to Union are convex, the result may be nonconvex. Approximations are resorted to in order to satisfy this closure property. These approximations introduce imprecision in the analyses and, furthermore, the imprecisions resulting from successive operations have a cumulative effect. Delayed merging is a technique suggested and used in some of the existing analyses to minimize the effects of approximation. However, this technique does not guarantee an exact solution in a general setting. This article presents a generalized technique to precisely compute Union which can overcome these imprecisions.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod-Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark`s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm. [DOI: 10.1115/1.3142903]

Four-level systems and a universal quantum gate

We discuss the possibility of implementing a universal quantum XOR gate by using two coupled quantum dots subject to external magnetic fields that are parallel and slightly different. We consider this system in two different field configurations. In the first case, parallel external fields with the intensity difference at each spin being proportional to the time-dependent interaction between the spins. A general exact solution describing this system is presented and analyzed to adjust field parameters. Then we consider parallel fields with intensity difference at each spin being constant and the interaction between the spins switching on and off adiabatically. In both cases we adjust characteristics of the external fields (their intensities and duration) in order to have the parallel pulse adequate for constructing the XOR gate. In order to provide a complete theoretical description of all the cases, we derive relations between the spin interaction, the inter-dot distance, and the external field. (C) 2008 WILEYNCH Verlag GmbH & Co. KGaA. Weinheim.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Colorizing Grey Scale Images

The purpose of this thesis is to develop a working methodology to color a grey scale image. This thesis is based on approach of using a colored reference image. Coloring grey scale images has no exact solution till date and all available methods are based on approximation. This technique of using a color reference image for approximating color information in grey scale image is among most modern techniques.Method developed here in this paper is better than existing methods of approximation of color information addition in grey scale images in brightness, sharpness, color shade gradients and distribution of colors over objects.Color and grey scale images are analyzed for statistical and textural features. This analysis is done only on basis of luminance value in images. These features are then segmented and segments of color and grey scale images are mapped on basis of distances of segments from origin. Then chromatic values are transferred between these matched segments from color image to grey scale image.Technique proposed in this paper uses better mechanism of mapping clusters and mapping colors between segments, resulting in notable improvement in existing techniques in this category.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quantization rules for bound states in quantum wells

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl-Teller potential and several anharmonic oscillator potentials. which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

Reply to Comment on 'validity of Feynman's prescription of disregarding the Pauli principle in intermediate states'

In a recent paper, we raised a question on the validity of Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory. In the preceding Comment, Cavalcanti correctly pointed out that Feynman's prescription is consistent with the exact solution of the model that we used. This means that the Pauli principle does not necessarily apply to intermediate states. We discuss implications of this puzzling aspect.

Nonabelian Toda theories from parafermionic reductions of the WZW model

We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R)(q) algebra spanned by charges of the chiral and antichiral nonlocal currents and the U(1) charge. The classical (Poisson brackets) algebras of symmetries VG(n), of these models appear to be of mixed PF-WG(n) type. They contain together with the local quadratic terms specific for the W-n-algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum VA(n)-algebras. The quantum VA(2)-algebra and its degenerate representations are studied in detail. (C) 1999 Academic Press.

Two-Point Function at Two Loops via Triangle Diagram Insertion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Electronic correlations for a two-level dimer: dynamical susceptibilities

The exact solution for the full electronic Hamiltonian for a two-level dimer is obtained. The parameter constellation (20) is reparametrized via orthogonal Slater atomic orbitals, yielding a three-parameter model. With the dimer embedded in a thermal bath, several temperature-dependent dynamical susceptibilities are computed. (C) 2002 Elsevier B.V. B.V. All rights reserved.

A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.