Introduction to Hubbard model and exact diagonalization
S. Akbar Jafari
2008-06-01
Full Text Available Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.
Exact diagonalization of quantum-spin models
Lin, H. Q.
1990-10-01
We have developed a technique to replace hashing in implementing the Lanczös method for exact diagonalization of quantum-spin models that enables us to carry out numerical studies on substantially larger lattices than previously studied. We describe the algorithm in detail and present results for the ground-state energy, the first-excited-state energy, and the spin-spin correlations on various finite lattices for spins S=1/2, 1, 3/2, and 2. Results for an infinite system are obtained by extrapolation. We also discuss the generalization of our method to other models.
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.;
2000-01-01
We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positive...
Off-diagonal Bethe ansatz for exactly solvable models
Wang, Yupeng; Cao, Junpeng; Shi, Kangjie
2015-01-01
This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.
Exact diagonalization: the Bose-Hubbard model as an example
Zhang, J. M.; Dong, R. X.
2010-05-01
We take the Bose-Hubbard model to illustrate exact diagonalization techniques in a pedagogical way. We follow the route of first generating all the basis vectors, then setting up the Hamiltonian matrix with respect to this basis and finally using the Lanczos algorithm to solve low lying eigenstates and eigenvalues. Emphasis is placed on how to enumerate all the basis vectors and how to use the hashing trick to set up the Hamiltonian matrix or matrices corresponding to other quantities. Although our route is not necessarily the most efficient one in practice, the techniques and ideas introduced are quite general and may find use in many other problems.
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.
2000-01-01
We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positive...... and negative temperatures follow the second-order high-temperature series expansions for \\T\\ > 3 nK. Our findings do not agree with the measurements of the former Rh experiment in Helsinki, where a deviation is seen at much higher temperatures. (C) 2000 Elsevier Science B.V. All rights reserved....
Block-bordered diagonalization and parallel iterative solvers
Alvarado, F.; Dag, H.; Bruggencate, M. ten [Univ. of Wisconsin, Madison, WI (United States)
1994-12-31
One of the most common techniques for enhancing parallelism in direct sparse matrix methods is the reorganization of a matrix into a blocked-bordered structure. Incomplete LDU factorization is a very good preconditioner for PCG in serial environments. However, the inherent sequential nature of the preconditioning step makes it less desirable in parallel environments. This paper explores the use of BBD (Blocked Bordered Diagonalization) in connection with ILU preconditioners. The paper shows that BBD-based ILU preconditioners are quite amenable to parallel processing. Neglecting entries from the entire border can result in a blocked diagonal matrix. The result is a great increase in parallelism at the expense of additional iterations. Experiments on the Sequent Symmetry shared memory machine using (mostly) power system that matrices indicate that the method is generally better than conventional ILU preconditioners and in many cases even better than partitioned inverse preconditioners, without the initial setup disadvantages of partitioned inverse preconditioners.
Cold bosons in optical lattices: a tutorial for exact diagonalization
Raventós, David; Graß, Tobias; Lewenstein, Maciej; Juliá-Díaz, Bruno
2017-06-01
Exact diagonalization (ED) techniques are a powerful method for studying many-body problems. Here, we apply this method to systems of few bosons in an optical lattice, and use it to demonstrate the emergence of interesting quantum phenomena such as fragmentation and coherence. Starting with a standard Bose-Hubbard Hamiltonian, we first revise the characterisation of the superfluid to Mott insulator (MI) transitions. We then consider an inhomogeneous lattice, where one potential minimum is made much deeper than the others. The MI phase due to repulsive on-site interactions then competes with the trapping of all atoms in the deep potential. Finally, we turn our attention to attractively interacting systems, and discuss the appearance of strongly correlated phases and the onset of localisation for a slightly biased lattice. The article is intended to serve as a tutorial for ED of Bose-Hubbard models.
Exact Diagonalization of Heisenberg SU(N) models.
Nataf, Pierre; Mila, Frédéric
2014-09-19
Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).
Xiaotian Xu
2015-09-01
Full Text Available The small polaron, a one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary fields gives rise to a typical U(1-symmetry-broken fermionic model. The exact spectra of the Hamiltonian and the associated Bethe ansatz equations are derived by constructing an inhomogeneous T–Q relation.
Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
Weinstein, Marvin; /SLAC; Auerbach, Assa; /Stanford U., Phys. Dept. /Technion; Chandra, V.Ravi; /Technion
2011-11-04
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. The lattice of size N is partitioned into two subclusters. At each iteration the Lanczos vector is projected into a set of n{sub svd} smaller subcluster vectors using singular value decomposition. For low entanglement entropy S{sub ee}, (satisfied by short range Hamiltonians), we expect the truncation error to vanish as exp(-n{sup 1/S{sub ee}}{sub svd}). Convergence is tested for the Heisenberg model on Kagome clusters of up to 36 sites, with no symmetries exploited, using less than 15GB of memory. Generalization to multiple partitioning is discussed.
Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations
Vacaru, Sergiu I
2014-01-01
There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of solutions may posses, or not, Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormholes like objects matching external black ellipsoid - de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/ massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.
Exact solutions in modified massive gravity and off-diagonal wormhole deformations
Vacaru, Sergiu I. [Alexandru Ioan Cuza University, Rector' s Office, Iasi (Romania); CERN, Theory Division, Geneva 23 (Switzerland)
2014-03-15
We explore off-diagonal deformations of 'prime' metrics in Einstein gravity (for instance, for wormhole configurations) into 'target' exact solutions in f(R,T)-modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid--de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions. (orig.)
An exact solver for the DCJ median problem.
Zhang, Meng; Arndt, William; Tang, Jijun
2009-01-01
The "double-cut-and-join" (DCJ) model of genome rearrangement proposed by Yancopoulos et al. uses the single DCJ operation to account for all genome rearrangement events. Given three signed permutations, the DCJ median problem is to find a fourth permutation that minimizes the sum of the pairwise DCJ distances between it and the three others. In this paper, we present a branch-and-bound method that provides accurate solution to the multichromosomal DCJ median problems. We conduct extensive simulations and the results show that the DCJ median solver performs better than other median solvers for most of the test cases. These experiments also suggest that DCJ model is more suitable for real datasets where both reversals and transpositions occur.
Kondo physics of the Anderson impurity model by distributional exact diagonalization
Motahari, S.; Requist, R.; Jacob, D.
2016-12-01
The distributional exact diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble-averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on the ensemble-averaged self-energy, and thus is essential for the description of Kondo physics within DED. Using the numerical renormalization group (NRG) method as a benchmark, we show that DED yields excellent spectra, both inside and outside the Kondo regime for a moderate number of bath sites. Only for very strong correlations (U /Γ ≫10 ) does the number of bath sites needed to achieve good quantitative agreement become too large to be computationally feasible.
High-precision evaluation of Wigner's d-matrix by exact diagonalization
Feng, X M; Yang, W; Jin, G R
2015-01-01
The precise calculations of the Wigner's d-matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using the Wigner's formula suffer from loss of precision. We present a simple method to avoid this problem by expanding the d-matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular-momentum operator $J_{y}$ in the eigenbasis of $J_{z}$. This method allows us to compute the d-matrix and its various derivatives for spins up to a few thousand. The precision of the d-matrix from our method is about $10^{-14}$ for spins up to $100$.
Pairing in the two-dimensional Hubbard model: An exact diagonalization study
Lin, H. Q.; Hirsch, J. E.; Scalapino, D. J.
1988-05-01
We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.
Beyond the Tamm-Dancoff approximation for extended systems using exact diagonalization
Sander, Tobias; Maggio, Emanuele; Kresse, Georg
2015-07-01
Linear optical properties can be accurately calculated using the Bethe-Salpeter equation. After introducing a suitable product basis for the electron-hole pairs, the Bethe-Salpeter equation is usually recast into a complex non-Hermitian eigenvalue problem that is difficult to solve using standard eigenvalue solvers. In solid-state physics, it is therefore common practice to neglect the problematic coupling between the positive- and negative-frequency branches, reducing the problem to a Hermitian eigenvalue problem [Tamm-Dancoff approximation (TDA)]. We use time-inversion symmetry to recast the full problem into a quadratic Hermitian eigenvalue problem, which can be solved routinely using standard eigenvalue solvers even at a finite wave vector q . This allows us to access the importance of the coupling between the positive- and negative-frequency branch for prototypical solids. As a starting point for the Bethe-Salpeter calculations, we use self-consistent Green's-function methods (GW ), making the present scheme entirely ab initio. We calculate the optical spectra of carbon (C), silicon (Si), lithium fluoride (LiF), and the cyclic dimer Li2F2 and discuss why the differences between the TDA and the full solution are tiny. However, at finite momentum transfer q , significant differences between the TDA and our exact treatment are found. The origin of these differences is explained.
Notes on the ExactPack Implementation of the DSD Rate Stick Solver
Kaul, Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-08-01
It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Rate Stick equation is consistent with the Rate Stick PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat. In the solver I implemented in ExactPack, I used the one-sided boundary condition described above at the outer boundary. In addition, I used 80% of the time step calculated in the stability analysis above. By making these two changes, I was able to implement a solver that calculates the solution without any arbitrary limits placed on the values of the curvature at the boundary. Thus, the calculation is driven directly by the conditions at the boundary as formulated in the DSD theory. The chosen scheme is completely coherent and defensible from a mathematical standpoint.
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
Notes on the ExactPack Implementation of the DSD Explosive Arc Solver
Kaul, Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Doebling, Scott William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-12
It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Explosive Arc equation is consistent with the Explosive Arc PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat.
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
Li, Guang-Liang; Cao, Junpeng; Hao, Kun; Wen, Fakai; Yang, Wen-Li; Shi, Kangjie
2016-09-01
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the SUq (3)R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the SUq (n) algebra.
Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
Li, Guang-Liang; Hao, Kun; Yang, Wen-Li; Shi, Kangjie
2016-01-01
The nested off-diagonal Bethe Ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe Ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the $SU_q(n)$ algebra.
Exact solution of the trigonometric SU(3 spin chain with generic off-diagonal boundary reflections
Guang-Liang Li
2016-09-01
Full Text Available The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the SUq(3 R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T–Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the SUq(n algebra.
POLARONS IN THE 3-BAND PEIERLS-HUBBARD MODEL - AN EXACT DIAGONALIZATION STUDY
DOBRY, A; GRECO, A; LORENZANA, J; RIERA, J
1994-01-01
We have studied the three-band Peierls-Hubbard model describing the Cu-O layers in high-T(c) superconductors by using Lanczos diagonalization and assuming infinite mass for the ions. When the system is doped with one hole, and for lambda (the electron-lattice coupling strength) greater than a critic
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Exact diagonalization of non-Hermitian so(3,2) models: Generalized two-mode boson systems
Zhang, Hong-Biao; Wang, Gangcheng
2016-12-01
We propose a unified approach to exactly diagonalize generalized non-Hermitian so(3,2) models. This approach is a series of similarity transformations, which is constructed by some similarity transformation operators associated with su(1,1) and su(2) subalgebras of so(3,2) Lie algebra. During this diagonalization, it is worth noting that a key step is to get rid of the terms E ˆ ± and F ˆ ± together via the proper similarity transformations first. In this way, exact solutions of the non-Hermitian so(3,2) models are obtained. Meanwhile we give the corresponding eigenstates, which are regarded as Lie algebra so(3,2) coherent-like number states. The results can cover the generic form of the eigenvalues and eigenstates to the generalized non-Hermitian two-mode boson systems with the discrete spectrum, including 2D PT-symmetric and non-PT-symmetric oscillators as the special cases. Also they are true for the Hermitian case.
Exact diagonalization study of a half-filled extended hard-core boson model in one dimension
Kim, Sung Moon; Choi, Hwan Bin; Lee, Yong Woo; Lee, Ji-Woo
2015-09-01
We study a model for interacting spinless bosons in one dimension. The bosons are under a hard-core condition, which does not allow two or more bosons in the same site. However, nearestneighbor interactions between bosons ( V) and hoppings to the nearest empty site ( t) are allowed. As V increases from a large negative value, the system undergoes a quantum phase transition from a phase-separation (PS) phase to a superfluid (SF) phase because the hopping term overcomes the attractive energy. When V becomes positive and is increased more, the superfluid phase becomes a charge-density-wave (CDW) phase because the repulsive energy blocks the movements of bosons. Via exact diagonalizations, we calculated the ground-state energies, the correlation energies, and the kinetic energies to obtain signatures of the quantum phase transitions. We adopted a fast stateseeking algorithm that enabled us to calculate the ground states and the ground-state energies up to L = 32 more efficiently. Some results are compared with those of quantum Monte Carlo simulations by using stochastic series expansion for the Heisenberg point, and the momentum distribution functions for the three phases are discussed.
Saha, Madhumita; Maiti, Santanu K.
2016-01-01
The interplay between Hubbard interaction, long-range hopping and disorder on persistent current in a mesoscopic one-dimensional conducting ring threaded by a magnetic flux $\\phi$ is analyzed in detail. Two different methods, exact numerical diagonalization and Hartree-Fock mean field theory, are used to obtain numerical results from the many-body Hamiltonian. The current in a disordered ring gets enhanced as a result of electronic correlation and it becomes more significant when contribution...
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
Langari, A; Pollmann, F; Siahatgar, M
2013-10-09
We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing calculation of the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetry-protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.
Cheng, Lan; Gauss, Jürgen
2011-08-28
We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of properties is taken into account by considering the full derivative of the two-component Hamiltonian matrix with respect to the external perturbation. The applicability of the analytic-gradient scheme presented here is demonstrated in benchmark calculations. SFX2c-1e results for the dipole moments and electric-field gradients of the hydrogen halides are compared with those obtained from nonrelativistic, SF high-order Douglas-Kroll-Hess, and SF Dirac-Coulomb calculations. It is shown that the use of untransformed two-electron interactions introduces rather small errors for these properties. As a first application of the analytic geometrical gradient, we report the equilibrium geometry of methylcopper (CuCH(3)) determined at various levels of theory.
Saha, Madhumita; Maiti, Santanu K.
2016-10-01
The interplay between Hubbard interaction, long-range hopping and disorder on persistent current in a mesoscopic one-dimensional conducting ring threaded by a magnetic flux ϕ is analyzed in detail. Two different methods, exact numerical diagonalization and Hartree-Fock mean field theory, are used to obtain numerical results from the many-body Hamiltonian. The current in a disordered ring gets enhanced as a result of electronic correlation and it becomes more significant when contributions from higher order hoppings, even if they are too small compared to nearest-neighbor hopping, are taken into account. Certainly this can be an interesting observation in the era of long-standing controversy between theoretical and experimental results of persistent current amplitudes. Along with these we also find half-flux quantum periodic current for some typical electron fillings and kink-like structures at different magnetic fluxes apart from ϕ = 0 and ±ϕ0 / 2. The scaling behavior of current is also discussed for the sake of completeness of our present analysis.
Rubin, P., E-mail: rubin@fi.tartu.ee; Sherman, A.
2014-11-07
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest-neighbor and antiferromagnetic third-nearest-neighbor exchange interactions, J{sub 1}=−(1−p)J and J{sub 2}=pJ, J>0(0≤p≤1), is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa{sub 2}S{sub 4}. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained with Mori's projection operator technique. - Highlights: • The S=1J{sub 1}–J{sub 3} Heisenberg model on a triangular lattice is studied. • The ferromagnetic nearest and AF 3rd-nearest-neighbor couplings are considered. • The exact diagonalization study of finite lattices was done. • The SPINPACK code using Lanczos' method is used for calculations. • The obtained results are in agreement with those obtained by Mori's approach.
许涛
2004-01-01
M r.Sm ith liked to be exact. O ne day when he was w alking in thestreet a m an cam e over and asked him E xcuse m e but w here's the , : “ ,nearest bookshop ?” The nearest bookshop Y ou have to cross a bridge and then turn “ ?to the right. ” A nd is the bridge long “ ?” Thirty m eters. “ ” The m an thanked him and went towards the bridge. Suddenly heheard som eone running after him . Stop M r.Sm ith w as shouting. I'm sorry. I just rem em bered ...
Stupfel, Bruno; Lecouvez, Matthieu
2016-10-01
For the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous 3-D objects, a one-way domain decomposition method (DDM) is considered: the computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions (TCs) are prescribed; an integral representation of the electromagnetic fields on the outer boundary constitutes an exact radiation condition. The global system obtained after discretization of the finite element (FE) formulations is solved via a Krylov subspace iterative method (GMRES). It is preconditioned in such a way that, essentially, only the solution of the FE subsystems in each subdomain is required. This is made possible by a computationally cheap H (curl)- H (div) transformation performed on the interfaces that separate the two outermost subdomains. The eigenvalues of the preconditioned matrix of the system are bounded by two, and optimized values of the coefficients involved in the local TCs on the interfaces are determined so as to maximize the minimum eigenvalue. Numerical experiments are presented that illustrate the numerical accuracy of this technique, its fast convergence, and legitimate the choices made for the optimized coefficients.
Pan Feng [Department of Physics, Liaoning Normal University, Dalian 116029 (China); Guan Xin [Department of Physics, Liaoning Normal University, Dalian 116029 (China); Ma Nan [Department of Physics, Liaoning Normal University, Dalian 116029 (China); Han Wenjuan [Department of Physics, Liaoning Normal University, Dalian 116029 (China); Draayer, J P [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)
2007-09-26
A simple Mathematica code based on the differential realization of hard-core boson operators for finding exact solutions of the periodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed; it can easily be used to study general spin-1/2 interaction systems. As an example, the code is applied to study XXX spin-1/2 chains with nearest neighbor interaction in a uniform transverse field. It shows that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitional behavior in the ground state of the system in the thermodynamic limit is also studied.
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Garrido, L. M.; Pascual, P.
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
Exact solution for generalized pairing
Pan, Feng; J.P. Draayer
1997-01-01
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.
A new fast direct solver for the boundary element method
Huang, S.; Liu, Y. J.
2017-04-01
A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.
Zoeteweij, P.
2005-01-01
Composing constraint solvers based on tree search and constraint propagation through generic iteration leads to efficient and flexible constraint solvers. This was demonstrated using OpenSolver, an abstract branch-and-propagate tree search engine that supports a wide range of relevant solver configu
Chaotic diagonal recurrent neural network
Wang Xing-Yuan; Zhang Yi
2012-01-01
We propose a novel neural network based on a diagonal recurrent neural network and chaos,and its structure andlearning algorithm are designed.The multilayer feedforward neural network,diagonal recurrent neural network,and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map.The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks.
Using off-diagonal confinement as a cooling method
Rousseau, Valery; Hettiarachchilage, Kalani; Moreno, Juana; Jarrell, Mark; Sheehy, Dan
2011-03-01
We show that the recently proposed ``off-diagonal confining" (ODC) method (Phys. Rev. Lett. 104, 167201 (2010)) can lead to temperatures that are smaller than with the conventional ``diagonal confining" (DC) method, depending on the control parameters of the system. We determine these parameters using exact diagonalizations for the hard-core case, then we extend our results to the soft-core case by performing quantum Monte Carlo simulations for both DC and ODC systems at fixed temperatures, and analysing the corresponding entropies. This work was supported by NSF OISE-0952300.
Benchmarking optimization solvers for structural topology optimization
Rojas Labanda, Susana; Stolpe, Mathias
2015-01-01
The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different...... sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point...... profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving...
The diagonalization of cubic matrices
Cocolicchio, D.; Viggiano, M.
2000-08-01
This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.
Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2013-10-01
Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T-Q relation and the Bethe ansatz equations are derived.
Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
Cao, Junpeng; Shi, Kangjie; Wang, Yupeng
2013-01-01
With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated $T-Q$ relation and the Bethe ansatz equations are derived.
Correlations and diagonal entropy after quantum quenches in XXZ chains
Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale; Rigol, Marcos
2017-02-01
We study quantum quenches in the XXZ spin-1 /2 Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasilocal conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble, finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we use exact diagonalization to compute the diagonal entropy in the postquench steady state. We show that the Yang-Yang entropy for the complete GGE is consistent with twice the value of the diagonal entropy in the largest chains or the extrapolated result in the thermodynamic limit. Finally, the complete GGE is quantitatively contrasted with the GGE built using only the local conserved charges (local GGE). The predictions of the two ensembles are found to differ significantly in the case of ferromagnetic initial states. Such initial states are better suited than others considered in the literature to experimentally test the validity of the complete GGE and contrast it to the failure of the local GGE.
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
A parallel PCG solver for MODFLOW.
Dong, Yanhui; Li, Guomin
2009-01-01
In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree.
EXACT DIAGONALIZATION RESULTS FOR MULTIMAGNON IR ABSORPTION IN THE CUPRATES
Lorenzana, J.; Eder, R; Meinders, M.B J; Sawatzky, G.A
1995-01-01
Recent measured bands in the mid IR of parent insulating compounds of cuprate superconductors [Perkins et al. Phys. Rev. Lett. 71 1621 (1993)] are interpreted as multimagnon infrared (IR) absorption assisted by phonons. We present results for the coupling constant of light with this excitations and
Exact diagonalization of quantum lattice models on coprocessors
Siro, T.; Harju, A.
2016-10-01
We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice models with different particle numbers, and conclude that for small systems, the multi-core CPU is the fastest platform, while for large systems, the graphics processor is the clear winner, reaching speedups of up to 7.6 compared to the CPU. The Xeon Phi outperforms the CPU with sufficiently large particle number, reaching a speedup of 2.5.
Inductive ionospheric solver for magnetospheric MHD simulations
H. Vanhamäki
2011-01-01
Full Text Available We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances and similar output is produced (ionospheric electric field. The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km^{−1} in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981.
Inductive ionospheric solver for magnetospheric MHD simulations
Vanhamäki, H.
2011-01-01
We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).
Batell, Brian
2012-09-01
The focus of this brief review is on new physics (NP) sources of CP violation, especially related to the flavor-diagonal phenomena of electric dipole moments (EDMs) of elementary particles and atoms. Using weak scale supersymmetry as an example, we illustrate various aspects of the "new physics CP-problem". We also explore the interplay between flavor-changing and flavor-diagonal CP violation in the context of the recent hints from the Tevatron for new sources of CP violation in the B-meson systems.
Efficient variational diagonalization of fully many-body localized Hamiltonians
Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio; Sondhi, S. L.
2016-07-01
We introduce a variational unitary matrix product operator based variational method that approximately finds all the eigenstates of fully many-body localized one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed depth of the UTN ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.
An iterative solver for the 3D Helmholtz equation
Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir
2017-09-01
We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.
Spectral diagonal ensemble Kalman filters
Kasanický, Ivan; Vejmelka, Martin
2015-01-01
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields, which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.
Jankiewicz, Justyna
2004-01-01
We study the properties of time evolution of the $K^{0}-\\bar{K}^{0} $ system in spectral formulation. Within the one--pole model we find the exact form of the diagonal matrix elements of the effective Hamiltonian for this system. It appears that, contrary to the Lee--Oehme--Yang (LOY) result, these exact diagonal matrix elements are different if the total system is CPT--invariant but CP--noninvariant.
Experiments with Succinct Solvers
Buchholtz, Mikael; Nielson, Hanne Riis; Nielson, Flemming
2002-01-01
time of the solver and the aim of this note is to provide some insight into which formulations are better than others. The experiments addresses three general issues: (i) the order of the parameters of relations, (ii) the order of conjuncts in preconditions and (iii) the use of memoisation....... The experiments are performed for Control Flow Analyses for Discretionary Ambients....
Using a satisfiability solver to identify deterministic finite state automata
Heule, M.J.H.; Verwer, S.
2009-01-01
We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach seems to be competitive with alternative techniques. Our contributions are threefold: First, we p
Electric circuits problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av
Advanced calculus problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av
A note on generalized nonlinear diagonal dominance
Gan, Tai-Bin; Huang, Ting-Zhu; Gao, Jian
2006-01-01
In this paper, an open problem, proposed by A. Frommer, about nonlinear generalized diagonal dominance, is solved on some weak restriction, a counterexample is presented if such a restriction is omitted, and some new properties of nonlinear generalized diagonally dominant functions are investigated.
Simultaneous diagonalization of two quaternion matrices
ZhouJianhua
2003-01-01
The simultaneous diagonalization by congruence of pairs of Hermitian quatemion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quatemion matrix. It is proved that any two semi-positive definite Hermitian quatemion matrices can be simultaneously diagonalized by congruence.
Propagation in Diagonal Anisotropic Chirowaveguides
S. Aib
2017-01-01
Full Text Available A theoretical study of electromagnetic wave propagation in parallel plate chirowaveguide is presented. The waveguide is filled with a chiral material having diagonal anisotropic constitutive parameters. The propagation characterization in this medium is based on algebraic formulation of Maxwell’s equations combined with the constitutive relations. Three propagation regions are identified: the fast-fast-wave region, the fast-slow-wave region, and the slow-slow-wave region. This paper focuses completely on the propagation in the first region, where the dispersion modal equations are obtained and solved. The cut-off frequencies calculation leads to three cases of the plane wave propagation in anisotropic chiral medium. The particularity of these results is the possibility of controlling the appropriate cut-off frequencies by choosing the adequate physical parameters values. The specificity of this study lies in the bifurcation modes confirmation and the possible contribution to the design of optical devices such as high-pass filters, as well as positive and negative propagation constants. This negative constant is an important feature of metamaterials which shows the phenomena of backward waves. Original results of the biaxial anisotropic chiral metamaterial are obtained and discussed.
Exact Numerical Solutions of Bose-Hubbard Model
ZHANG Dan; PAN Feng
2004-01-01
Hamiltonian of a one-dimensional Bose-Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The output can be taken as the input of other diagonalization codes. As examples, exact energy eigenvalues and the corresponding wavefunctions for some cases are obtained with a Fortran diagonalization code. Phase transition of the model is analyzed.
A class of Bell diagonal states and entanglement witnesses
Chruscinski, D; Mlodawski, K; Matsuoka, T
2010-01-01
We analyze special class of bipartite states - so called Bell diagonal states. In particular we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis.
An Exactly Solvable Many-Fermion Model
Zettili, Nouredine
2001-04-01
We deal with the construction of a simple many-body model that can be solved exactly. This model serves as a tool for testing the validity and accuracy of many-body approximation methods. The model consists of a system of two distinguishable, one-dimensional sets of fermions interacting via a schematic two-body force. We construct the Hamiltonian of the model by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(2,1) group. The Hamiltonian depends on an adjustable parameter which regulates the strength of the two-body interaction. The size of the Hamiltonian's matrix is rendered finite by means of a built-in symmetry: the Hamiltonian is represented by a five-diagonal square matrix of finite size. The energy spectrum of the model is obtained by diagonalizing this matrix. The energy eigenvalues obtained from this diagonalization are exact, for we don't resort to any approximation in the diagonalization. This model offers a rich and flexible platform for testing quantitatively the various many-body approximation methods especially those that deal with nuclear collective motion.
An Exactly Solvable Many-Body Model
Zettili, Nouredine; Boukahil, Abdelkrim
2012-03-01
We deal here with the construction of a simple many-body model that can be solved exactly. This model serves as a tool for testing the validity and accuracy of many-body approximation methods, most notably those encountered in nuclear theory. The model consists of a system of two distinguishable, one-dimensional sets fermions interacting via a schematic two-body force. We construct the Hamiltonian of the model by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(2,1) group. The Hamiltonian depends on an adjustable parameter which regulates the strength of the two-body interaction. The size of the Hamiltonian's matrix is rendered finite by means of a built-in symmetry: the Hamiltonian is represented by a five-diagonal square matrix of finite size. The energy spectrum of the model is obtained by diagonalizing this matrix. The energy eigenvalues obtained from this diagonalization are exact, for we don't need to resort to any approximation in the diagonalization. This model offers a rich and flexible platform for testing quantitatively the various many-body approximation methods especially those that deal with nuclear collective motion.
Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas; Galgon, Martin; Fehske, Holger; Hager, Georg; Lang, Bruno; Wellein, Gerhard
2016-11-01
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 102 innermost eigenpairs of a topological insulator matrix with dimension 109 derived from quantum physics applications.
On triangular algebras with noncommutative diagonals
2008-01-01
We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections. Moreover we prove that our triangular algebra is maximal.
Diagonal loading least squares time delay estimation
LI Xuan; YAN Shefeng; MA Xiaochuan
2012-01-01
Least squares （LS） time delay estimation is a classical and effective method. However, the performance is degraded severely in the scenario of low ratio of signal-noise （SNR） due to the instability of matrix inversing. In order to solve the problem, diagonal loading least squares （DL-LS） is proposed by adding a positive definite matrix to the inverse matrix. Furthermore, the shortcoming of fixed diagonal loading is analyzed from the point of regularization that when the tolerance of low SNR is increased, veracity is decreased. This problem is resolved by reloading. The primary estimation＇s reciprocal is introduced as diagonal loading and it leads to small diagonal loading at the time of arrival and larger loading at other time. Simulation and pool experiment prove the algorithm has better performance.
On triangular algebras with noncommutative diagonals
DONG AiJu
2008-01-01
We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections.Moreover we prove that our triangular algebra is maximal.
Diagonal chromatography to study plant protein modifications
Walton, Alan; Tsiatsiani, Liana; Jacques, Silke; Stes, Elisabeth; Messens, Joris; Van Breusegem, Frank; Goormachtig, Sofie; Gevaert, Kris
2016-01-01
An interesting asset of diagonal chromatography, which we have introduced for contemporary proteome research, is its high versatility concerning proteomic applications. Indeed, the peptide modification or sorting step that is required between consecutive peptide separations can easily be altered and
On the Marginal Distribution of the Diagonal Blocks in a Blocked Wishart Random Matrix
Kjetil B. Halvorsen
2016-01-01
Full Text Available Let A be a (m1+m2×(m1+m2 blocked Wishart random matrix with diagonal blocks of orders m1×m1 and m2×m2. The goal of the paper is to find the exact marginal distribution of the two diagonal blocks of A. We find an expression for this marginal density involving the matrix-variate generalized hypergeometric function. We became interested in this problem because of an application in spatial interpolation of random fields of positive definite matrices, where this result will be used for parameter estimation, using composite likelihood methods.
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2010-01-01
control applied to high order methods for temporal discretization in reservoir simulation. The family of Runge-Kutta methods is presented and in particular the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method with an embedded error estimate is described. A predictive stepsize adjustment...... rule based on error estimates and convergence control of the integrated iterative solver is presented. We try to improve the predictive stepsize control through an extended communication between the convergence rate, the error control and the stepsize. Keywords: Reservoir simulation, implicit Runge-Kutta...
Quantum Electrodynamics vacuum polarization solver
Carneiro, Pedro; Fonseca, Ricardo; Silva, Luís
2016-01-01
The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing scenarios of extreme energy density. We present a generalized finite-difference time-domain solver that can incorporate the modifications to Maxwells equations due to virtual vacuum polarization. Our multidimensional solver reproduced in one dimensional configurations the results for which an analytic treatment is possible, yielding vacuum harmonic generation and birefringence. The solver has also been tested for two-dimensional scenarios where finite laser beam spot sizes must be taken into account. We employ this solver to explore different types of counter-propagating configurations that can be relevant for future planned experiments aiming to detect quantum vacuum dynamics at ultra-high electromagnetic field intensities.
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Wrapping corrections for non-diagonal boundaries in AdS/CFT
Bajnok, Zoltán [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Nepomechie, Rafael I. [Physics Department, P.O. Box 248046, University of Miami,Coral Gables, FL 33124 (United States)
2016-02-03
We consider an open string stretched between a Y=0 brane and a Y{sub θ}=0 brane. The latter brane is rotated with respect to the former by an angle θ, and is described by a non-diagonal boundary S-matrix. This system interpolates smoothly between the Y−Y (θ=0) and the Y−Ȳ (θ=π/2) systems, which are described by diagonal boundary S-matrices. We use integrability to compute the energies of one-particle states at weak coupling up to leading wrapping order (4, 6 loops) as a function of the angle. The results for the diagonal cases exactly match with those obtained previously.
Exact axisymmetric Taylor states for shaped plasmas
Cerfon, Antoine J., E-mail: cerfon@cims.nyu.edu; O' Neil, Michael, E-mail: oneil@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-06-15
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.
Diagonal chromatography to study plant protein modifications.
Walton, Alan; Tsiatsiani, Liana; Jacques, Silke; Stes, Elisabeth; Messens, Joris; Van Breusegem, Frank; Goormachtig, Sofie; Gevaert, Kris
2016-08-01
An interesting asset of diagonal chromatography, which we have introduced for contemporary proteome research, is its high versatility concerning proteomic applications. Indeed, the peptide modification or sorting step that is required between consecutive peptide separations can easily be altered and thereby allows for the enrichment of specific, though different types of peptides. Here, we focus on the application of diagonal chromatography for the study of modifications of plant proteins. In particular, we show how diagonal chromatography allows for studying proteins processed by proteases, protein ubiquitination, and the oxidation of protein-bound methionines. We discuss the actual sorting steps needed for each of these applications and the obtained results. This article is part of a Special Issue entitled: Plant Proteomics--a bridge between fundamental processes and crop production, edited by Dr. Hans-Peter Mock.
Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
Vacaru, Sergiu I
2016-01-01
Geometric methods for constructing exact solutions of motion equations with first order $\\alpha ^{\\prime }$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-K\\"{a}hler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections. In particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The correspond...
Modern solvers for Helmholtz problems
Tang, Jok; Vuik, Kees
2017-01-01
This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...
Spin-12 XYZ model revisit: General solutions via off-diagonal Bethe ansatz
Junpeng Cao
2014-09-01
Full Text Available The spin-12 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T–Q relations, which allow us to treat both the even N (the number of lattice sites and odd N cases simultaneously in a unified approach.
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
Self-correcting Multigrid Solver
Jerome L.V. Lewandowski
2004-06-29
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.
Diagonal and off-diagonal quark number susceptibilities at high temperatures
Ding, H -T; Ohno, H; Petreczky, P; Schadler, H -P
2015-01-01
We present continuum extrapolated lattice QCD results for up to fourth order diagonal and off-diagonal quark number susceptibilities in the high temperature region of 300-700 MeV. Lattice QCD calculations are performed using 2+1 flavors of highly improved staggered quarks with nearly physical quark masses and at four different lattice spacings. Comparisons of our results with recent weak coupling perturbative calculations yield reasonably good agreements for the entire temperature range.
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as
An exact algorithm for graph partitioning
Hager, William; Zhang, Hongchao
2009-01-01
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained by decomposing the objective function into convex and concave parts and replacing the concave part by an affine underestimate. It is shown that the best affine underestimate can be expressed in terms of the center and the radius of the smallest sphere containing the feasible set. The concave term is obtained either by a constant diagonal shift associated with the smallest eigenvalue of the objective function Hessian, or by a diagonal shift obtained by solving a semidefinite programming problem. Numerical results show that the proposed algorithm is competitive with state-of-the-art graph partitioning codes.
New Criteria for Judging Generalized Strictly Diagonally Dominant Matrix
ZHANG Jin-song
2015-01-01
Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc. But it is diﬃcult to judge a matrix is or not generalized strictly diagonally dominant matrix. In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.
A comparison of SuperLU solvers on the intel MIC architecture
Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.
2016-10-01
In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.
Diagonalizing sensing matrix of broadband RSE
Sato, Shuichi; Kokeyama, Keiko; Kawazoe, Fumiko; Somiya, Kentaro; Kawamura, Seiji
2006-03-01
For a broadband-operated RSE interferometer, a simple and smart length sensing and control scheme was newly proposed. The sensing matrix could be diagonal, owing to a simple allocation of two RF modulations and to a macroscopic displacement of cavity mirrors, which cause a detuning of the RF modulation sidebands. In this article, the idea of the sensing scheme and an optimization of the relevant parameters will be described.
A hybrid Eulerian-Lagrangian flow solver
Palha, Artur; Ferreira, Carlos Simao; van Bussel, Gerard
2015-01-01
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...
A generalized gyrokinetic Poisson solver
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms.
Lohmann, E.R.M.A.; Borm, P.E.M.; Herings, P.J.J.
2011-01-01
To verify whether a transferable utility game is exact, one has to check a linear inequality for each exact balanced collection of coalitions. This paper studies the structure and properties of the class of exact balanced collections. Comparing the definition of exact balanced collections with the
Diagonal gates in the Clifford hierarchy
Cui, Shawn X.; Gottesman, Daniel; Krishna, Anirudh
2017-01-01
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for prime-dimensional qudits. They turn out to be pmth roots of unity raised to polynomial functions of the basis state to which they are applied, and we determine which level of the Clifford hierarchy a given gate sits in based on m and the degree of the polynomial.
Diagonally non-computable functions and fireworks
Bienvenu, Laurent; Patey, Ludovic
2014-01-01
A set C of reals is said to be negligible if there is no probabilistic algorithm which generates a member of C with positive probability. Various classes have been proven to be negligible, for example the Turing upper-cone of a non-computable real, the class of coherent completions of Peano Arithmetic or the class of reals of minimal degrees. One class of particular interest in the study of negligibility is the class of diagonally non-computable (DNC) functions, proven by Kucera to be non-neg...
Linear optical response of finite systems using multishift linear system solvers.
Hübener, Hannes; Giustino, Feliciano
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Linear optical response of finite systems using multishift linear system solvers
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2010-01-01
The implicit Euler method, normally refered to as the fully implicit (FIM) method, and the implicit pressure explicit saturation (IMPES) method are the traditional choices for temporal discretization in reservoir simulation. The FIM method offers unconditionally stability in the sense of discrete....... Current reservoir simulators apply timestepping algorithms that are based on safeguarded heuristics, and can neither guarantee convergence in the underlying equation solver, nor provide estimates of the relations between convergence, integration error and stepsizes. We establish predictive stepsize...... control applied to high order methods for temporal discretization in reservoir simulation. The family of Runge-Kutta methods is presented and in particular the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method with an embedded error estimate is described. A predictive stepsize adjustment...
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-12-07
architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. Fast multipole-based solvers and preconditioners are demonstrably poised to play a leading role in exascale computing.
Gong, Weiwei; Zhou, Xu
2017-06-01
In Computer Science, the Boolean Satisfiability Problem(SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. SAT is one of the first problems that was proven to be NP-complete, which is also fundamental to artificial intelligence, algorithm and hardware design. This paper reviews the main algorithms of the SAT solver in recent years, including serial SAT algorithms, parallel SAT algorithms, SAT algorithms based on GPU, and SAT algorithms based on FPGA. The development of SAT is analyzed comprehensively in this paper. Finally, several possible directions for the development of the SAT problem are proposed.
An Energy Conserving Parallel Hybrid Plasma Solver
Holmstrom, M
2010-01-01
We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is done in the FLASH software framework. It is shown that the solver conserves energy well over time, and that the parallelization is efficient (it exhibits weak scaling).
An HLLC Solver for Relativistic Flows
Mignone, A
2005-01-01
We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.
Predicting SMT Solver Performance for Software Verification
Andrew Healy
2017-01-01
Full Text Available The Why3 IDE and verification system facilitates the use of a wide range of Satisfiability Modulo Theories (SMT solvers through a driver-based architecture. We present Where4: a portfolio-based approach to discharge Why3 proof obligations. We use data analysis and machine learning techniques on static metrics derived from program source code. Our approach benefits software engineers by providing a single utility to delegate proof obligations to the solvers most likely to return a useful result. It does this in a time-efficient way using existing Why3 and solver installations - without requiring low-level knowledge about SMT solver operation from the user.
Diagonal stripes in the spin glass phase of cuprates
Seibold, G., E-mail: goetz@physik.tu-cottbus.d [Institut fuer Physik, BTU Cottbus, Post Box 101344, 03013 Cottbus (Germany); Lorenzana, J. [SMC-INFM-CNR and Dipartimento di Fisica, Universita di Roma ' La Sapienza' , P.le Aldo Moro 5, I-00185 Roma (Italy)
2010-12-15
Based on the unrestricted Gutzwiller approximation we study the possibility that the diagonal incommensurate spin scattering in the spin glass phase of lanthanum cuprates originates from stripe formation. Similar to the metallic phase two types of diagonal stripe structures appear to be stable: (a) site-centered textures which have one hole per site along the stripe and (b) ferromagnetic stair-case structures which are the diagonal equivalent to bond-centered stripes in the metallic phase and which on average have a filling of 3/4 holes per stripe site. We give a detailed analysis of the stability of both diagonal textures with regard to the vertical ones.
Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity
Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al. I. Cuza' ' , Project IDEI, Iasi (Romania); Irwin, Klee [Quantum Gravity Research, Topanga, CA (United States)
2017-01-15
Geometric methods for constructing exact solutions of equations of motion with first order α{sup '} corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almost-Kaehler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kaehler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories. (orig.)
Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity
Vacaru, Sergiu I.; Irwin, Klee
2017-01-01
Geometric methods for constructing exact solutions of equations of motion with first order α ^' } corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almost-Kähler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kähler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories.
Exact solution of an su(n) spin torus
Hao, Kun; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2016-01-01
The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhomogeneous T-Q relation via the off-diagonal Bethe Ansatz.
Exact solution of an su(n) spin torus
Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2016-07-01
The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhomogeneous T - Q relation via the off-diagonal Bethe Ansatz.
Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays
T. S. Doan
2012-01-01
Full Text Available We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.
Newton-Raphson preconditioner for Krylov type solvers on GPU devices.
Kushida, Noriyuki
2016-01-01
A new Newton-Raphson method based preconditioner for Krylov type linear equation solvers for GPGPU is developed, and the performance is investigated. Conventional preconditioners improve the convergence of Krylov type solvers, and perform well on CPUs. However, they do not perform well on GPGPUs, because of the complexity of implementing powerful preconditioners. The developed preconditioner is based on the BFGS Hessian matrix approximation technique, which is well known as a robust and fast nonlinear equation solver. Because the Hessian matrix in the BFGS represents the coefficient matrix of a system of linear equations in some sense, the approximated Hessian matrix can be a preconditioner. On the other hand, BFGS is required to store dense matrices and to invert them, which should be avoided on modern computers and supercomputers. To overcome these disadvantages, we therefore introduce a limited memory BFGS, which requires less memory space and less computational effort than the BFGS. In addition, a limited memory BFGS can be implemented with BLAS libraries, which are well optimized for target architectures. There are advantages and disadvantages to the Hessian matrix approximation becoming better as the Krylov solver iteration continues. The preconditioning matrix varies through Krylov solver iterations, and only flexible Krylov solvers can work well with the developed preconditioner. The GCR method, which is a flexible Krylov solver, is employed because of the prevalence of GCR as a Krylov solver with a variable preconditioner. As a result of the performance investigation, the new preconditioner indicates the following benefits: (1) The new preconditioner is robust; i.e., it converges while conventional preconditioners (the diagonal scaling, and the SSOR preconditioners) fail. (2) In the best case scenarios, it is over 10 times faster than conventional preconditioners on a CPU. (3) Because it requries only simple operations, it performs well on a GPGPU. In
Quantum Monte Carlo diagonalization method as a variational calculation
Mizusaki, Takahiro; Otsuka, Takaharu [Tokyo Univ. (Japan). Dept. of Physics; Honma, Michio
1997-05-01
A stochastic method for performing large-scale shell model calculations is presented, which utilizes the auxiliary field Monte Carlo technique and diagonalization method. This method overcomes the limitation of the conventional shell model diagonalization and can extremely widen the feasibility of shell model calculations with realistic interactions for spectroscopic study of nuclear structure. (author)
Generalized coordinate Bethe ansatz for non diagonal boundaries
Crampe, N
2011-01-01
We compute the spectrum and the eigenstates of the open XXX model with non-diagonal (triangular) boundary matrices. Since the boundary matrices are not diagonal, the usual coordinate Bethe ansatz does not work anymore, and we use a generalization of it to solve the problem.
Optimization of fuzzy logic analysis by diagonals for pattern recognition
Habiballa, Hashim; Hires, Matej
2017-07-01
The article presents an optimization of the fuzzy logic analysis method for pattern recognition. The enhancements of the original method through the usage of additional two types of pattern components - leftwise diagonal and rightwise diagonal ones. The method is described in theoretical background and further articles show the implementation and experimental verification of the approach.
Navas-Montilla, A.; Murillo, J.
2016-07-01
In this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) [1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the FS solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the FS solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed FS and LFS solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed.
Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver
Shantsev, Daniil V.; Jaysaval, Piyoosh; de la Kethulle de Ryhove, Sébastien; Amestoy, Patrick R.; Buttari, Alfredo; L'Excellent, Jean-Yves; Mary, Theo
2017-06-01
We put forward the idea of using a Block Low-Rank (BLR) multifrontal direct solver to efficiently solve the linear systems of equations arising from a finite-difference discretization of the frequency-domain Maxwell equations for 3-D electromagnetic (EM) problems. The solver uses a low-rank representation for the off-diagonal blocks of the intermediate dense matrices arising in the multifrontal method to reduce the computational load. A numerical threshold, the so-called BLR threshold, controlling the accuracy of low-rank representations was optimized by balancing errors in the computed EM fields against savings in floating point operations (flops). Simulations were carried out over large-scale 3-D resistivity models representing typical scenarios for marine controlled-source EM surveys, and in particular the SEG SEAM model which contains an irregular salt body. The flop count, size of factor matrices and elapsed run time for matrix factorization are reduced dramatically by using BLR representations and can go down to, respectively, 10, 30 and 40 per cent of their full-rank values for our largest system with N = 20.6 million unknowns. The reductions are almost independent of the number of MPI tasks and threads at least up to 90 × 10 = 900 cores. The BLR savings increase for larger systems, which reduces the factorization flop complexity from O(N2) for the full-rank solver to O(Nm) with m = 1.4-1.6. The BLR savings are significantly larger for deep-water environments that exclude the highly resistive air layer from the computational domain. A study in a scenario where simulations are required at multiple source locations shows that the BLR solver can become competitive in comparison to iterative solvers as an engine for 3-D controlled-source electromagnetic Gauss-Newton inversion that requires forward modelling for a few thousand right-hand sides.
An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry
Shiozaki, Toru
2015-01-01
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N > 10000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige-Van Loan algorithm [D. Kressner, BIT 43, 775 (2003)], which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of two than state-of-the-art implementations of complex Hermitian diagonalization; diagonalizing a 12800 x 12800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel MKL's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD license.
GARDNER, P.R.
2006-04-01
Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully
SIERRA framework version 4 : solver services.
Williams, Alan B.
2005-02-01
Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.
An optimal iterative solver for the Stokes problem
Wathen, A. [Univ. of Bristol (United Kingdom); Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
Clock Math — a System for Solving SLEs Exactly
Jakub Hladík
2013-01-01
Full Text Available In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers.
Teleportation of an arbitrary mixture of diagonal states of multiqudit
Du Qian-Hua; Lin Xiu-Min; Chen Zhi-Hua; Lin Gong-Wei; Chen Li-Bo; Gu Yong-Jian
2008-01-01
This paper proposes a scheme to teleport an arbitrary mixture of diagonal states of multiqutrit via classical correlation and classical communication. To teleport an arbitrary mixture of diagonal states of N qutrits, N classically correlated pairs of two qutrits are used as channel. The sender (Alice) makes Fourier transform and conditional gate (i.e., XOR(3) gate) on her qutrits and does measurement in appropriate computation bases. Then she sends N ctrits to the receiver (Bob). Based on the received information, Bob performs the corresponding unitary transformation on his qutrits and obtains the teleported state. Teleportation of an arbitrary mixture of diagonal states of multiqudit is also discussed.
NONLINEAR BENDING THEORY OF DIAGONAL SQUARE PYRAMID RETICULATED SHALLOW SHELLS
肖潭; 刘人怀
2001-01-01
Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle .
Diagonal representation for a generic matrix valued quantum Hamiltonian
Gosselin, Pierre [Universite Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF UFR de Mathematiques, BP74, Saint Martin d' Heres Cedex (France); Mohrbach, Herve [Universite Paul Verlaine-Metz, Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Metz Cedex 3 (France)
2009-12-15
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields. (orig.)
Singleton, Jr., Robert [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Israel, Daniel M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Doebling, Scott William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Woods, Charles Nathan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kaul, Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Walter, Jr., John William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rogers, Michael Lloyd [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Na, Y. W.; Park, C. E.; Lee, S. Y. [KOPEC, Daejeon (Korea, Republic of)
2009-10-15
reliability. The main object of this work is not to investigate the whole transient behavior of the models at hand but to focus on the behavior of numerical solutions part of the sparse asymmetric matrix equations in the transient of hydraulic system. It is outside of the scope of this work to improve the diagonal dominance or to pre-condition the matrix in the process of differencing and linearizing the governing equation, even though it is better to do it that way before applying the solver if there is any efficient way available.
Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave with the ......We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave...... with the well-studied corresponding hierarchies defined using ordinary threshold gates. A major open problem in Boolean circuit complexity is to provide an explicit super-polynomial lower bound for depth two threshold circuits. We identify the class of depth two exact threshold circuits as a natural subclass...
Phase Selection Heuristics for Satisfiability Solvers
Chen, Jingchao
2011-01-01
In general, a SAT Solver based on conflict-driven DPLL consists of variable selection, phase selection, Boolean Constraint Propagation, conflict analysis, clause learning and its database maintenance. Optimizing any part of these components can enhance the performance of a solver. This paper focuses on optimizing phase selection. Although the ACE (Approximation of the Combined lookahead Evaluation) weight is applied to a lookahead SAT solver such as March, so far, no conflict-driven SAT solver applies successfully the ACE weight, since computing the ACE weight is time-consuming. Here we apply the ACE weight to partial phase selection of conflict-driven SAT solvers. This can be seen as an improvement of the heuristic proposed by Jeroslow-Wang (1990). We incorporate the ACE heuristic and the existing phase selection heuristics in the new solver MPhaseSAT, and select a phase heuristic in a way similar to portfolio methods. Experimental results show that adding the ACE heuristic can improve the conflict-driven so...
Improved Stiff ODE Solvers for Combustion CFD
Imren, A.; Haworth, D. C.
2016-11-01
Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. In this work, a fresh look at stiff ODE solvers is taken that includes how the solver is integrated into a turbulent combustion CFD code, and the advantages of extrapolation-based solvers in this regard are demonstrated. Benefits in CPU time and accuracy are demonstrated for homogeneous systems and compression-ignition engines, for chemical mechanisms that range in size from fewer than 50 to more than 7,000 species.
EXTREME POINTS IN DIAGONAL-DISJOINT IDEALS OF NEST ALGEBRAS
董浙; 鲁世杰
2002-01-01
In this paper, the extreme points of the unit ball of diagonal-disjoint ideals in nest algebras are characterized completely; Furthermore, it is shown that every extreme point of the unit ball of 2 has essential-norm one.
Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups
Bergeron, Francois
2011-01-01
For finite complex reflexion groups, we consider the graded $W$-modules of diagonally harmonic polynomials in $r$ sets of variables, and show that associated Hilbert series may be described in a global manner, independent of the value of $r$.
Multivariable Decoupling Control System Based on Generalized Diagonal Dominance
S. Jamebozorg
2015-03-01
Full Text Available In this paper, the design of static precompensator for the reduction of interaction in linear multivariable systems is proposed. In the previous studies, the diagonal dominance of systems in special frequency range has been less paid attention to. In the proposed method, some static compensators with matrix coefficients are combined so that the final static compensator can make system diagonal dominance in a wide range of frequencies. These coefficients are obtained with optimization algorithm. In this method, to achieve diagonal dominance with less conservativeness, the criterion of generalized diagonal dominance is used. The proposed method does not have any limitation for systems with high interaction or non-minimum phase systems. In comparison with some common methods, it has a simpler structure with easy implementation. Simulation examples demonstrate the usefulness of the proposed method
Online blind source separation based on joint diagonalization
Li Ronghua; Zhou Guoxu; Fang Zuyuan; Xie Shengli
2009-01-01
A now algorithm is proposed for joint diagonalization. With a modified objective function, the now algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation (BSS) for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.
Self-excitation of a diagonal MHD channel
Doperchuk, I.I.; Koneyev, S.M.A.
1982-01-01
Questions are examined of self-excitation of a diagonal MHD channel. Conditions are obtained for self-excitation using 0-dimensional approximation. An algorithm is presented for calculating the optimal self-exciting diagonal channel with regard for development and separation of the boundary layers, presence of near-electrode drops in voltage. Graphs are presented for the transitional regimes of channel operation with intermediate point of connection of the excitation winding.
Exactly Solvable Quantum Mechanics
Sasaki, Ryu
2014-01-01
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Discriminative Block-Diagonal Representation Learning for Image Recognition.
Zhang, Zheng; Xu, Yong; Shao, Ling; Yang, Jian
2017-07-04
Existing block-diagonal representation studies mainly focuses on casting block-diagonal regularization on training data, while only little attention is dedicated to concurrently learning both block-diagonal representations of training and test data. In this paper, we propose a discriminative block-diagonal low-rank representation (BDLRR) method for recognition. In particular, the elaborate BDLRR is formulated as a joint optimization problem of shrinking the unfavorable representation from off-block-diagonal elements and strengthening the compact block-diagonal representation under the semisupervised framework of LRR. To this end, we first impose penalty constraints on the negative representation to eliminate the correlation between different classes such that the incoherence criterion of the extra-class representation is boosted. Moreover, a constructed subspace model is developed to enhance the self-expressive power of training samples and further build the representation bridge between the training and test samples, such that the coherence of the learned intraclass representation is consistently heightened. Finally, the resulting optimization problem is solved elegantly by employing an alternative optimization strategy, and a simple recognition algorithm on the learned representation is utilized for final prediction. Extensive experimental results demonstrate that the proposed method achieves superb recognition results on four face image data sets, three character data sets, and the 15 scene multicategories data set. It not only shows superior potential on image recognition but also outperforms the state-of-the-art methods.
Chatterjee, Arghya; Nayak, Tapan K; Sahoo, Nihar Ranjan
2016-01-01
Susceptibilities of conserved quantities, such as baryon number, strangeness and electric charge are sensitive to the onset of quantum chromodynamics (QCD) phase transition and are expected to provide information on the matter produced in heavy-ion collision experiments. A comprehensive study of the second-order diagonal susceptibilities and cross correlations has been made within a thermal model approach of the hadron resonance gas (HRG) model as well as with a hadronic transport model, UrQMD. We perform a detailed analysis of the effect of detector acceptances and choice of particle species in the experimental measurements of the susceptibilities for heavy-ion collisions corresponding to \\sNN = 4 GeV to 200 GeV. The transverse momentum cutoff dependence of suitably normalised susceptibilities are proposed as useful observables to probe the properties of the medium at freezeout.
Chatterjee, Arghya; Chatterjee, Sandeep; Nayak, Tapan K.; Ranjan Sahoo, Nihar
2016-12-01
Susceptibilities of conserved quantities, such as baryon number, strangeness and electric charge are sensitive to the onset of quantum chromodynamics phase transition, and are expected to provide information on the matter produced in heavy-ion collision experiments. A comprehensive study of the second order diagonal susceptibilities and cross correlations has been made within a thermal model approach of the hadron resonance gas model as well as with a hadronic transport model, ultra-relativistic quantum molecular dynamics. We perform a detailed analysis of the effect of detector acceptances and choice of particle species in the experimental measurements of the susceptibilities for heavy-ion collisions corresponding to \\sqrt{{s}{NN}} = 4 GeV to 200 GeV. The transverse momentum cutoff dependence of suitably normalised susceptibilities are proposed as useful observables to probe the properties of the medium at freezeout.
A Taxonomy of Exact Methods for Partial Max-SAT
Mohamed El Bachir Menai; Tasniem Nasser Al-Yahya
2013-01-01
Partial Maximum Boolean Satisfiability (Partial Max-SAT or PMSAT) is an optimization variant of Boolean satisfiability (SAT) problem,in which a variable assignment is required to satisfy all hard clauses and a maximum number of soft clauses in a Boolean formula.PMSAT is considered as an interesting encoding domain to many real-life problems for which a solution is acceptable even if some constraints are violated.Amongst the problems that can be formulated as such are planning and scheduling.New insights into the study of PMSAT problem have been gained since the introduction of the Max-SAT evaluations in 2006.Indeed,several PMSAT exact solvers have been developed based mainly on the DavisPutnam-Logemann-Loveland (DPLL) procedure and Branch and Bound (B&B) algorithms.In this paper,we investigate and analyze a number of exact methods for PMSAT.We propose a taxonomy of the main exact methods within a general framework that integrates their various techniques into a unified perspective.We show its effectiveness by using it to classify PMSAT exact solvers which participated in the 2007～2011 Max-SAT evaluations,emphasizing on the most promising research directions.
Auditory spatial resolution in horizontal, vertical, and diagonal planes.
Grantham, D Wesley; Hornsby, Benjamin W Y; Erpenbeck, Eric A
2003-08-01
Minimum audible angle (MAA) and minimum audible movement angle (MAMA) thresholds were measured for stimuli in horizontal, vertical, and diagonal (60 degrees) planes. A pseudovirtual technique was employed in which signals were recorded through KEMAR's ears and played back to subjects through insert earphones. Thresholds were obtained for wideband, high-pass, and low-pass noises. Only 6 of 20 subjects obtained wideband vertical-plane MAAs less than 10 degrees, and only these 6 subjects were retained for the complete study. For all three filter conditions thresholds were lowest in the horizontal plane, slightly (but significantly) higher in the diagonal plane, and highest for the vertical plane. These results were similar in magnitude and pattern to those reported by Perrott and Saberi [J. Acoust. Soc. Am. 87, 1728-1731 (1990)] and Saberi and Perrott [J. Acoust. Soc. Am. 88, 2639-2644 (1990)], except that these investigators generally found that thresholds for diagonal planes were as good as those for the horizontal plane. The present results are consistent with the hypothesis that diagonal-plane performance is based on independent contributions from a horizontal-plane system (sensitive to interaural differences) and a vertical-plane system (sensitive to pinna-based spectral changes). Measurements of the stimuli recorded through KEMAR indicated that sources presented from diagonal planes can produce larger interaural level differences (ILDs) in certain frequency regions than would be expected based on the horizontal projection of the trajectory. Such frequency-specific ILD cues may underlie the very good performance reported in previous studies for diagonal spatial resolution. Subjects in the present study could apparently not take advantage of these cues in the diagonal-plane condition, possibly because they did not externalize the images to their appropriate positions in space or possibly because of the absence of a patterned visual field.
Fidelity of the diagonal ensemble signals the many-body localization transition
Hu, Taotao; Xue, Kang; Li, Xiaodan; Zhang, Yan; Ren, Hang
2016-11-01
In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transition in a random-field Heisenberg chain. We demonstrate that the fidelity and fidelity susceptibility can be utilized to characterize the interaction-driven many-body localization transition in this closed spin system which is in agreement with previous analytical and numerical results [S. Garnerone, N. T. Jacobson, S. Haas, and P. Zanardi, Phys. Rev. Lett. 102, 057205 (2009), 10.1103/PhysRevLett.102.057205; P. Zanardi and N. Paunkovic, Phys. Rev. E 74, 031123 (2006), 10.1103/PhysRevE.74.031123]. In particular, instead of ground-state fidelity, we test the fidelity between two diagonal ensembles related by a small parameter perturbation δ h , it is special that here the parameter perturbation δ hi for each site are random variables like hi. It shows that fidelity of the diagonal ensemble develop a pronounced drop at the transition. We utilize fidelity to estimate the critical disorder strength hc for different system size, we get hc∈ [2.5,3.9] and get a power-law decay with an exponent of roughly -1.49 (2 ) for system size N , and can extrapolate hcinf of the infinite system is about 2.07 which all agree with a recent work by Huse and Pal, in which the MBL transition in the same model was predicted to be hc [2,4]. We also estimate the scaling of maximum of averaged fidelity susceptibility as a function of system size N , it shows a power law increase with an exponent of about 5.05(1).
A Novel Preconditioner for Electromagnetic Solvers
无
2006-01-01
A novel preconditioning scheme for electromagnetic scattering solver is presented to improve the convergence of the iterative solver for the linear system resulted by the integral quations. Its kernel idea is the selection of the main contribution of the matrix elements, which affect the matrix condition number the most. We employ the important part similar to the near-field to build the preconditioning matrix. A parameter delta is given to control the balance between the computational expense to get the preconditioner and the effectiveness of the preconditioner. A practical selection of the control parameter delta of the preconditioner is discussed, which indicates the preconditioner is effective in conjunction with a BiCGstab(l) solver.
New iterative solvers for the NAG Libraries
Salvini, S.; Shaw, G. [Numerical Algorithms Group Ltd., Oxford (United Kingdom)
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Modification of Ordinary Differential Equations MATLAB Solver
E. Cocherova
2003-12-01
Full Text Available Various linear or nonlinear electronic circuits can be described bythe set of ordinary differential equations (ODEs. The ordinarydifferential equations can be solved in the MATLAB environment inanalytical (symbolic toolbox or numerical way. The set of nonlinearODEs with high complexity can be usually solved only by use ofnumerical integrator (solver. The modification of ode23 MATLABnumerical solver has been suggested in this article for the applicationin solution of some special cases of ODEs. The main feature of thismodification is that the solution is found at every prescribed point,in which the special behavior of system is anticipated. Theextrapolation of solution is not allowed in those points.
Net efficiency of roller skiing with a diagonal stride.
Nakai, Akira; Ito, Akira
2011-02-01
The aims of this study were: (a) to determine net efficiency during roller skiing with a diagonal stride at various speeds; (b) to assess the development of net efficiency across speeds; and (c) to examine the characteristics of efficiency in diagonal roller skiing. Two-dimensional kinematics and oxygen uptake were determined in eight male collegiate cross-country ski athletes who roller skied with the diagonal stride at various speeds on a level track. Net efficiency was calculated from rates of internal and external work and net energy expenditure. Individual net efficiency ranged from 17.7% to 52.1%. Net efficiency in the entire group of athletes increased with increasing speed, reached a maximum value of 37.3% at 3.68 m · s(-1), before slowly decreasing. These findings indicate that roller skiing with the diagonal stride at high speed is a highly efficient movement and that an optimal speed exists at which net efficiency can be maximally enhanced in diagonal roller skiing.
Seismic Behavior of Steel Off-Diagonal Bracing System (ODBS Utilized in Reinforced Concrete Frame
Keyvan Ramin
2014-01-01
Full Text Available The introduction of an eccentricity in this system results in a geometric nonlinearity behavior. The midpoint of the diagonal member is connected to the corner joint using a brace member with a relatively low stiffness, thus forming a three-member bracing system in each braced panel. An iterative method of analysis has been developed to study the nonlinear load-deflection behavior of ODBS. The results indicate that the load-deflection behavior of this system follows a nonlinear stiffness-hardening pattern with two yielding points, which reflect the tensile failure of different bracings; the present study aims to investigate the efficiency of applying off-diagonal steel braces to reinforced concrete frames. To achieve this, three types of 2-story, 6-story, and 15-story structures without and with X-bracing and off-center bracing systems were modeled using SAP2000 software, and for micromodeling ANSYS software was used to achieve finite element results for an exact comparison between various retrofitting systems. The results showed that the structures strengthened by toggle bracing system revealed better behavior for low oscillation periods. Moreover, this type of bracing system is quite suitable for 10-story structures but not for higher ones. Its main problem, which requires special contrivances to solve, is the existence of a soft ground floor.
VDJSeq-Solver: in silico V(DJ recombination detection tool.
Giulia Paciello
Full Text Available In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(DJ rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/.
Exact Verification of Hybrid Systems Based on Bilinear SOS Representation
Yang, Zhengfeng; Lin, Wang
2012-01-01
In this paper, we address the problem of safety verification of nonlinear hybrid systems and stability analysis of nonlinear autonomous systems. A hybrid symbolic-numeric method is presented to compute exact inequality invariants of hybrid systems and exact estimates of regions of attraction of autonomous systems efficiently. Some numerical invariants of a hybrid system or an estimate of region of attraction can be obtained by solving a bilinear SOS program via PENBMI solver or iterative method, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact polynomial invariants and estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.
Analytical diagonalization study of a two-orbital Hubbard model on a two-site molecule
Amendola, Maria Emilia, E-mail: canio@sa.infn.it [Dipartimento di Matematica, Università di Salerno, I-84084 Fisciano (Italy); Romano, Alfonso [CNR-SPIN, I-84084 Fisciano (Italy); Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, I-84084 Fisciano (Italy); Noce, Canio, E-mail: canio@sa.infn.it [CNR-SPIN, I-84084 Fisciano (Italy); Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, I-84084 Fisciano (Italy)
2015-12-15
We present the exact solution of a two-orbital Hubbard model on a two-site molecule for arbitrary electron filling and arbitrary interaction couplings. The knowledge of the many-particle spectrum, determined via a diagonalization procedure performed by fully taking into account the symmetry properties of the model, has been used to investigate the temperature dependence of charge, spin and orbital response functions as well as of the intra- and inter-orbital on-site occupations. We point out that this study may allow easy access to many interesting features of the model and may serve as a reference tool for various numerical or perturbation methods dealing with complex correlated electron models defined on a lattice, in particular in the case in which strong local interactions dominate over kinetic effects.
On exactly conservative integrators
Bowman, J.C. [Max-Planck-Inst. fuer Plasmaphysik, Garching (Germany); Shadwick, B.A. [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Morrison, P.J. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1997-06-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. The authors discuss a general approach for developing explicit algorithms that conserve such invariants exactly. They illustrate the method by applying it to the truncated two-dimensional Euler equations.
On exactly conservative integrators
Bowman, J.C. [Max-Planck-Inst. fuer Plasmaphysik, Garching (Germany); Shadwick, B.A. [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Morrison, P.J. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1997-06-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. The authors discuss a general approach for developing explicit algorithms that conserve such invariants exactly. They illustrate the method by applying it to the truncated two-dimensional Euler equations.
A mimetic spectral element solver for the Grad-Shafranov equation
Palha, A.; Koren, B.; Felici, F.
2016-07-01
In this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in [56] to the solution of the Grad-Shafranov equation. This approach combines a finite volume discretization with the mixed finite element method. In this way the discrete differential operators (∇, ∇×, ∇ṡ) can be represented exactly and metric and all approximation errors are present in the constitutive relations. The result of this formulation is an arbitrary order method even on highly curved meshes. Additionally, the integral of the toroidal current Jϕ is exactly equal to the boundary integral of the poloidal field over the plasma boundary. This property can play an important role in the coupling between equilibrium and transport solvers. The proposed solver is tested on a varied set of plasma cross sections (smooth and with an X-point) and also for a wide range of pressure and toroidal magnetic flux profiles. Equilibria accurate up to machine precision are obtained. Optimal algebraic convergence rates of order p + 1 and geometric convergence rates are shown for Soloviev solutions (including high Shafranov shifts), field-reversed configuration (FRC) solutions and spheromak analytical solutions. The robustness of the method is demonstrated for non-linear test cases, in particular on an equilibrium solution with a pressure pedestal.
Novel Scalable 3-D MT Inverse Solver
Kuvshinov, A. V.; Kruglyakov, M.; Geraskin, A.
2016-12-01
We present a new, robust and fast, three-dimensional (3-D) magnetotelluric (MT) inverse solver. As a forward modelling engine a highly-scalable solver extrEMe [1] is used. The (regularized) inversion is based on an iterative gradient-type optimization (quasi-Newton method) and exploits adjoint sources approach for fast calculation of the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT (single-site and/or inter-site) responses, and supports massive parallelization. Different parallelization strategies implemented in the code allow for optimal usage of available computational resources for a given problem set up. To parameterize an inverse domain a mask approach is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to high-performance clusters demonstrate practically linear scalability of the code up to thousands of nodes. 1. Kruglyakov, M., A. Geraskin, A. Kuvshinov, 2016. Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method, Computers and Geosciences, in press.
Bjørner, Nikolaj; Dung, Phan Anh; Fleckenstein, Lars
2015-01-01
vZ is a part of the SMT solver Z3. It allows users to pose and solve optimization problems modulo theories. Many SMT applications use models to provide satisfying assignments, and a growing number of these build on top of Z3 to get optimal assignments with respect to objective functions. vZ provi...
Exact solutions and ladder operators for a new anharmonic oscillator
Dong Shihai [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico DF (Mexico)]. E-mail: dongsh2@yahoo.com; Sun Guohua [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, UNAM, A.P. 20-726, Del. Alvaro Obregon, 01000 Mexico DF (Mexico); Lozada-Cassou, M. [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico DF (Mexico)
2005-06-06
In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrodinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r->ir.
Diagonal invariant ideals of Toeplitz algebras on discrete groups
许庆祥
2002-01-01
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable is clarified. It is proved that when G is Abelian, a closed two-sided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given.
Diagonal Limit for Conformal Blocks in d Dimensions
Hogervorst, Matthijs; Rychkov, Slava
2013-01-01
Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.
Diagonally loaded SMI algorithm based on inverse matrix recursion
Cao Jianshu; Wang Xuegang
2007-01-01
The derivation of a diagonally loaded sample-matrix inversion (LSMI) algorithm on the busis of inverse matrix recursion (i.e. LSMI-IMR algorithm) is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, acorresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings.Simulations show that the LSMI-IMR algorithm is valid.
Benchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization
Markovich, Thomas; Sanders, Jacob N; Aspuru-Guzik, Alan
2015-01-01
Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in order to discover when and how each method can be used most profitably. We find that filter diagonalization provides the best results for Lorentzian signals, while compressed sensing and super-resolution perform better for arbitrary signals.
An exact Riemann-solver-based solution for regular shock refraction
Delmont, P.; Keppens, R.; van der Holst, B.
2009-01-01
We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest. When the shock impinges on the density discontinuity, it refracts, and in the hydrodynamical case three signals arise. Regular refraction means that these signals meet at a si
An exact Riemann-solver-based solution for regular shock refraction
Delmont, P.; Keppens, R.; van der Holst, B.
2009-01-01
We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest. When the shock impinges on the density discontinuity, it refracts, and in the hydrodynamical case three signals arise. Regular refraction means that these signals meet at a
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung
1996-01-01
The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.
A fast, high-order solver for the Grad–Shafranov equation
Pataki, Andras, E-mail: apataki@apataki.net [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States); Cerfon, Antoine J., E-mail: cerfon@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States); Freidberg, Jeffrey P., E-mail: jpfreid@mit.edu [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Greengard, Leslie, E-mail: greengard@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States); O’Neil, Michael, E-mail: oneil@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States)
2013-06-15
We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.
Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew
2013-11-01
A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of the fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/lubz/afmpb.html for updates and changes. Running time: The running time varies with the number of discretized elements (N) in the system and their distributions. In most cases, it scales linearly as a function of N.
Izdebski, Marek
2006-11-10
An analytical approach is presented for studying the convergence of the general Jacobi method applied to diagonalizing the second-rank tensors that describe the optical properties of a medium subjected to an external field. This approach utilizes the fact that the components of such tensors are usually given in field-free principal axes as power series in the field strength, neglecting terms beyond a chosen power of the field. It is shown that for a biaxial or uniaxial medium, the finite number of iterations, which guarantees exact reduction of all the initial terms up to the required power in the series expansions of all off-diagonal elements, can always be found. Moreover, a fixed sequence of rotations in the Jacobi algorithm can be predicted. These findings allow one to derive analytical formulas in noniterative form for a given highest order of the effects being considered and also to optimize numerical iterative diagonalization procedures. Formulas for eigenvalues and eigenvectors applicable to biaxial and uniaxial mediums perturbed by the linear and quadratic effects are presented. Illustrations are given of the electro-optic and piezo-optic effects for the point group 3m. Conditions for biaxial and uniaxial perturbation of a uniaxial crystal are discussed.
Exact Relativistic 'Antigravity' Propulsion
Felber, F S
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Penguins and Pandas: A Note on Teaching Cantor's Diagonal Argument
Rauff, James V.
2008-01-01
Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…
Convergence of GAOR Iterative Method with Strictly Diagonally Dominant Matrices
Guangbin Wang
2011-01-01
Full Text Available We discuss the convergence of GAOR method for linear systems with strictly diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006, Tian et al. (2008 by using three numerical examples.
Why the South Pacific Convergence Zone is diagonal
van der Wiel, Karin; Matthews, Adrian J.; Joshi, Manoj M.; Stevens, David P.
2016-03-01
During austral summer, the majority of precipitation over the Pacific Ocean is concentrated in the South Pacific Convergence Zone (SPCZ). The surface boundary conditions required to support the diagonally (northwest-southeast) oriented SPCZ are determined through a series of experiments with an atmospheric general circulation model. Continental configuration and orography do not have a significant influence on SPCZ orientation and strength. The key necessary boundary condition is the zonally asymmetric component of the sea surface temperature (SST) distribution. This leads to a strong subtropical anticyclone over the southeast Pacific that, on its western flank, transports warm moist air from the equator into the SPCZ region. This moisture then intensifies (diagonal) bands of convection that are initiated by regions of ascent and reduced static stability ahead of the cyclonic vorticity in Rossby waves that are refracted toward the westerly duct over the equatorial Pacific. The climatological SPCZ is comprised of the superposition of these diagonal bands of convection. When the zonally asymmetric SST component is reduced or removed, the subtropical anticyclone and its associated moisture source is weakened. Despite the presence of Rossby waves, significant moist convection is no longer triggered; the SPCZ disappears. The diagonal SPCZ is robust to large changes (up to ±6 °C) in absolute SST (i.e. where the SST asymmetry is preserved). Extreme cooling (change <-6 °C) results in a weaker and more zonal SPCZ, due to decreasing atmospheric temperature, moisture content and convective available potential energy.
Green function diagonal for a class of heat equations
Kwiatkowski, Grzegorz
2011-01-01
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expression in the case of finite-gap potential coefficient of the heat equation are constructed.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
Penile torsion correction by diagonal corporal plication sutures
Brent W. Snow
2009-02-01
Full Text Available Penile torsion is commonly encountered. It can be caused by skin and dartos adherence or Buck’s fascia attachments. The authors suggest a new surgical approach to solve both problems. If Buck’s fascia involvement is demonstrated by artificial erection then a new diagonal corporal plication suture is described to effectively solve this problem.
Tamil Nadu and the Diagonal Divide in Sex Ratios
A.S. Bedi (Arjun Singh); S. Srinivasan (Sharada)
2009-01-01
textabstractBetween 1961 and 2001, India’s 0-6 sex ratio has steadily declined. Despite evidence to the contrary, this ratio is often characterised in terms of a diagonal divide with low 0-6 sex ratios in northern and western India and normal 0-6 sex ratios in eastern and southern India. While unexp
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
Exact exchange with non-orthogonal generalized Wannier functions
Mountjoy, Jeff; Todd, Michelle; Mosey, Nicholas J.
2017-03-01
The evaluation of exact exchange (EXX) is an important component of quantum chemical calculations performed with ab initio and hybrid density functional methods. While evaluating exact exchange is routine in molecular quantum chemical calculations performed with localized basis sets, the non-local nature of the exchange operator presents a major impediment to the efficient use of exact exchange in calculations that employ planewave basis sets. Non-orthogonal generalized Wannier functions (NGWFs) corresponding to planewave expansions of localized basis functions are an alternative form of basis set that can be used in quantum chemical calculations. The periodic nature of these functions renders them suitable for calculations of periodic systems, while the contraction of sets of planewaves into individual basis functions reduces the number of variational parameters, permitting the construction and direct diagonalization of the Fock matrix. The present study examines how NGWFs corresponding to Fourier series representations of conventional atom-centered basis sets can be used to evaluate exact exchange in periodic systems. Specifically, an approach for constructing the exchange operator with NGWFs is presented and used to perform Hartree-Fock calculations with a series of molecules in periodically repeated simulation cells. The results demonstrate that the NGWF approach is significantly faster than the EXX method, which is a standard approach for evaluating exact exchange in periodic systems.
Mathematical programming solver based on local search
Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain
2014-01-01
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...
Aleph Field Solver Challenge Problem Results Summary
Hooper, Russell [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.
Integrating Standard Dependency Schemes in QCSP Solvers
Ji-Wei Jin; Fei-Fei Ma; Jian Zhang
2012-01-01
Quantified constraint satisfaction problems (QCSPs) are an extension to constraint satisfaction problems (CSPs) with both universal quantifiers and existential quantifiers.In this paper we apply variable ordering heuristics and integrate standard dependency schemes in QCSP solvers.The technique can help to decide the next variable to be assigned in QCSP solving.We also introduce a new factor into the variable ordering heuristics:a variable's dep is the number of variables depending on it.This factor represents the probability of getting more candidates for the next variable to be assigned.Experimental results show that variable ordering heuristics with standard dependency schemes and the new factor dep can improve the performance of QCSP solvers.
Implicit compressible flow solvers on unstructured meshes
Nagaoka, Makoto; Horinouchi, Nariaki
1993-09-01
An implicit solver for compressible flows using Bi-CGSTAB method is proposed. The Euler equations are discretized with the delta-form by the finite volume method on the cell-centered triangular unstructured meshes. The numerical flux is calculated by Roe's upwind scheme. The linearized simultaneous equations with the irregular nonsymmetric sparse matrix are solved by the Bi-CGSTAB method with the preconditioner of incomplete LU factorization. This method is also vectorized by the multi-colored ordering. Although the solver requires more computational memory, it shows faster and more robust convergence than the other conventional methods: three-stage Runge-Kutta method, point Gauss-Seidel method, and Jacobi method for two-dimensional inviscid steady flows.
On an exactly solvable many-fermion model
Zettili, N. [Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia); Bouayd, N. [Institut de Physique, Universite de Blida, Blida, (Algeria)
1998-12-31
We deal with the construction of a simple many-fermion model that can be solved exactly. This model provides a useful testing ground for studying the accuracy of many-body approximation methods. The model consists of a system of two distinguishable, one- dimensional sets of fermions interacting via a schematic two-body force. We construct the model`s Hamiltonian by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(2, 1) group. Due to a built-in symmetry, the size of the Hamiltonian`s matrix is finite; the diagonalization of the Hamiltonian yields exact values for the energy spectrum. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd) 3 refs., 1 tab., E-mail: nzettili/dpc.kfupm.edu.sa
Chemical Mechanism Solvers in Air Quality Models
John C. Linford
2011-09-01
Full Text Available The solution of chemical kinetics is one of the most computationally intensivetasks in atmospheric chemical transport simulations. Due to the stiff nature of the system,implicit time stepping algorithms which repeatedly solve linear systems of equations arenecessary. This paper reviews the issues and challenges associated with the construction ofefficient chemical solvers, discusses several families of algorithms, presents strategies forincreasing computational efficiency, and gives insight into implementing chemical solverson accelerated computer architectures.
AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation
Koehl, Patrice; Delarue, Marc
2010-01-01
the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
Koehl, Patrice; Delarue, Marc
2010-02-14
solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.
Systematically improvable multiscale solver for correlated electron systems
Kananenka, Alexei A.; Gull, Emanuel; Zgid, Dominika
2015-03-01
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe a framework for a general multiscale method based on embedding a self-energy of a strongly correlated subsystem into a self-energy generated by a method able to treat large weakly correlated systems approximately. As an example, we present the embedding of an exact diagonalization self-energy into a self-energy generated from self-consistent second-order perturbation theory. Using a quantum impurity model, generated from a cluster dynamical mean field approximation to the two-dimensional Hubbard model, as a benchmark, we illustrate that our method allows us to obtain accurate results at a fraction of the cost of typical Monte Carlo calculations. We test the method in multiple regimes of interaction strengths and dopings of the model. The general embedding framework we present avoids difficulties such as double counting corrections, frequency-dependent interactions, or vertex functions. As it is solely formulated at the level of the single-particle Green's function, it provides a promising route for the simulation of realistic materials that are currently difficult to study with other methods.
A multigrid solver for the semiconductor equations
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
Exactly conservation integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J. [Univ. of Texas, Austin, TX (United States)
1999-03-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants. In this work the authors present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly. They illustrate the method by applying it to the three-wave truncation of the Euler equations, the Lotka-Volterra predator-prey model, and the Kepler problem. The ideas are discussed in the context of symplectic (phase-space-conserving) integration methods as well as nonsymplectic conservative methods. They comment on the application of the method to general conservative systems.
Exactly conservative integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Exactly conservative integrators
Shadwick, B A; Morrison, P J; Bowman, John C
1995-01-01
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Exactly conservative integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Localization & Exact Holography
Dabholkar, Atish; Murthy, Sameer
2011-01-01
We consider the AdS_2/CFT_1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory. The boundary partition function of CFT_1 is given by the known quantum degeneracies of these black holes. The bulk partition function is given by a functional integral over string fields in AdS_2. Using recent results on localization we reduce the infinite-dimensional functional integral to a finite number of ordinary integrals over a space of localizing instantons. Under reasonable assumptions about the relevant terms in the effective action, these integrals can be evaluated exactly to obtain a bulk partition function. It precisely reproduces all terms in the exact Rademacher expansion of the boundary partition function as nontrivial functions of charges except for the Kloosterman sum which can in principle follow from an analysis of phases in the background of orbifolded instantons. Our results can be regarded as a step ...
Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
Dunajski, Maciej
2016-01-01
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non--diagonal Bianchi type VIII Einstein metrics with self--dual Weyl tensor.
Diagonal multi-soliton matrix elements in finite volume
Pálmai, T
2012-01-01
We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Tak\\'acs which were only valid for diagonal scattering. In order to test the conjecture we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Natures of Rotating Stall Cell in a Diagonal Flow Fan
N. SHIOMI; K. KANEKO; T. SETOGUCHI
2005-01-01
In order to clarify the natures of a rotating stall cell, the experimental investigation was carried out in a high specific-speed diagonal flow fan. The pressure field on the casing wall and the velocity fields at the rotor inlet and outlet were measured under rotating stall condition with a fast response pressure transducer and a single slant hot-wire probe, respectively. The data were processed using the "Double Phase-Locked Averaging (DPLA)"technique, which enabled to obtain the unsteady flow field with a rotating stall cell in the relative co-ordinate system fixed to the rotor. As a result, the structure and behavior of the rotating stall cell in a high specific-speed diagonal flow fan were shown.
GEAR CRACK EARLY DIAGNOSIS USING BISPECTRUM DIAGONAL SLICE
无
2003-01-01
A study of bispectral analysis in gearbox condition monitoring is presented.The theory of bispectrum and quadratic phase coupling (QPC) is first introduced, and then equations for computing bispectrum slices are obtained.To meet the needs of online monitoring, a simplified method of computing bispectrum diagonal slice is adopted.Industrial gearbox vibration signals measured from normal and tooth cracked conditions are analyzed using the above method.Experiments results indicate that bispectrum can effectively suppress the additive Gaussian noise and chracterize the QPC phenomenon.It is also shown that the 1-D bispectrum diagonal slice can capture the non-Gaussian and nonlinear feature of gearbox vibration when crack occurred, hence, this method can be employed to gearbox real time monitoring and early diagnosis.
Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory
Gramsch, Christian; Balzer, Karsten; Eckstein, Martin; Kollar, Marcus
2013-12-01
We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Construction of an exactly solvable model of the many-body problem
Zettili, N. [King Fahd Univ. of Petrolium and Minerals, Dhahran (Saudi Arabia). Dept. of Phys.]|[Institut de Physique, Universite de Blida, Blida (Algeria); Bouayad, N. [Institut de Physique, Universite de Blida, Blida (Algeria)
1996-11-11
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model`s Hamiltonian by means of vector operators that are the generators of an SO(2,1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum. (orig.).
Construction of an exactly solvable model of the many-body problem
Zettili, Nouredine; Bouayad, Nouredine
1996-02-01
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model's Hamiltonian by means of vector operators that are the generators of an SO(2, 1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum.
Parallel preconditioning techniques for sparse CG solvers
Basermann, A.; Reichel, B.; Schelthoff, C. [Central Institute for Applied Mathematics, Juelich (Germany)
1996-12-31
Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial differential equations. The large size and the condition of many technical or physical applications in this area result in the need for efficient parallelization and preconditioning techniques of the CG method. In particular for very ill-conditioned matrices, sophisticated preconditioner are necessary to obtain both acceptable convergence and accuracy of CG. Here, we investigate variants of polynomial and incomplete Cholesky preconditioners that markedly reduce the iterations of the simply diagonally scaled CG and are shown to be well suited for massively parallel machines.
Strong Linear Correlation Between Eigenvalues and Diagonal Matrix Elements
Shen, J J; Zhao, Y M; Yoshinaga, N
2008-01-01
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of given shell model Hamiltonian without complicated iterations.
Diagonalization and representation results for nonpositive sesquilinear form measures
Hytönen, Tuomas; Pellonpää, Juha-Pekka; Ylinen, Kari
2008-02-01
We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.
The Diagonal Compression Field Method using Circular Fans
Hansen, Thomas
2005-01-01
This paper presents a new design method, which is a modification of the diagonal compression field method, the modification consisting of the introduction of circular fan stress fields. The traditional method does not allow changes of the concrete compression direction throughout a given beam...... fields may be used whenever changes in the concrete compression direction are desired. To illustrate the new design method, a specific example of a prestressed concrete beam is calculated....
A method of diagonalization for sfermion mass matrices
Aranda, Alfredo; Noriega-Papaqui, R
2009-01-01
We present a method of diagonalization for the sfermion mass matrices of the minimal supersymmetric standard model (MSSM). It provides analytical expressions for the masses and mixing angles of rather general hermitian sfermion mass matrices, and allows the study of scenarios that extend the usual constrained - MSSM. Three signature cases are presented explicitly and a general study of flavor changing neutral current processes is outlined in the discussion.
Exact Solutions to Maccari's System
PAN Jun-Ting; GONG Lun-Xun
2007-01-01
Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.
Quantum Diagonalization Method in the TAVIS-CUMMINGS Model
Fujii, Kazuyuki; Higashida, Kyoko; Kato, Ryosuke; Suzuki, Tatsuo; Wada, Yukako
2005-06-01
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\\equiv S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.
Optimized Paraunitary Filter Banks for Time-Frequency Channel Diagonalization
Ju Ziyang
2010-01-01
Full Text Available We adopt the concept of channel diagonalization to time-frequency signal expansions obtained by DFT filter banks. As a generalization of the frequency domain channel representation used by conventional orthogonal frequency-division multiplexing receivers, the time-frequency domain channel diagonalization can be applied to time-variant channels and aperiodic signals. An inherent error in the case of doubly dispersive channels can be limited by choosing adequate windows underlying the filter banks. We derive a formula for the mean-squared sample error in the case of wide-sense stationary uncorrelated scattering (WSSUS channels, which serves as objective function in the window optimization. Furthermore, an enhanced scheme for the parameterization of tight Gabor frames enables us to constrain the window in order to define paraunitary filter banks. We show that the design of windows optimized for WSSUS channels with known statistical properties can be formulated as a convex optimization problem. The performance of the resulting windows is investigated under different channel conditions, for different oversampling factors, and compared against the performance of alternative windows. Finally, a generic matched filter receiver incorporating the proposed channel diagonalization is discussed which may be essential for future reconfigurable radio systems.
Optimized Paraunitary Filter Banks for Time-Frequency Channel Diagonalization
Ju, Ziyang; Hunziker, Thomas; Dahlhaus, Dirk
2010-12-01
We adopt the concept of channel diagonalization to time-frequency signal expansions obtained by DFT filter banks. As a generalization of the frequency domain channel representation used by conventional orthogonal frequency-division multiplexing receivers, the time-frequency domain channel diagonalization can be applied to time-variant channels and aperiodic signals. An inherent error in the case of doubly dispersive channels can be limited by choosing adequate windows underlying the filter banks. We derive a formula for the mean-squared sample error in the case of wide-sense stationary uncorrelated scattering (WSSUS) channels, which serves as objective function in the window optimization. Furthermore, an enhanced scheme for the parameterization of tight Gabor frames enables us to constrain the window in order to define paraunitary filter banks. We show that the design of windows optimized for WSSUS channels with known statistical properties can be formulated as a convex optimization problem. The performance of the resulting windows is investigated under different channel conditions, for different oversampling factors, and compared against the performance of alternative windows. Finally, a generic matched filter receiver incorporating the proposed channel diagonalization is discussed which may be essential for future reconfigurable radio systems.
UNDERSTANDING OF PROSPECTIVE MATHEMATICS TEACHERS OF THE CONCEPT OF DIAGONAL
Ülkü Ayvaz
2017-06-01
Full Text Available This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the participants and the criterion was determined as taking the course of geometry in the graduate program. Data was collected in two steps: a diagnostic test form about the definition and features of diagonal was applied to participants firstly and according to the answers of the participants to the diagnostic test form, semi-structured interviews were carried out. Data collected form the diagnostic test form and the semi-structured interviews were analyzed with descriptive analysis. According to the results of the study, it is understood that the prospective teachers had difficulties with the diagonals of parallelogram, rhombus and deltoid. Moreover, it is also seen that the prospective teachers were inadequate to support their ideas with further explanations although they could answer correctly. İt is thought that the inadequacy of the prospective teachers stems from the inadequacy related to proof.DOI: http://dx.doi.org/10.22342/jme.8.2.4102.165-184
Quantum Diagonalization Method in the Tavis-Cummings Model
Fujii, K; Kato, R; Suzuki, T; Wada, Y; Fujii, Kazuyuki; Higashida, Kyoko; Kato, Ryosuke; Suzuki, Tatsuo; Wada, Yukako
2004-01-01
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\\equiv S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.
Exact Maps in Density Functional Theory for Lattice Models
Dimitrov, Tanja; Fuks, Johanna I; Rubio, Angel
2015-01-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragmen...
On the verification of polynomial system solvers
Changbo CHEN; Marc MORENO MAZA; Wei PAN; Yuzhen XI
2008-01-01
We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which manipulates constructible sets represented by regular systems. We provide comparative benchmarks of different verification procedures applied to four solvers on a large set of well-known polynomial systems. Our experimental results illustrate the high effi-ciency of our new approach. In particular, we are able to verify triangular decompositions of polynomial systems which are not easy to solve.
Some topics of Navier-Stokes solvers
Honma, H.; Nishikawa, N.
1990-03-01
The process of numerical simulation consists of selection of some items: a mathematical model, a numerical scheme, the level of the computer, and post processing. From this point of view, recent numerical studies of viscous flows are described especially for the fluid engineering laboratories in the Chiba University. The examples of simulations are Mach reflection on a wedge using a kinetic model equation and a cylinder-plate juncture flow using incompressible Navier Stokes equation. Some attempts at graphic monitoring of fluid mechanical calculations are also shown for some combinations of computers with Computational Fluid Dynamics (CFD) solvers.
Input-output-controlled nonlinear equation solvers
Padovan, Joseph
1988-01-01
To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.
Preconditioners for Incompressible Navier-Stokes Solvers
A.Segal; M.ur Rehman; C.Vuik
2010-01-01
In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block precon- ditioners form an excellent approach for the solution, however if the grids are not to fine preconditioning with a Saddle point ILU matrix (SILU) may be an attractive al- ternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.
DPS--a computerised diagnostic problem solver.
Bartos, P; Gyárfas, F; Popper, M
1982-01-01
The paper contains a short description of the DPS system which is a computerized diagnostic problem solver. The system is under development of the Research Institute of Medical Bionics in Bratislava, Czechoslovakia. Its underlying philosophy yields from viewing the diagnostic process as process of cognitive problem solving. The implementation of the system is based on the methods of Artificial Intelligence and utilisation of production systems and frame theory should be noted in this context. Finally a list of program modules and their characterisation is presented.
Metaheuristics progress as real problem solvers
Nonobe, Koji; Yagiura, Mutsunori
2005-01-01
Metaheuristics: Progress as Real Problem Solvers is a peer-reviewed volume of eighteen current, cutting-edge papers by leading researchers in the field. Included are an invited paper by F. Glover and G. Kochenberger, which discusses the concept of Metaheuristic agent processes, and a tutorial paper by M.G.C. Resende and C.C. Ribeiro discussing GRASP with path-relinking. Other papers discuss problem-solving approaches to timetabling, automated planograms, elevators, space allocation, shift design, cutting stock, flexible shop scheduling, colorectal cancer and cartography. A final group of methodology papers clarify various aspects of Metaheuristics from the computational view point.
Wouters, B; De Nardis, J; Brockmann, M; Fioretto, D; Rigol, M; Caux, J-S
2014-09-12
We study quenches in integrable spin-1/2 chains in which we evolve the ground state of the antiferromagnetic Ising model with the anisotropic Heisenberg Hamiltonian. For this nontrivially interacting situation, an application of the first-principles-based quench-action method allows us to give an exact description of the postquench steady state in the thermodynamic limit. We show that a generalized Gibbs ensemble, implemented using all known local conserved charges, fails to reproduce the exact quench-action steady state and to correctly predict postquench equilibrium expectation values of physical observables. This is supported by numerical linked-cluster calculations within the diagonal ensemble in the thermodynamic limit.
Fiol, Bartomeu; Torrents, Genis
2014-01-01
We compute the exact vacuum expectation value of circular Wilson loops for Euclidean ${\\cal N}=4$ super Yang-Mills with $G=SO(N),Sp(N)$, in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on $AdS_5\\times {\\mathbb R} {\\mathbb P}^5$ plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having $AdS_5\\times {\\mathbb R} {\\mathbb P}^5$ as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely ...
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-01-01
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reprod...
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Exact maps in density functional theory for lattice models
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
Diagonal queue medical image steganography with Rabin cryptosystem.
Jain, Mamta; Lenka, Saroj Kumar
2016-03-01
The main purpose of this work is to provide a novel and efficient method to the image steganography area of research in the field of biomedical, so that the security can be given to the very precious and confidential sensitive data of the patient and at the same time with the implication of the highly reliable algorithms will explode the high security to the precious brain information from the intruders. The patient information such as patient medical records with personal identification information of patients can be stored in both storage and transmission. This paper describes a novel methodology for hiding medical records like HIV reports, baby girl fetus, and patient's identity information inside their Brain disease medical image files viz. scan image or MRI image using the notion of obscurity with respect to a diagonal queue least significant bit substitution. Data structure queue plays a dynamic role in resource sharing between multiple communication parties and when secret medical data are transferred asynchronously (secret medical data not necessarily received at the same rate they were sent). Rabin cryptosystem is used for secret medical data writing, since it is computationally secure against a chosen-plaintext attack and shows the difficulty of integer factoring. The outcome of the cryptosystem is organized in various blocks and equally distributed sub-blocks. In steganography process, various Brain disease cover images are organized into various blocks of diagonal queues. The secret cipher blocks and sub-blocks are assigned dynamically to selected diagonal queues for embedding. The receiver gets four values of medical data plaintext corresponding to one ciphertext, so only authorized receiver can identify the correct medical data. Performance analysis was conducted using MSE, PSNR, maximum embedding capacity as well as by histogram analysis between various Brain disease stego and cover images.
Performance Theory of Diagonal Conducting Wall MHD Accelerators
Litchford, R. J.
2003-01-01
The theoretical performance of diagonal conducting wall crossed field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm's law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm's law by imposing appropriate configuration and loading constraints. A current dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities lead to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed field accelerator operation.
Experimental Investigation of Stator Flow in Diagonal Flow Fan
Jie Wang; Yoichi Kinoue; Norimasa Shiomi; Toshiaki Setoguchi; Kenji Kaneko; Yingzi Jin
2008-01-01
perimental investigations were conducted for the internal flow of the stator of the diagonal flow fan. Comer separation near the hub surface and the suction surface of the stator blade are focused on. At the design flow rate, the values of the axial velocity and the total pressure at stator outlet decrease near the suction surface at around the hub surface by the influence of the comer wall. At low flow rate of 80-90 % of the design flow rate, the comer separation between the suction surface and the hub surface can be found, which become widely spread at 80 % of the design flow rate.
Experimental investigation of stator flow in diagonal flow fan
Wang, Jie; Kinoue, Yoichi; Shiomi, Norimasa; Setoguchi, Toshiaki; Kaneko, Kenji; Jin, Yingzi
2008-12-01
Experimental investigations were conducted for the internal flow of the stator of the diagonal flow fan. Corner separation near the hub surface and the suction surface of the stator blade are focused on. At the design flow rate, the values of the axial velocity and the total pressure at stator outlet decrease near the suction surface at around the hub surface by the influence of the corner wall. At low flow rate of 80-90 % of the design flow rate, the corner separation between the suction surface and the hub surface can be found, which become widely spread at 80 % of the design flow rate.
Diagonal Cracking and Shear Strength of Reinforced Concrete Beams
Zhang, Jin-Ping
1997-01-01
found by the usual plastic theory, a physical explanation is given for this phenomenon and a way to estimate the shear capacity of reinforced concrete beams, based on the theory of plasticity, is described. The theoretical calculations are shown to be in fairly good agreement with test results from......The shear failure of non-shear-reinforced concrete beams with normal shear span ratios is observed to be governed in general by the formation of a critical diagonal crack. Under the hypothesis that the cracking of concrete introduces potential yield lines which may be more dangerous than the ones...
Quasi-exact evaluation of time domain MFIE MOT matrix elements
Shi, Yifei
2013-07-01
A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.
Endom, Joerg
2014-05-01
negligible any more. Locating for example the exact position of joints, rebars on site, getting correct calibration information or overlaying measurements of independent methods requires high accuracy positioning for all data. Different technologies of synchronizing and stabilizing are discussed in this presentation. Furthermore a scale problem for interdisciplinary work between the geotechnical engineer, the civil engineer, the surveyor and the geophysicist is presented. Manufacturers as well as users are addressed to work on a unified methodology that could be implemented in future. This presentation is a contribution to COST Action TU1208.
A Novel Interactive MINLP Solver for CAPE Applications
Henriksen, Jens Peter; Støy, S.; Russel, Boris Mariboe;
2000-01-01
This paper presents an interactive MINLP solver that is particularly suitable for solution of process synthesis, design and analysis problems. The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master...
Efficient use of iterative solvers in nested topology optimization
Amir, Oded; Stolpe, Mathias; Sigmund, Ole
2009-01-01
by a Krylov subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence...
Experiences with linear solvers for oil reservoir simulation problems
Joubert, W.; Janardhan, R. [Los Alamos National Lab., NM (United States); Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Parallel sparse direct solver for integrated circuit simulation
Chen, Xiaoming; Yang, Huazhong
2017-01-01
This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Xu, Jinchao
2014-12-01
In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.
Integrating advanced reasoning into a SAT solver
DING Min; TANG Pushan; ZHOU Dian
2005-01-01
In this paper, we present a SAT solver based on the combination of DPLL (Davis Putnam Logemann and Loveland) algorithm and Failed Literal Detection (FLD), one of the advanced reasoning techniques. We propose a Dynamic Filtering method that consists of two restriction rules for FLD: internal and external filtering. The method reduces the number of tested literals in FLD and its computational time while maintaining the ability to find most of the failed literals in each decision level. Unlike the pre-defined criteria, literals are removed dynamically in our approach. In this way, our FLD can adapt itself to different real-life benchmarks. Many useless tests are therefore avoided and as a consequence it makes FLD fast. Some other static restrictions are also added to further improve the efficiency of FLD. Experiments show that our optimized FLD is much more efficient than other advanced reasoning techniques.
Optimising a parallel conjugate gradient solver
Field, M.R. [O`Reilly Institute, Dublin (Ireland)
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
Asynchronous Parallelization of a CFD Solver
Daniel S. Abdi
2015-01-01
Full Text Available A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used in CFD codes; however, it has a potential to alleviate scaling bottlenecks incurred due to processors having to wait for each other at designated synchronization points. A common way to avoid this idle time is to overlap asynchronous communication with computation. For this to work, however, there must be something useful and independent a processor can do while waiting for messages to arrive. We investigate an alternative approach of computation, namely, conducting asynchronous iterations to improve local subdomain solution while communication is in progress. An in-house CFD code is parallelized using message passing interface (MPI, and scalability tests are conducted that suggest asynchronous iterations are a viable way of parallelizing CFD code.
On the performance of diagonal lattice space-time codes
Abediseid, Walid
2013-11-01
There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria [1]-[9]. In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding. © 2013 IEEE.
Alcohol dimers--how much diagonal OH anharmonicity?
Kollipost, Franz; Papendorf, Kim; Lee, Yu-Fang; Lee, Yuan-Pern; Suhm, Martin A
2014-08-14
The OH bond of methanol, ethanol and t-butyl alcohol becomes more anharmonic upon hydrogen bonding and the infrared intensity ratio between the overtone and the fundamental transition of the bridging OH stretching mode decreases drastically. FTIR spectroscopy of supersonic slit jet expansions allows to quantify these effects for isolated alcohol dimers, enabling a direct comparison to anharmonic vibrational predictions. The diagonal anharmonicity increase amounts to 15-18%, growing with increasing alkyl substitution. The overtone/fundamental IR intensity ratio, which is on the order of 0.1 or more for isolated alcohols, drops to 0.004-0.001 in the hydrogen-bonded OH group, making overtone detection very challenging. Again, alkyl substitution enhances the intensity suppression. Vibrational second order perturbation theory appears to capture these effects in a semiquantitative way. Harmonic quantum chemistry predictions for the hydrogen bond-induced OH stretching frequency shift (the widely used infrared signature of hydrogen bonding) are insufficient, and diagonal anharmonicity corrections from experiment make the agreement between theory and experiment worse. Inclusion of anharmonic cross terms between hydrogen bond modes and the OH stretching mode is thus essential, as is a high level electronic structure theory. The isolated molecule results are compared to matrix isolation data, complementing earlier studies in N2 and Ar by the more weakly interacting Ne and p-H2 matrices. Matrix effects on the hydrogen bond donor vibration are quantified.
The "diagonal effect": a systematic error in oblique antisaccades.
Koehn, John D; Roy, Elizabeth; Barton, Jason J S
2008-08-01
Antisaccades are known to show greater variable error and also a systematic hypometria in their amplitude compared with visually guided prosaccades. In this study, we examined whether their accuracy in direction (as opposed to amplitude) also showed a systematic error. We had human subjects perform prosaccades and antisaccades to goals located at a variety of polar angles. In the first experiment, subjects made prosaccades or antisaccades to one of eight equidistant locations in each block, whereas in the second, they made saccades to one of two equidistant locations per block. In the third, they made antisaccades to one of two locations at different distances but with the same polar angle in each block. Regardless of block design, the results consistently showed a saccadic systematic error, in that oblique antisaccades (but not prosaccades) requiring unequal vertical and horizontal vector components were deviated toward the 45 degrees diagonal meridians. This finding could not be attributed to range effects in either Cartesian or polar coordinates. A perceptual origin of the diagonal effect is suggested by similar systematic errors in other studies of memory-guided manual reaching or perceptual estimation of direction, and may indicate a common spatial bias when there is uncertain information about spatial location.
Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting
Saunderson, James; Parrilo, Pablo A; Willsky, Alan S
2012-01-01
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\\in \\R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \\emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspac...
Del Rey Fernández, David C.; Boom, Pieter D.; Zingg, David W.
2017-02-01
Combined with simultaneous approximation terms, summation-by-parts (SBP) operators offer a versatile and efficient methodology that leads to consistent, conservative, and provably stable discretizations. However, diagonal-norm operators with a repeating interior-point operator that have thus far been constructed suffer from a loss of accuracy. While on the interior, these operators are of degree 2p, at a number of nodes near the boundaries, they are of degree p, and therefore of global degree p - meaning the highest degree monomial for which the operators are exact at all nodes. This implies that for hyperbolic problems and operators of degree greater than unity they lead to solutions with a global order of accuracy lower than the degree of the interior-point operator. In this paper, we develop a procedure to construct diagonal-norm first-derivative SBP operators that are of degree 2p at all nodes and therefore can lead to solutions of hyperbolic problems of order 2 p + 1. This is accomplished by adding nonzero entries in the upper-right and lower-left corners of SBP operator matrices with a repeating interior-point operator. This modification necessitates treating these new operators as elements, where mesh refinement is accomplished by increasing the number of elements in the mesh rather than increasing the number of nodes. The significant improvements in accuracy of this new family, for the same repeating interior-point operator, are demonstrated in the context of the linear convection equation.
Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion
Hassan, Absar U.; Zhen, Bo; Soljačić, Marin; Khajavikhan, Mercedeh; Christodoulides, Demetrios N.
2017-03-01
We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate—irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.
Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles
Druta-Romaniuc, Simona-Luiza
2011-01-01
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\\"ahlerian structures on the total spaces of the cotangent bundle.
Diagonal complexes and the integral homology of the automorphism group of a free product
Griffin, James
2010-01-01
We calculate the integral (co)homology of the group of symmetric automorphisms of a free product. We proceed by constructing a moduli space of cactus products and to describe this space a theory of diagonal complexes is introduced. In doing so we offer a generalisation of the theory of right-angled Artin groups in that each diagonal complex defines what we call a diagonal right-angled Artin group (DRAAG).
Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei
2015-12-01
In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.
Froese, Brittany D
2010-01-01
The elliptic Monge-Amp\\`ere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. Novel solution methods are required for stability and convergence to weak solutions. In this article we build a monotone finite difference solver for the \\MA equation, which we prove converges to the weak (viscosity) solution. The resulting nonlinear equations are then solved by a damped Newton's method. We prove convergence and provide a close initial value for Newton's method. Computational results are presented in two and three dimensions, comparing solution time and accuracy to previous solvers using exact solutions which range in regularity from smooth to non-differentiable.
Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report
Saad, Yousef
2014-01-16
The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the
High-Performance Solvers for Dense Hermitian Eigenproblems
Petschow, Matthias; Bientinesi, Paolo
2012-01-01
We introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the Algorithm of Multiple Relatively Robust Representations - referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is designed to fully support both message-passing (MPI) and multithreading parallelism (SMP). As a result, the solvers can equally be used in pure MPI or in hybrid MPI-SMP fashion. We conducted a thorough performance study of EleMRRR and ScaLAPACK's solvers on two supercomputers. Such a study, performed with up to 8,192 cores, provides precise guidelines to assemble the fastest solver within the ScaLAPACK framework; it also ind...
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Exact solutions to model surface and volume charge distributions
Mukhopadhyay, S.; Majumdar, N.; Bhattacharya, P.; Jash, A.; Bhattacharya, D. S.
2016-10-01
Many important problems in several branches of science and technology deal with charges distributed along a line, over a surface and within a volume. Recently, we have made use of new exact analytic solutions of surface charge distributions to develop the nearly exact Boundary Element Method (neBEM) toolkit. This 3D solver has been successful in removing some of the major drawbacks of the otherwise elegant Green's function approach and has been found to be very accurate throughout the computational domain, including near- and far-field regions. Use of truly distributed singularities (in contrast to nodally concentrated ones) on rectangular and right-triangular elements used for discretizing any three-dimensional geometry has essentially removed many of the numerical and physical singularities associated with the conventional BEM. In this work, we will present this toolkit and the development of several numerical models of space charge based on exact closed-form expressions. In one of the models, Particles on Surface (ParSur), the space charge inside a small elemental volume of any arbitrary shape is represented as being smeared on several surfaces representing the volume. From the studies, it can be concluded that the ParSur model is successful in getting the estimates close to those obtained using the first-principles, especially close to and within the cell. In the paper, we will show initial applications of ParSur and other models in problems related to high energy physics.
The Diagonal Compression Field Method using Circular Fans
Hansen, Thomas
2006-01-01
In a concrete beam with transverse stirrups the shear forces are carried by inclined compression in the concrete. Along the tensile zone and the compression zone of the beam the transverse components of the inclined compressions are transferred to the stirrups, which are thus subjected to tension....... Since the eighties the diagonal compression field method has been used to design transverse shear reinforcement in concrete beams. The method is based on the lower-bound theorem of the theory of plasticity, and it has been adopted in Eurocode 2. The paper presents a new design method, which...... with low shear stresses. The larger inclination (the smaller -value) of the uniaxial concrete stress the more transverse shear reinforcement is needed; hence it would be optimal if the -value for a given beam could be set to a low value in regions with high shear stresses and thereafter increased...
Non-Diagonal and Mixed Squark Production at Hadron Colliders
Bozzi, G; Klasen, M
2005-01-01
We calculate squared helicity amplitudes for non-diagonal and mixed squark pair production at hadron colliders, taking into account not only loop-induced QCD diagrams, but also previously unconsidered electroweak channels, which turn out to be dominant. Mixing effects are included for both top and bottom squarks. Numerical results are presented for several SUSY benchmark scenarios at both the CERN LHC and the Fermilab Tevatron, including the possibilities of light stops or sbottoms. The latter should be easily observed at the Tevatron in associated production of stops and sbottoms for a large range of stop masses and almost independently of the stop mixing angle. Asymmetry measurements for light stops at the polarized BNL RHIC collider are also briefly discussed.
Eye movements during mental time travel follow a diagonal line.
Hartmann, Matthias; Martarelli, Corinna S; Mast, Fred W; Stocker, Kurt
2014-11-01
Recent research showed that past events are associated with the back and left side, whereas future events are associated with the front and right side of space. These spatial-temporal associations have an impact on our sensorimotor system: thinking about one's past and future leads to subtle body sways in the sagittal dimension of space (Miles, Nind, & Macrae, 2010). In this study we investigated whether mental time travel leads to sensorimotor correlates in the horizontal dimension of space. Participants were asked to mentally displace themselves into the past or future while measuring their spontaneous eye movements on a blank screen. Eye gaze was directed more rightward and upward when thinking about the future than when thinking about the past. Our results provide further insight into the spatial nature of temporal thoughts, and show that not only body, but also eye movements follow a (diagonal) "time line" during mental time travel.
Performance Theory of Diagonal Conducting Wall Magnetohydrodynamic Accelerators
Litchford, R. J.
2004-01-01
The theoretical performance of diagonal conducting wall crossed-field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm s law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm s law by imposing appropriate configuration and loading constraints. A current-dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects, including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities leads to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed-field accelerator operation.
Quantum transport in chains with noisy off-diagonal couplings.
Pereverzev, Andrey; Bittner, Eric R
2005-12-22
We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.
An Off Diagonal Marcinkiewicz Interpolation Theorem on Lorentz Spaces
Yi Yu LIANG; Li Guang LIU; Da Chun YANG
2011-01-01
Let(X,μ)be a measure space.In this paper,using some ideas from Grafakos and Kalton,the authors establish an of diagonal Marcinkiewicz interpolation theorem for a quasilinear operator T in Lorentz spaces Lp,q(X)with p,q∈(0,∞],which is a corrected version of Theorem 1.4.19 in[Grafakos,L.:Classical Fourier Analysis,Second Edition,Graduate Texts in Math.,No.249,Springer,New York,2008]and which,in the case that T is linear or nonnegative sublineaa,P∈[1,∞)and q∈[1,∞),was obtained by Stein and Weiss [Introduction to Fourier Analysis on Euclidean Spaces,Princeton University Press,Princeton,N.J.,1971].
Efficient numerical diagonalization of hermitian 3x3 matrices
Kopp, J
2006-01-01
A very common problem in science is the numerical diagonalization of symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be very inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with a new, carefully designed analytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. This analytical algorithm outperforms the other algorithms by more than a factor of 2, but may be less accurate if the eigenvalues differ greatly in magnitude. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from http://www.mpi-hd.mpg.de/~jkopp/3x3/ .
Diagonalization of the XXZ Hamiltonian by Vertex Operators
Davies, B; Jimbo, M; Miwa, T; Nakayashiki, A; Davies, Brian; Foda, Omar; Jimbo, Michio; Miwa, Tetsuji; Nakayashiki, Atsushi
1993-01-01
We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.
Performance Study of Diagonally Segmented Piezoelectric Vibration Energy Harvester
Kim, Jae Eun [Catholic Univ. of Daegu, Daegu (Korea, Republic of)
2013-08-15
This study proposes a piezoelectric vibration energy harvester composed of two diagonally segmented energy harvesting units. An auxiliary structural unit is attached to the tip of a host structural unit cantilevered to a vibrating base, where the two components have beam axes in opposite directions from each other and matched short-circuit resonant frequencies. Contrary to the usual observations in two resonant frequency-matched structures, the proposed structure shows little eigenfrequency separation and yields a mode sequence change between the first two modes. These lead to maximum power generation around a specific frequency. By using commercial finite element software, it is shown that the magnitude of the output power from the proposed vibration energy harvester can be substantially improved in comparison with those from conventional cantilevered energy harvesters with the same footprint area and magnitude of a tip mass.
Exact cosmological solutions for MOG
Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2015-09-15
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Multiscale Universal Interface: A Concurrent Framework for Coupling Heterogeneous Solvers
Tang, Yu-Hang; Bian, Xin; Li, Zhen; Karniadakis, George E
2014-01-01
Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and c...
Uncertainty Quantification for Production Navier-Stokes Solvers Project
National Aeronautics and Space Administration — The uncertainty quantification methods developed under this program are designed for use with current state-of-the-art flow solvers developed by and in use at NASA....
Integrating Problem Solvers from Analogous Markets in New Product Ideation
Franke, Nikolaus; Poetz, Marion; Schreier, Martin
2014-01-01
Who provides better inputs to new product ideation tasks, problem solvers with expertise in the area for which new products are to be developed or problem solvers from “analogous” markets that are distant but share an analogous problem or need? Conventional wisdom appears to suggest that target...... that including problem solvers from analogous markets versus the target market accounts for almost two-thirds of the well-known effect of involving lead users instead of average problem solvers. This effect is further amplified when the analogous distance between the markets increases, i.e., when searching...... market expertise is indispensable, which is why most managers searching for new ideas tend to stay within their own market context even when they do search outside their firms' boundaries. However, in a unique symmetric experiment that isolates the effect of market origin, we find evidence...
Adaptive Kinetic-Fluid Solvers for Heterogeneous Computing Architectures
Zabelok, Sergey; Kolobov, Vladimir
2015-01-01
This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. UFS is an adaptive kinetic-fluid simulation tool, which combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with AMR. Double digit speedups on single GPU and good scaling for multi-GPU have been demonstrated.
Hybrid Riemann Solvers for Large Systems of Conservation Laws
Schmidtmann, Birte; Torrilhon, Manuel
2016-01-01
In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid computing the characteristic decomposition of the flux Jacobian. Instead, they require only an estimate of the globally fastest wave speeds in both directions. Thus, this family of solvers is particularly efficient for large systems of conservation laws, i.e. with many different propagation speeds, and when no explicit expression for the eigensystem is available. Even though only fastest wave speeds are needed as input values, the new family of Riemann solvers reproduces all waves with less dissipation than HLL, which has the same prerequisites, requiring only one additional flux evaluation.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
On the diagonal susceptibility of the two-dimensional Ising model
Tracy, Craig A. [Department of Mathematics, University of California, Davis, California 95616 (United States); Widom, Harold [Department of Mathematics, University of California, Santa Cruz, California 95064 (United States)
2013-12-15
We consider the diagonal susceptibility of the isotropic 2D Ising model for temperatures below the critical temperature. For a parameter k related to temperature and the interaction constant, we extend the diagonal susceptibility to complex k inside the unit disc, and prove the conjecture that the unit circle is a natural boundary.
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
Diagonally implicit Runge-Kutta methods for 3D shallow water applications
P.J. van der Houwen; B.P. Sommeijer (Ben)
1999-01-01
textabstractWe construct A-stable and L-stable diagonally implicit Runge-Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge-Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamás [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Institute for Theoretical Physics, Roland Eötvös University,1117 Budapest, Pázmány s. 1/A (Hungary); Palla, László [Institute for Theoretical Physics, Roland Eötvös University,1117 Budapest, Pázmány s. 1/A (Hungary)
2016-02-24
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
A Python interface to Diffpack-based classes and solvers
Munthe-Kaas, Heidi Vikki
2013-01-01
Python is a programming language that has gained a lot of popularity during the last 15 years, and as a very easy-to-learn and flexible scripting language it is very well suited for computa- tional science, both in mathematics and in physics. Diffpack is a PDE library written in C++, made for easier implementation of both smaller PDE solvers and for larger libraries of simu- lators. It contains large class hierarchies for different solvers, grids, arrays, parallel computing and almost everyth...
An Interactive Chemical Equilibrium Solver for the Personal Computer
Negus, Charles H.
1997-01-01
AN INTERACTIVE CHEMICAL EQUILIBRIUM SOLVER FOR THE PERSONAL COMPUTER Charles Hugh Negus Felix J. Pierce, Chairman Mechanical Engineering The Virginia Tech Equilibrium Chemistry (VTEC) code is a keyboard interactive, user friendly, chemical equilibrium solver for use on a personal computer. The code is particularly suitable for a teaching / learning environment. For a set of reactants at a defined thermodynamic state given by a user, the program will select all species...
2016-01-01
We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and co...
Iterative algorithm for joint zero diagonalization with application in blind source separation.
Zhang, Wei-Tao; Lou, Shun-Tian
2011-07-01
A new iterative algorithm for the nonunitary joint zero diagonalization of a set of matrices is proposed for blind source separation applications. On one hand, since the zero diagonalizer of the proposed algorithm is constructed iteratively by successive multiplications of an invertible matrix, the singular solutions that occur in the existing nonunitary iterative algorithms are naturally avoided. On the other hand, compared to the algebraic method for joint zero diagonalization, the proposed algorithm requires fewer matrices to be zero diagonalized to yield even better performance. The extension of the algorithm to the complex and nonsquare mixing cases is also addressed. Numerical simulations on both synthetic data and blind source separation using time-frequency distributions illustrate the performance of the algorithm and provide a comparison to the leading joint zero diagonalization schemes.
Leistedt, B
2012-01-01
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact harmonic transform on the radial line using damped Laguerre polynomials and develop a corresponding quadrature rule. Combined with the spherical harmonic transform, this approach leads to a sampling theorem on the ball and a novel three-dimensional decomposition which we call the Fourier-Laguerre transform. We relate this new transform to the well-known Fourier-Bessel decomposition and show that band-limitness in the Fourier-Laguerre basis is a sufficient condition to compute the Fourier-Bessel decomposition exactly. We then construct the flaglet transform on the ball through a harmonic tiling, which is exact thanks to the exactness of the Fourier-Laguerre transform (from which the name flaglets is coined). The corresponding wavelet kernels have compact localisation properties in real and harmonic space and their angular aperture is i...
Exact completions and small sheaves
Shulman, Michael
2012-01-01
We prove a general theorem which includes most notions of "exact completion". The theorem is that "k-ary exact categories" are a reflective sub-2-category of "k-ary sites", for any regular cardinal k. A k-ary exact category is an exact category with disjoint and universal k-small coproducts, and a k-ary site is a site whose covering sieves are generated by k-small families and which satisfies a weak size condition. For different values of k, this includes the exact completions of a regular category or a category with (weak) finite limits; the pretopos completion of a coherent category; and the category of sheaves on a small site. For a large site with k the size of the universe, it gives a well-behaved "category of small sheaves". Along the way, we define a slightly generalized notion of "morphism of sites", and show that k-ary sites are equivalent to a type of "enhanced allegory".
An advanced implicit solver for MHD
Udrea, Bogdan
A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel
A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing
Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo
2009-01-01
The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.
BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint
Wang, Q.; Sprague, M.; Jonkman, J.; Johnson, N.
2015-01-01
BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented as validation.
Sparse Approximations of the Schur Complement for Parallel Algebraic Hybrid Solvers in 3D
L.Giraud; A.Haidar; Y.Saad
2010-01-01
In this paper we study the computational performance of variants of an al-gebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems. In earlier works, the local Schur complements were com- puted exactly using a sparse direct solver. The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems. In this work we investigate the use of sparse approximation of the dense local Schur complements. These approximations are com-puted using a partial incomplete LU factorization. Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
A characterisation of algebraic exactness
Garner, Richard
2011-01-01
An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Ad\\'amek, Lawvere and Rosick\\'y: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conjectured that a complete and sifted-cocomplete category should be algebraically exact just when it is Barr-exact, finite limits commute with filtered colimits, regular epimorphisms are stable by small products, and filtered colimits distribute over small products. We prove this conjecture.
A Comparison of Stiff ODE Solvers for Astrochemical Kinetics Problems
Nejad, Lida A. M.
2005-09-01
The time dependent chemical rate equations arising from astrochemical kinetics problems are described by a system of stiff ordinary differential equations (ODEs). In this paper, using three astrochemical models of varying physical and computational complexity, and hence different degrees of stiffness, we present a comprehensive performance survey of a set of well-established ODE solver packages from the ODEPACK collection, namely LSODE, LSODES, VODE and VODPK. For completeness, we include results from the GEAR package in one of the test models. The results demonstrate that significant performance improvements can be obtained over GEAR which is still being used by many astrochemists by default. We show that a simple appropriate ordering of the species set results in a substantial improvement in the performance of the tested ODE solvers. The sparsity of the associated Jacobian matrix can be exploited and results using the sparse direct solver routine LSODES show an extensive reduction in CPU time without any loss in accuracy. We compare the performance and the computed abundances of one model with a 175 species set and a reduced set of 88 species, keeping all physical and chemical parameters identical with both sets.We found that the calculated abundances using two different size models agree quite well. However, with no extra computational effort and more reliable results, it is possible for the computation to be many times faster with the larger species set than the reduced set, depending on the use of solvers, the ordering and the chosen options. It is also shown that though a particular solver with certain chosen parameters may have severe difficulty or even fail to complete a run over the required integration time, another solver can easily complete the run with a wider range of control parameters and options. As a result of the superior performance of LSODES for the solution of astrochemical kinetics systems, we have tailor-made a sparse version of the VODE
A fast Laplace solver approach to pore scale permeability
Arns, Christoph; Adler, Pierre
2017-04-01
The permeability of a porous medium can be derived by solving the Stokes equations in the pore space with no slip at the walls. The resulting velocity averaged over the pore volume yields the permeability KS by application of the Darcy law. The Stokes equations can be solved by a number of different techniques such as finite differences, finite volume, Lattice Boltzmann, but whatever the technique it remains a heavy task since there are four unknowns at each node (the three velocity components and the pressure) which necessitate the solution of four equations (the projection of Newton's law on each axis and mass conservation). By comparison, the Laplace equation is scalar with a single unknown at each node. The objective of this work is to replace the Stokes equations by an elliptical equation with a space dependent permeability. More precisely, the local permeability k is supposed to be proportional to (r-alpha)**2 where r is the distance of the voxel to the closest wall, and alpha a constant; k is zero in the solid phase. The elliptical equation is div(k gradp)=0. A macroscopic pressure gradient is assumed to be exerted on the medium and again the resulting velocity averaged over space yields a permeability K_L. In order to validate this method, systematic calculations have been performed. First, elementary shapes (plane channel, circular pipe, rectangular channels) were studied for which flow occurs along parallel lines in which case KL is the arithmetic average of the k's. KL was calculated for various discretizations of the pore space and various values of alpha. For alpha=0.5, the agreement with the exact analytical value of KS is excellent for the plane and rectangular channels while it is only approximate for circular pipes. Second, the permeability KL of channels with sinusoidal walls was calculated and compared with analytical results and numerical ones provided by a Lattice Boltzmann algorithm. Generally speaking, the discrepancy does not exceed 25% when
[Improvement of child survival in Mexico: the diagonal approach].
Sepúlveda, Jaime; Bustreo, Flavia; Tapia, Roberto; Rivera, Juan; Lozano, Rafael; Olaiz, Gustavo; Partida, Virgilio; García-García, Ma de Lourdes; Valdespino, José Luis
2007-01-01
Public health interventions aimed at children in Mexico have placed the country among the seven countries on track to achieve the goal of child mortality reduction by 2015. We analysed census data, mortality registries, the nominal registry of children, national nutrition surveys, and explored temporal association and biological plausibility to explain the reduction of child, infant, and neonatal mortality rates. During the past 25 years, child mortality rates declined from 64 to 23 per 1000 livebirths. A dramatic decline in diarrhoea mortality rates was recorded. Polio, diphtheria, and measles were eliminated. Nutritional status of children improved significantly for wasting, stunting, and underweight. A selection of highly cost-effective interventions bridging clinics and homes, what we called the diagonal approach, were central to this progress. Although a causal link to the reduction of child mortality was not possible to establish, we saw evidence of temporal association and biological plausibility to the high level of coverage of public health interventions, as well as significant association to the investments in women education, social protection, water, and sanitation. Leadership and continuity of public health policies, along with investments on institutions and human resources strengthening, were also among the reasons for these achievements.
Improvement of child survival in Mexico: the diagonal approach.
Sepúlveda, Jaime; Bustreo, Flavia; Tapia, Roberto; Rivera, Juan; Lozano, Rafael; Oláiz, Gustavo; Partida, Virgilio; García-García, Lourdes; Valdespino, José Luis
2006-12-01
Public health interventions aimed at children in Mexico have placed the country among the seven countries on track to achieve the goal of child mortality reduction by 2015. We analysed census data, mortality registries, the nominal registry of children, national nutrition surveys, and explored temporal association and biological plausibility to explain the reduction of child, infant, and neonatal mortality rates. During the past 25 years, child mortality rates declined from 64 to 23 per 1000 livebirths. A dramatic decline in diarrhoea mortality rates was recorded. Polio, diphtheria, and measles were eliminated. Nutritional status of children improved significantly for wasting, stunting, and underweight. A selection of highly cost-effective interventions bridging clinics and homes, what we called the diagonal approach, were central to this progress. Although a causal link to the reduction of child mortality was not possible to establish, we saw evidence of temporal association and biological plausibility to the high level of coverage of public health interventions, as well as significant association to the investments in women education, social protection, water, and sanitation. Leadership and continuity of public health policies, along with investments on institutions and human resources strengthening, were also among the reasons for these achievements.
On the Gravitational Energy Associated with Spacetimes of Diagonal Metric
Korunur, M; Salti, M; Korunur, Murat; Havare, Ali; Salti, Mustafa
2006-01-01
In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a spacetime model of generalized diagonal metric, we consider the Einstein, Bergmann-Thomson and Landau-Lifshitz energy and/or momentum definitions both in Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We find the same energy distribution using Einstein and Bergmann-Thomson formulations, but we also find that the energy-momentum prescription of Landau-Lifshitz disagree in general with these definitions. We also give eight different well-known spacetime models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianci type-I all the formulations give the same result. This result agrees with the previous works of Cooperstock-Israelit, Rosen, Johri {\\it et al.}, Banerjee-Sen, Xulu, Vargas and Salt{\\i} {\\it et al.} and supports the viewpoints...
Efficient Numerical Diagonalization of Hermitian 3 × 3 Matrices
Kopp, Joachim
A very common problem in science is the numerical diagonalization of symmetric or hermitian 3 × 3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an alytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from .
Euler/Navier-Stokes Solvers Applied to Ducted Fan Configurations
Keith, Theo G., Jr.; Srivastava, Rakesh
1997-01-01
Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.
Sub-Ohmic spin-boson model with off-diagonal coupling: ground state properties.
Lü, Zhiguo; Duan, Liwei; Li, Xin; Shenai, Prathamesh M; Zhao, Yang
2013-10-28
We have carried out analytical and numerical studies of the spin-boson model in the sub-ohmic regime with the influence of both the diagonal and the off-diagonal coupling accounted for, via the Davydov D1 variational ansatz. While a second-order phase transition is known to be exhibited by this model in the presence of diagonal coupling only, we demonstrate the emergence of a discontinuous first order phase transition upon incorporation of the off-diagonal coupling. A plot of the ground state energy versus magnetization highlights the discontinuous nature of the transition between the isotropic (zero magnetization) state and nematic (finite magnetization) phases. We have also calculated the entanglement entropy and a discontinuity found at a critical coupling strength further supports the discontinuous crossover in the spin-boson model in the presence of off-diagonal coupling. It is further revealed via a canonical transformation approach that for the special case of identical exponents for the spectral densities of the diagonal and the off-diagonal coupling, there exists a continuous crossover from a single localized phase to doubly degenerate localized phase with differing magnetizations.
Weights of Exact Threshold Functions
Babai, László; Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case...
Exactly solvable models of nuclei
Van Isacker, P
2014-01-01
In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.
Chavez, Gustavo Ivan
2017-07-10
This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.
Accuracy analysis of a spectral Poisson solver
Rambaldi, S. [Dipartimento di Fisica Universita di Bologna and INFN, Bologna, Via Irnerio 46, 40126 (Italy)]. E-mail: rambaldi@bo.infn.it; Turchetti, G. [Dipartimento di Fisica Universita di Bologna and INFN, Bologna, Via Irnerio 46, 40126 (Italy); Benedetti, C. [Dipartimento di Fisica Universita di Bologna and INFN, Bologna, Via Irnerio 46, 40126 (Italy); Mattioli, F. [Dipartimento di Fisica Universita di Bologna, Bologna, Via Irnerio 46, 40126 (Italy); Franchi, A. [GSI, Darmstadt, Planckstr. 1, 64291 (Germany)
2006-06-01
We solve Poisson's equation in d=2,3 space dimensions by using a spectral method based on Fourier decomposition. The choice of the basis implies that Dirichlet boundary conditions on a box are satisfied. A Green's function-based procedure allows us to impose Dirichlet conditions on any smooth closed boundary, by doubling the computational complexity. The error introduced by the spectral truncation and the discretization of the charge distribution is evaluated by comparison with the exact solution, known in the case of elliptical symmetry. To this end boundary conditions on an equipotential ellipse (ellipsoid) are imposed on the numerical solution. Scaling laws for the error dependence on the number K of Fourier components for each space dimension and the number N of point charges used to simulate the charge distribution are presented and tested. A procedure to increase the accuracy of the method in the beam core region is briefly outlined.
Exactly energy conserving semi-implicit particle in cell formulation
Lapenta, Giovanni
2017-04-01
We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested.
When 'exact recovery' is exact recovery in compressed sensing simulation
Sturm, Bob L.
2012-01-01
In a simulation of compressed sensing (CS), one must test whether the recovered solution \\(\\vax\\) is the true solution \\(\\vx\\), i.e., ``exact recovery.'' Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than...... for a given distribution of \\(\\vx\\)? We show that, in a best case scenario, \\(\\epsilon^2\\) sets a maximum allowed missed detection rate in a majority sense....
The novel high-performance 3-D MT inverse solver
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
2016-04-01
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.
A robust HLLC-type Riemann solver for strong shock
Shen, Zhijun; Yan, Wei; Yuan, Guangwei
2016-03-01
It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipative flux can cure the shock instability, but also may lead to other problems, such as certain arbitrariness of choosing switching parameters or contact interface becoming smeared. In order to overcome these drawbacks, this paper proposes a simple and robust HLLC-type Riemann solver for inviscid, compressible gas flows, which is capable of preserving sharp contact surface and is free from instability. The main work is to construct a HLL-type Riemann solver and a HLLC-type Riemann solver by modifying the shear viscosity of the original HLL and HLLC methods. Both of the two new schemes are positively conservative under some typical wavespeed estimations. Moreover, a linear matrix stability analysis for the proposed schemes is accomplished, which illustrates the HLLC-type solver with shear viscosity is stable whereas the HLL-type solver with vorticity wave is unstable. Our arguments and numerical experiments demonstrate that the inadequate dissipation associated to the shear wave may be a unique reason to cause the instability.
Comparative study on diagonal equivalent methods of masonry infill panel
Amalia, Aniendhita Rizki; Iranata, Data
2017-06-01
ratio of height to width of 1 to 1.5. Load used in the experiment was based on Uniform Building Code (UBC) 1991. Every method compared was calculated first to get equivalent diagonal strut width. The second step was modelling method using structure analysis software as a frame with a diagonal in a linear mode. The linear mode was chosen based on structure analysis commonly used by structure designers. The frame was loaded and for every model, its load and deformation values were identified. The values of load - deformation of every method were compared to those of experimental test specimen by Mehrabi and open frame. From comparative study performed, Holmes' and Bazan-Meli's equations gave results the closest to the experimental test specimen by Mehrabi. Other equations that gave close values within the limit (by comparing it to the open frame) are Saneinejad-Hobbs, Stafford-Smith, Bazan-Meli, Liauw Kwan, Paulay and Priestley, FEMA 356, Durani Luo, Hendry, Papia and Chen-Iranata.
Numerical comparison of Riemann solvers for astrophysical hydrodynamics
Klingenberg, Christian; Waagan, Knut
2007-01-01
The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo
2015-09-13
In this research we are particularly interested in extending the robustness of multigrid solvers to encounter complex systems related to subsurface reservoir applications for flow problems in porous media. In many cases, the step for solving the pressure filed in subsurface flow simulation becomes a bottleneck for the performance of the simulator. For solving large sparse linear system arising from MPFA discretization, we choose multigrid methods as the linear solver. The possible difficulties and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately goal which we desire to achieve.
Gpu Implementation of a Viscous Flow Solver on Unstructured Grids
Xu, Tianhao; Chen, Long
2016-06-01
Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.
Constraint solvers: An empirical evaluation of design decisions
Kotthoff, Lars
2010-01-01
This paper presents an evaluation of the design decisions made in four state-of-the-art constraint solvers; Choco, ECLiPSe, Gecode, and Minion. To assess the impact of design decisions, instances of the five problem classes n-Queens, Golomb Ruler, Magic Square, Social Golfers, and Balanced Incomplete Block Design are modelled and solved with each solver. The results of the experiments are not meant to give an indication of the performance of a solver, but rather investigate what influence the choice of algorithms and data structures has. The analysis of the impact of the design decisions focuses on the different ways of memory management, behaviour with increasing problem size, and specialised algorithms for specific types of variables. It also briefly considers other, less significant decisions.
An adaptive fast multipole accelerated Poisson solver for complex geometries
Askham, T.; Cerfon, A. J.
2017-09-01
We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient ;black box; fast solver.
Exact models for isotropic matter
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Hewson, S F
1996-01-01
We investigate non-abelian gaugings of WZNW models. When the gauged group is semisimple we are able to present exact formulae for the dual conformal field theory, for all values of the level k. The results are then applied to non-abelian target space duality in string theory, showing that the standard formulae are quantum mechanically well defined in the low energy limit if the gauged group is semisimple.
A Summary of Design Formulas for Beams Having Thin Webs in Diagonal Tension
Kuhn, Paul
1933-01-01
This report presents an explanation of the fundamental principles and a summary of the essential formulas for the design of diagonal-tension field beams, i.e. beams with very thin webs, as developed by Professor Wagner of Germany.
Asymptotic correctability of Bell-diagonal quantum states and maximum tolerable bit error rates
Ranade, K S; Ranade, Kedar S.; Alber, Gernot
2005-01-01
The general conditions are discussed which quantum state purification protocols have to fulfill in order to be capable of purifying Bell-diagonal qubit-pair states, provided they consist of steps that map Bell-diagonal states to Bell-diagonal states and they finally apply a suitably chosen Calderbank-Shor-Steane code to the outcome of such steps. As a main result a necessary and a sufficient condition on asymptotic correctability are presented, which relate this problem to the magnitude of a characteristic exponent governing the relation between bit and phase errors under the purification steps. These conditions allow a straightforward determination of maximum tolerable bit error rates of quantum key distribution protocols whose security analysis can be reduced to the purification of Bell-diagonal states.
Free field approach to diagonalization of boundary transfer matrix : recent advances
Kojima, Takeo
2011-01-01
We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the solvable model with a boundary. When we diagonalize the boundary transfer matrix, we can calculate the correlation functions for the solvable model with a boundary. We review the free field approach to diagonalization of the boundary transfer matrix $T_B(z)$ associated with $U_q(A_2^{(2)})$ and $U_{q,p}(\\hat{sl_N})$. We construct the free field realizations of the eigenvectors of the boundary transfer matrix $T_B(z)$. This paper includes new unpublished formula of the eigenvector for $U_q(A_2^{(2)})$. It is thought that this diagonalization method can be extended to more general quantum group $U_q(g)$ and elliptic quantum group $U_{q,p}(g)$.
Localization in band random matrix models with and without increasing diagonal elements.
Wang, Wen-ge
2002-06-01
It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dimensions can be introduced for nonperturbative parts of eigenfunctions, and by employing intermediate basis states, which can improve the method of the reduced Hamiltonian matrix. The latter model deviates from the standard band random matrix model mainly in two aspects: (i) the root mean square of diagonal elements is larger than that of off-diagonal elements within the band, and (ii) statistical distributions of the matrix elements are close to the Lévy distribution in their central parts, except in the high top regions.
QUASI-DIAGONALIZATION FOR A SINGULARLY PERTURBED DIFFERENTIAL SYSTEM WITH TWO PARAMETERS
无
2011-01-01
By two successive linear transformations,a singularly perturbed differential system with two parameters is quasi-diagonalized. The method of variation of constants and the principle of contraction map are used to prove the existence of the transformations.
线性变换对角化问题浅析%Diagonalization of Linear Transformation
王玉梅
2011-01-01
For the linear transform and matrix diagonalization diagonalization similar to the link between the easily understood by matrix diagonalization to study the relative complexity of diagonalization of the linear transformation, and then by studying the eige%对于线性变换对角化与矩阵相似对角化之间的联系,通过对易理解的矩阵的对角化问题来研究相对复杂线性变换的对角化问题,然后通过研究特征值与特征向量的性质,再研究对角化的必要条件与充分条件,从而更轻松的理解并掌握线性变换的对角化问题。
Decomposition During Search for Propagation-Based Constraint Solvers
Mann, Martin; Will, Sebastian
2007-01-01
We describe decomposition during search (DDS), an integration of and/or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into independent partial problems, avoiding redundant work. The paper discusses how DDS interacts with key features that make propagation-based solvers successful: constraint propagation, especially for global constraints, and dynamic search heuristics. We have implemented DDS for the Gecode constraint programming library. Two applications, solution counting in graph coloring and protein structure prediction, exemplify the benefits of DDS in practice.
LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators
Gonzalez, Juan; Nunez, Rafael C, E-mail: juan.gonzalez@accelogic.co [Accelogic, 1830 Main Street, Suite 204, Weston, FL (United States)
2009-07-01
We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.
Efficient use of iterative solvers in nested topology optimization
Amir, Oded; Stolpe, Mathias; Sigmund, Ole
2010-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the analysis problem, generated by a Krylov...... subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence measures...
An Easy Method To Accelerate An Iterative Algebraic Equation Solver
Yao, Jin [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2014-01-06
This article proposes to add a simple term to an iterative algebraic equation solver with an order n convergence rate, and to raise the order of convergence to (2n - 1). In particular, a simple algebraic equation solver with the 5th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an low overhead cost of function evaluation that can be ignored as the size of the system increases.
Numerical System Solver Developed for the National Cycle Program
Binder, Michael P.
1999-01-01
As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.
Diagonal Kernel Point Estimation of th-Order Discrete Volterra-Wiener Systems
Pirani Massimiliano
2004-01-01
Full Text Available The estimation of diagonal elements of a Wiener model kernel is a well-known problem. The new operators and notations proposed here aim at the implementation of efficient and accurate nonparametric algorithms for the identification of diagonal points. The formulas presented here allow a direct implementation of Wiener kernel identification up to the th order. Their efficiency is demonstrated by simulations conducted on discrete Volterra systems up to fifth order.
Pietracaprina, Francesca; Gogolin, Christian; Goold, John
2016-01-01
The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics. In analogy to the time average of a classical phase space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper-bound on the multipartite entang...
The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator
Damanik, David
2008-01-01
We consider Jacobi matrices with zero diagonal and off-diagonals given by elements of the hull of the Fibonacci sequence and show that the spectrum has zero Lebesgue measure and all spectral measures are purely singular continuous. In addition, if the two hopping parameters are distinct but sufficiently close to each other, we show that the spectrum is a dynamically defined Cantor set, which has a variety of consequences for its local and global fractal dimension.
Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states
Wang, Xin-Wen; Tang, Shi-Qing; Yuan, Ji-Bing; Zhang, Deng-Yu
2017-06-01
It has been shown that a nearly pure Greenberger-Horne-Zeilinger (GHZ) state could be distilled from a large (even infinite) number of GHZ-diagonal states that can be obtained by depolarizing general multipartite mixed states (non-GHZ-diagonal states) through sequences of (probabilistic) local operations and classical communications. We here demonstrate that perfect GHZ states can be extracted, with certain probabilities, from two copies of non-GHZ-diagonal mixed states when some conditions are satisfied. This result implies that it is not necessary to depolarize these entangled mixed states to the GHZ-diagonal type, and that they are better than GHZ-diagonal states for distillation of pure GHZ states. We find a wide class of multipartite entangled mixed states that fulfill the requirements. Moreover, we display that the obtained result can be applied to practical noisy environments, e.g., amplitude-damping channels. Our findings provide an important complementarity to conventional GHZ-state distillation protocols (designed for GHZ-diagonal states) in theory, as well as having practical applications.
In Vivo Imaging Reveals Composite Coding for Diagonal Motion in the Drosophila Visual System
Zhou, Wei; Chang, Jin
2016-01-01
Understanding information coding is important for resolving the functions of visual neural circuits. The motion vision system is a classic model for studying information coding as it contains a concise and complete information-processing circuit. In Drosophila, the axon terminals of motion-detection neurons (T4 and T5) project to the lobula plate, which comprises four regions that respond to the four cardinal directions of motion. The lobula plate thus represents a topographic map on a transverse plane. This enables us to study the coding of diagonal motion by investigating its response pattern. By using in vivo two-photon calcium imaging, we found that the axon terminals of T4 and T5 cells in the lobula plate were activated during diagonal motion. Further experiments showed that the response to diagonal motion is distributed over the following two regions compared to the cardinal directions of motion—a diagonal motion selective response region and a non-selective response region—which overlap with the response regions of the two vector-correlated cardinal directions of motion. Interestingly, the sizes of the non-selective response regions are linearly correlated with the angle of the diagonal motion. These results revealed that the Drosophila visual system employs a composite coding for diagonal motion that includes both independent coding and vector decomposition coding. PMID:27695103
Diagonal Loading of Robust General-Rank Beamformer for Direction of Arrival Mismatch
Z.U. Khan
2013-05-01
Full Text Available This study presents a technique which utilizes the movement of the peak of the main beam towards the presumed signal direction with negative diagonal loading for robust general-rank beamformer. The main beam symmetry along presumed signal direction is improved by this movement. When desired signal is contained in the data snapshots, the conventional beamformers face the problem of performance degradation even if there is a small mismatch between the presumed and the actual signal direction. Diagonal loading is a popular technique to mitigate this problem. There is no definite criterion to find diagonal loading level. A new diagonal loading method has been proposed in the literature which utilizes the movement of the peak of main beam towards the presumed signal direction with positive diagonal loading. The proposed technique works iteratively for the selection of negative diagonal loading level to move the main beam at a position to get the beam symmetry at desired level and hence the desired robustness. The mismatched signal will not be cancelled as long as it is within the half of the width of the main beam. But there is the tradeoff between this robustness and interference cancelling capability.
Exact analytical solutions for ADAFs
Habibi, Asiyeh; Shadmehri, Mohsen
2016-01-01
We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is $T_{r\\varphi}$. Furthermore we assume that the value of viscosity coefficient $\\alpha$ varies with $\\theta$. We find radially self-similar solutions and compare them with the numerical and the analytical solutions already studied in the literature. The no-wind solution obtained in this paper may be applied to the nuclei of some cool-core clusters.
EXACT ALGORITHM FOR BIN COVERING
无
2001-01-01
This paper presents a new arc flow model for the one-dimensional bin covering problem and an algorithm to solve the problem exactly through a branch-and-bound procedure and the technique of column generation. The subproblems occuring in the procedure of branch-and-bound have the same structure and therefore can be solved by the same algorithm. In order to solve effectively the subproblems which are generally large scale, a column generation algorithm is employed. Many rules found in this paper can improve the performance of the methods.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Parallel time domain solvers for electrically large transient scattering problems
Liu, Yang
2014-09-26
Marching on in time (MOT)-based integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. MOT integral equation solvers for analyzing electromagnetic scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary to finite difference and element competitors, these solvers apply to nonlinear and multi-scale structures comprising geometrically intricate and deep sub-wavelength features residing atop electrically large platforms. Moreover, they are high-order accurate, stable in the low- and high-frequency limits, and applicable to conducting and penetrable structures represented by highly irregular meshes. This presentation reviews some recent advances in the parallel implementations of time domain integral equation solvers, specifically those that leverage multilevel plane-wave time-domain algorithm (PWTD) on modern manycore computer architectures including graphics processing units (GPUs) and distributed memory supercomputers. The GPU-based implementation achieves at least one order of magnitude speedups compared to serial implementations while the distributed parallel implementation are highly scalable to thousands of compute-nodes. A distributed parallel PWTD kernel has been adopted to solve time domain surface/volume integral equations (TDSIE/TDVIE) for analyzing transient scattering from large and complex-shaped perfectly electrically conducting (PEC)/dielectric objects involving ten million/tens of millions of spatial unknowns.
Implementing parallel elliptic solver on a Beowulf cluster
Marcin Paprzycki
1999-12-01
Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Time-varying Riemann solvers for conservation laws on networks
Garavello, Mauro; Piccoli, Benedetto
We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.
Performance evaluation of a parallel sparse lattice Boltzmann solver
Axner, L.; Bernsdorf, J.; Zeiser, T.; Lammers, P.; Linxweiler, J.; Hoekstra, A.G.
2008-01-01
We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and
Implementing parallel elliptic solver on a Beowulf cluster
Marcin Paprzycki; Svetozara Petrova; Julian Sanchez
1999-01-01
In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.
Navier-Stokes Solvers and Generalizations for Reacting Flow Problems
Elman, Howard C
2013-01-27
This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).
A vectorizable adaptive grid solver for PDEs in 3D
Blom, J.G.; Verwer, J.G.
1993-01-01
This paper describes the application of an adaptive-grid finite-difference solver to some time-dependent three-dimensional systems of partial differential equations. The code is a 3D extension of the 2D code VLUGR2[3].
PSH3D fast Poisson solver for petascale DNS
Adams, Darren; Dodd, Michael; Ferrante, Antonino
2016-11-01
Direct numerical simulation (DNS) of high Reynolds number, Re >= O (105) , turbulent flows requires computational meshes >= O (1012) grid points, and, thus, the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the solver. We have developed a parallel solver of the Helmholtz equation in 3D, PSH3D. The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform in two spatial directions, and a parallel linear solver in the third direction. For computational meshes up to 81923 grid points, our numerical results show that PSH3D scales up to at least 262k cores of Cray XT5 (Blue Waters). PSH3D has a peak performance 6 × faster than 3D FFT-based methods when used with the 'partial-global' optimization, and for a 81923 mesh solves the Poisson equation in 1 sec using 128k cores. Also, we have verified that the use of PSH3D with the 'partial-global' optimization in our DNS solver does not reduce the accuracy of the numerical solution of the incompressible Navier-Stokes equations.
Hypersonic simulations using open-source CFD and DSMC solvers
Casseau, V.; Scanlon, T. J.; John, B.; Emerson, D. R.; Brown, R. E.
2016-11-01
Hypersonic hybrid hydrodynamic-molecular gas flow solvers are required to satisfy the two essential requirements of any high-speed reacting code, these being physical accuracy and computational efficiency. The James Weir Fluids Laboratory at the University of Strathclyde is currently developing an open-source hybrid code which will eventually reconcile the direct simulation Monte-Carlo method, making use of the OpenFOAM application called dsmcFoam, and the newly coded open-source two-temperature computational fluid dynamics solver named hy2Foam. In conjunction with employing the CVDV chemistry-vibration model in hy2Foam, novel use is made of the QK rates in a CFD solver. In this paper, further testing is performed, in particular with the CFD solver, to ensure its efficacy before considering more advanced test cases. The hy2Foam and dsmcFoam codes have shown to compare reasonably well, thus providing a useful basis for other codes to compare against.
Parallel Solver for H(div) Problems Using Hybridization and AMG
Lee, Chak S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-15
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-01
Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang, E-mail: yuhang_tang@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Kudo, Shuhei, E-mail: shuhei-kudo@outlook.jp [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501 (Japan); Bian, Xin, E-mail: xin_bian@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Li, Zhen, E-mail: zhen_li@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Collaboratory on Mathematics for Mesoscopic Modeling of Materials, Pacific Northwest National Laboratory, Richland, WA 99354 (United States)
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
A High Performance QDWH-SVD Solver using Hardware Accelerators
Sukkari, Dalal E.
2015-04-08
This paper describes a new high performance implementation of the QR-based Dynamically Weighted Halley Singular Value Decomposition (QDWH-SVD) solver on multicore architecture enhanced with multiple GPUs. The standard QDWH-SVD algorithm was introduced by Nakatsukasa and Higham (SIAM SISC, 2013) and combines three successive computational stages: (1) the polar decomposition calculation of the original matrix using the QDWH algorithm, (2) the symmetric eigendecomposition of the resulting polar factor to obtain the singular values and the right singular vectors and (3) the matrix-matrix multiplication to get the associated left singular vectors. A comprehensive test suite highlights the numerical robustness of the QDWH-SVD solver. Although it performs up to two times more flops when computing all singular vectors compared to the standard SVD solver algorithm, our new high performance implementation on single GPU results in up to 3.8x improvements for asymptotic matrix sizes, compared to the equivalent routines from existing state-of-the-art open-source and commercial libraries. However, when only singular values are needed, QDWH-SVD is penalized by performing up to 14 times more flops. The singular value only implementation of QDWH-SVD on single GPU can still run up to 18% faster than the best existing equivalent routines. Integrating mixed precision techniques in the solver can additionally provide up to 40% improvement at the price of losing few digits of accuracy, compared to the full double precision floating point arithmetic. We further leverage the single GPU QDWH-SVD implementation by introducing the first multi-GPU SVD solver to study the scalability of the QDWH-SVD framework.
Advances in three-dimensional geoelectric forward solver techniques
Blome, M.; Maurer, H. R.; Schmidt, K.
2009-03-01
Modern geoelectrical data acquisition systems allow large amounts of data to be collected in a short time. Inversions of such data sets require powerful forward solvers for predicting the electrical potentials. State-of-the-art solvers are typically based on finite elements. Recent developments in numerical mathematics led to direct matrix solvers that allow the equation systems arising from such finite element problems to be solved very efficiently. They are particularly useful for 3-D geoelectrical problems, where many electrodes are involved. Although modern direct matrix solvers include optimized memory saving strategies, their application to realistic, large-scale 3-D problems is still somewhat limited. Therefore, we present two novel techniques that allow the number of gridpoints to be reduced considerably, while maintaining a high solution accuracy. In the areas surrounding an electrode array we attach infinite elements that continue the electrical potentials to infinity. This does not only reduce the number of gridpoints, but also avoids the artificial Dirichlet or mixed boundary conditions that are well known to be the cause of numerical inaccuracies. Our second development concerns the singularity removal in the presence of significant surface topography. We employ a fast multipole boundary element method for computing the singular potentials. This renders unnecessary mesh refinements near the electrodes, which results in substantial savings of gridpoints of up to more than 50 per cent. By means of extensive numerical tests we demonstrate that combined application of infinite elements and singularity removal allows the number of gridpoints to be reduced by a factor of ~6-10 compared with traditional finite element methods. This will be key for applying finite elements and direct matrix solver techniques to realistic 3-D inversion problems.
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
Migration of vectorized iterative solvers to distributed memory architectures
Pommerell, C. [AT& T Bell Labs., Murray Hill, NJ (United States); Ruehl, R. [CSCS-ETH, Manno (Switzerland)
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
Cwik, T.; Jamnejad, V.; Zuffada, C. [California Institute of Technology, Pasadena, CA (United States)
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
Exact Renormalization of Massless QED2
Casana, R; Casana, Rodolfo; Dias, Sebastiao Alves
2001-01-01
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Exact Renormalization of Massless QED2
Casana, Rodolfo; Dias, Sebastião Alves
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Exact finite elements for conduction and convection
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
A Multiscale Wavelet Solver with O( n) Complexity
Williams, John R.; Amaratunga, Kevin
1995-11-01
In this paper, we use the biorthogonal wavelets recently constructed by Dahlke and Weinreich to implement a highly efficient procedure for solving a certain class of one-dimensional problems, (∂21/∂x21)u = f,I ɛ Z, I > 0. For these problems, the discrete biorthogonal wavelet transform allows us to set up a system of wavelet-Galerkin equations in which the scales are uncoupled, so that a true multiscale solution procedure may be formulated. We prove that the resulting stiffness matrix is in fact an almost perfectly diagonal matrix (the original aim of the construction was to achieve a block diagonal structure) and we show that this leads to an algorithm whose cost is O(n). We also present numerical results which demonstrate that the multiscale biorthogonal wavelet algorithm is superior to the more conventional single scale orthogonal wavelet approach both in terms of speed and in terms of convergence.
Obtaining exact value by approximate computations
Jing-zhong ZHANG; Yong FENG
2007-01-01
Numerical approximate computations can solve large and complex problems fast. They have the advantage of high efficiency. However they only give approximate results, whereas we need exact results in some fields. There is a gap between approximate computations and exact results.In this paper, we build a bridge by which exact results can be obtained by numerical approximate computations.
Weakly exact categories and the snake lemma
Jafari, Amir
2009-01-01
We generalize the notion of an exact category and introduce weakly exact categories. A proof of the snake lemma in this general setting is given. Some applications are given to illustrate how one can do homological algebra in a weakly exact category.
Obtaining exact value by approximate computations
2007-01-01
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
Exact propagators in harmonic superspace
Kuzenko, Sergei M.
2004-10-01
Within the background field formulation in harmonic superspace for quantum N = 2 super-Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in arxiv:hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super-Yang-Mills theory.
Exact propagators in harmonic superspace
Kuzenko, S M
2004-01-01
Within the background field formulation in harmonic superspace for quantum N = 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super Yang-Mills theory.
Exact Bremsstrahlung and Effective Couplings
Mitev, Vladimir
2015-01-01
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of $\\mathcal{N}=2$ SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the $\\mathcal{N}=4$ SYM ones, we obtain interpolating functions $f(g^2)$ such that a given $\\mathcal{N}=2$ SCFT observable is obtained by replacing in the corresponding $\\mathcal{N}=4$ SYM result the coupling constant by $f(g^2)$. These ``exact effective couplings'' encode the finite, relative renormalization between the $\\mathcal{N}=2$ and the $\\mathcal{N}=4$ gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Exact Bremsstrahlung and effective couplings
Mitev, Vladimir; Pomoni, Elli
2016-06-01
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of mathcal{N} = 2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the mathcal{N} = 4 SYM ones, we obtain interpolating functions f ( g 2) such that a given mathcal{N} = 2 SCFT observable is obtained by replacing in the corresponding mathcal{N} = 4 SYM result the coupling constant by f ( g 2). These "exact effective couplings" encode the finite, relative renormalization between the mathcal{N} = 2 and the mathcal{N} = 4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Exact Bremsstrahlung and effective couplings
Mitev, Vladimir [Mainz Univ. (Germany). Inst. fuer Physik, WA THEP; Humboldt-Univ. Berlin (Germany). Inst. fuer Mathematik und Inst. fuer Physik; Pomoni, Elli [DESY Hamburg (Germany). Theory Group; National Technical Univ., Athens (Greece). Physics Div.
2015-11-15
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N=2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the N=4 SYM ones, we obtain interpolating functions f(g{sup 2}) such that a given N=2 SCFT observable is obtained by replacing in the corresponding N=4 SYM result the coupling constant by f(g{sup 2}). These ''exact effective couplings'' encode the finite, relative renormalization between the N = 2 and the N = 4 gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Lightning Surge Analysis Including Diagonal Wires Based on the FDTD Method
Yamamoto, Kazuo; Iki, Hiroyuki
This paper presents an arbitrary diagonal wire on an rectangular surface composing a cubic cell in an electromagnetic analysis based on the orthogonal FDTD (Finite-Difference Time-Domain) Algorithm. One of the numerical electromagnetic analyzing algorithms is the FDTD method based on Maxwell’s equation. The basic FDTD method divides the analyzed space into cubic cells and directly calculates the electrical and magnetic fields of the cells by discretizing the Maxwell’s equation of electromagnetic fields, where the derivatives with respect to time and space are replaced by a numerical difference. The development of computer performance brings about an actual execution of the FDTD method on a usual personal computer recently. In dealing with a diagonal and curved wire, the boundaries of which do not coincide with the finite-difference grid lines, the staircase approximation has been commonly used. However, the approximation causes the large error in a resonant frequency and a propagation time of a system including the diagonal or curved wire. The proposed method can express a diagonal and curved wires on a rectangular surface composing a cubic cell by transforming the general integral form of Maxwell’s equation to the different integral form around the wires. This proposed method is also useful to calculate surge propagation on an arbitrary three-dimensional skeleton structure including a diagonal or curved grid such as a tower model and so on.
Volume localized spin echo correlation spectroscopy with suppression of 'diagonal' peaks.
Banerjee, Abhishek; Chandrakumar, N
2014-02-01
Two dimensional homonuclear (1)H correlation spectroscopy is of considerable interest for volume localized spectral studies, both in vivo and in vitro, of biological as well as material objects. The information principally sought from correlation spectra resides in the cross-peaks, which are often masked however by the presence of diagonal peaks in COSY, or 'pseudo-diagonal' peaks at F1=0 in SECSY. It has therefore been a concern to suppress these diagonal or 'pseudo-diagonal' peaks, in order to ensure that cross-peak information is fully discernible. We present here a report of our work on volume localized DIagonal Suppressed Spin Echo Correlation specTroscopy (LDISSECT) and demonstrate its performance in comparison to the standard volume localized SECSY experiment, employing brain metabolite phantoms in a gel. The sequence works in the inhomogeneous, multi-component environment by exploiting the short acquisition time to suppress undesired information by employing an additional rf pulse. A brief description of the pulse sequence, its theory, and simulations are also included, besides experimental benchmarking on two brain metabolite phantoms in gel phase.
Sex determination in modern Greeks using diagonal measurements of molar teeth.
Zorba, Eleni; Moraitis, Konstantinos; Eliopoulos, Constantine; Spiliopoulou, Chara
2012-04-10
Sex determination is a necessary step in the investigation of unidentified human remains from a forensic context. Teeth, as one of the strongest tissues in the human body, can be used for this purpose. Most studies of sexual dimorphism in teeth are based on the traditional mesiodistal and buccolingual crown measurements. The purpose of this study is to examine the degree of sexual dimorphism in permanent molars of modern Greeks using crown and cervical diagonal diameters, and to evaluate their applicability in sex determination. A total of 344 permanent molars in 107 individuals (53 male and 54 female) from the Athens Collection were examined. Crown and cervical diagonal diameters of both maxillary and mandibular molars were measured. It was found that males have larger molars than females and in 19 out of 24 dimensions measured male molars exceeded female molars significantly (Pdiagonal diameters have found to be more sexually diamorphic than crown diagonal diameters. In discriminant function analysis the variables entered more frequently were the cervical diagonal diameters mainly of mandibular molars. Classification accuracy was found to be 93% for the total sample, 77.4% for upper jaw, and 88.4% for the lower jaw. Accuracy rates were higher for cervical than crown diagonal diameters. The data generated from the present study suggest that this metric method can be useful and reliable for sex determination, especially when the traditional dental measurements are not applicable.
三体Bell对角态的纠缠%Entanglement of Tripartite Bell Diagonal States
赵慧; 张兴华
2011-01-01
给出了三体2(×)2(×)3Bell对角态纠缠判定的一个必要条件和3(×)3(×)3Bell对角态纠缠的充分条件,进一步研究了3(×)3(×)3Bell对角态纠缠与密度矩阵部分转置的关系以及Bell对角态负性的数学表达式.%A necessary condition of entanglement for tripartite 2 (⊕)2 (⊕)3 Bell diagonal states and a sufficient condition of entanglement for 3 (⊕)3 (⊕)3 Bell diagonal states are presented. Moreover, the relation between entanglement of 3(⊕)3(⊕)3 Bell diagonal states and partial transpose of density matrix is investigated. And an analytical expression of negative for Bell diagonal states is presented.Key words: Bell diagonal states; entanglement; density matrix Robust Estimation for Varying Coefficient Model Abstract: This paper considers robust estimation of varying coefficient models with emphasis on resistance against outliers. By combining B-splines method with taut string method, a robust estimation procedure is proposed. Based on local quadratic approximation, an iterative algorithm is introduced. Simulation study indicates that the proposed method is robust.
Arif GÜRAY
2002-01-01
Full Text Available In this work, the diagonal tensile strength of furniture edge joints such as wooden dowel, minifix, and alyan screw was investigated in panel-constructed boards for Suntalam and MDF Lam. For this purpose, a diagonal tensile strength test was applied to the 72 samples. According to the results, the maximum diagonal tensile strength was found to be in MDF Lam boards that jointed with alyan screw.
Covariant Renormalizable Anisotropic Theories and Off-Diagonal Einstein-Yang-Mills-Higgs Solutions
Vacaru, Sergiu I
2011-01-01
We use an important decoupling property of gravitational field equations in the general relativity theory and modifications, written with respect to nonholonomic frames with 2+2 spacetime decomposition. This allows us to integrate the Einstein equations in very general forms with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (broken and un-broken) symmetry parameters. We associate families of off-diagonal Einstein manifolds to certain classes of covariant gravity theories which have a nice ultraviolet behavior and seem to be (super) renormalizable in a sense of covariant modifications of Ho\\v{r}ava-Lifshits gravity. The apparent breaking of Lorentz invariance is present in some "partner" anisotropically induced theories due to nonlinear coupling with effective parametric interactions determined by nonholonomic constraints and generic off-diagonal gravitational and matter fields configurations. Finally, we show how the constructions can...
Shrinkage-based diagonal discriminant analysis and its applications in high-dimensional data.
Pang, Herbert; Tong, Tiejun; Zhao, Hongyu
2009-12-01
High-dimensional data such as microarrays have brought us new statistical challenges. For example, using a large number of genes to classify samples based on a small number of microarrays remains a difficult problem. Diagonal discriminant analysis, support vector machines, and k-nearest neighbor have been suggested as among the best methods for small sample size situations, but none was found to be superior to others. In this article, we propose an improved diagonal discriminant approach through shrinkage and regularization of the variances. The performance of our new approach along with the existing methods is studied through simulations and applications to real data. These studies show that the proposed shrinkage-based and regularization diagonal discriminant methods have lower misclassification rates than existing methods in many cases.
Rossi-Arnaud, Clelia; Pieroni, Laura; Spataro, Pietro; Baddeley, Alan
2012-09-01
Previous studies, using a modified version of the sequential Corsi block task to examine the impact of symmetry on visuospatial memory, showed an advantage of vertical symmetry over non-symmetrical sequences, but no effect of horizontal or diagonal symmetry. The present four experiments investigated the mechanisms underlying the encoding of vertical, horizontal and diagonal configurations using simultaneous presentation and a dual-task paradigm. Results indicated that the recall of vertically symmetric arrays was always better than that of all other patterns and was not influenced by any of the concurrent tasks. Performance with horizontally or diagonally symmetrical patterns differed, with high performing participants showing little effect of concurrent tasks, while low performers were disrupted by concurrent visuospatial and executive tasks. A verbal interference had no effect on either group. Implications for processes involved in the encoding of symmetry are discussed, together with the crucial importance of individual differences.
Gevaert, Kris; Van Damme, Petra; Martens, Lennart; Vandekerckhove, Joël
2005-10-01
Diagonal electrophoresis/chromatography was described 40 years ago and was used to isolate specific sets of peptides from simple peptide mixtures such as protease digests of purified proteins. Recently, we have adapted the core technology of diagonal chromatography so that the technique can be used in so-called gel-free, peptide-centric proteome studies. Here we review the different procedures we have developed over the past few years, sorting of methionyl, cysteinyl, amino terminal, and phosphorylated peptides. We illustrate the power of the technique, termed COFRADIC (combined fractional diagonal chromatography), in the case of a peptide-centric analysis of a sputum sol phase sample of a patient suffering from chronic obstructive pulmonary disease (COPD). We were able to identify an unexpectedly high number of intracellular proteins next to known biomarkers.
Perras, Frédéric A; Widdifield, Cory M; Bryce, David L
2012-01-01
We present a new program for the exact simulation of solid-state NMR spectra of quadrupolar nuclei in stationary powdered samples which employs diagonalization of the combined Zeeman-quadrupolar Hamiltonian. The program, which we call QUEST (QUadrupolar Exact SofTware), can simulate NMR spectra over the full regime of Larmor and quadrupolar frequency ratios, which encompasses scenarios ranging from high-field NMR to nuclear quadrupole resonance (NQR, where the Larmor frequency is zero) and does not make use of approximations when treating the quadrupolar interaction. With the use of the fast powder averaging scheme of Alderman, Solum, and Grant, exact NMR spectral simulations are only marginally slower than the second-order perturbation theory counterpart. The program, which uses a graphical user interface, also incorporates chemical shift anisotropy and non-coincident chemical shift and quadrupolar tensor frames. The program is validated against newly-acquired experimental data through several examples including: the low-field (79/81)Br NMR spectra of CaBr(2), the (14)N overtone NMR spectrum of glycine, the (187)Re NQR spectra of Re(2)(CO)(10), and lastly the (127)I overtone NQR spectrum of SrI(2), which, to the best of our knowledge, represents the first direct acquisition of an overtone NQR spectrum for a powdered sample.
On improving linear solver performance: a block variant of GMRES
Baker, A H; Dennis, J M; Jessup, E R
2004-05-10
The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.
Error Control of Iterative Linear Solvers for Integrated Groundwater Models
Dixon, Matthew; Brush, Charles; Chung, Francis; Dogrul, Emin; Kadir, Tariq
2010-01-01
An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a prac...
LDRD report : parallel repartitioning for optimal solver performance.
Heaphy, Robert; Devine, Karen Dragon; Preis, Robert (University of Paderborn, Paderborn, Germany); Hendrickson, Bruce Alan; Heroux, Michael Allen; Boman, Erik Gunnar
2004-02-01
We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
HLL Riemann Solvers and Alfven Waves in Black Hole Magnetospheres
Punsly, Brian; Kim, Jinho; Garain, Sudip
2016-01-01
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. However, numerical simulations of black hole magnetospheres are often based on 1-D HLL Riemann solvers that readily dissipate Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, it is unclear how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. The HLL Riemann solver is also notorious for producing large recurring...
Scalable Out-of-Core Solvers on Xeon Phi Cluster
D' Azevedo, Ed F [ORNL; Chan, Ki Shing [Chinese University of Hong Kong (CUHK); Su, Shiquan [Center for Computational Materials Science; Wong, Kwai [ORNL
2015-01-01
This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.
Benchmarking ICRF Full-wave Solvers for ITER
R. V. Budny, L. Berry, R. Bilato, P. Bonoli, M. Brambilla, R. J. Dumont, A. Fukuyama, R. Harvey, E. F. Jaeger, K. Indireshkumar, E. Lerche, D. McCune, C. K. Phillips, V. Vdovin, J. Wright, and members of the ITPA-IOS
2011-01-06
Abstract Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
Optimizing communication satellites payload configuration with exact approaches
Stathakis, Apostolos; Danoy, Grégoire; Bouvry, Pascal; Talbi, El-Ghazali; Morelli, Gianluigi
2015-12-01
The satellite communications market is competitive and rapidly evolving. The payload, which is in charge of applying frequency conversion and amplification to the signals received from Earth before their retransmission, is made of various components. These include reconfigurable switches that permit the re-routing of signals based on market demand or because of some hardware failure. In order to meet modern requirements, the size and the complexity of current communication payloads are increasing significantly. Consequently, the optimal payload configuration, which was previously done manually by the engineers with the use of computerized schematics, is now becoming a difficult and time consuming task. Efficient optimization techniques are therefore required to find the optimal set(s) of switch positions to optimize some operational objective(s). In order to tackle this challenging problem for the satellite industry, this work proposes two Integer Linear Programming (ILP) models. The first one is single-objective and focuses on the minimization of the length of the longest channel path, while the second one is bi-objective and additionally aims at minimizing the number of switch changes in the payload switch matrix. Experiments are conducted on a large set of instances of realistic payload sizes using the CPLEX® solver and two well-known exact multi-objective algorithms. Numerical results demonstrate the efficiency and limitations of the ILP approach on this real-world problem.
Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm
Gubernatis, James
2014-03-01
A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.
Brittle Solvers: Lessons and insights into effective solvers for visco-plasticity in geodynamics
Spiegelman, M. W.; May, D.; Wilson, C. R.
2014-12-01
Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear solvers. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to
Parallel Nonnegative Least Squares Solvers for Model Order Reduction
2016-03-01
not for the PQN method. For the latter method the size of the active set is controlled to promote sparse solutions. This is described in Section 3.2.1...or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington...21005-5066 primary author’s email: <james.p.collins106.civ@mail.mil>. Parallel nonnegative least squares (NNLS) solvers are developed specifically for
Surviving Solver Sensitivity: An ASP Practitioners Guide
Silverthorn, Bryan; Lierler, Yuliya; Schneider, Marius
2012-01-01
Answer set programming (ASP) is a declarative programming formalism that allows a practitioner to specify a problem without describing an algorithm for solving it. In ASP, the tools for processing problem specifications are called answer set solvers. Because specified problems are often NP complete, these systems often require significant computational effort to succeed. Furthermore, they offer different heuristics, expose numerous parameters, and their running time is sensitive to the config...
Direct linear programming solver in C for structural applications
Damkilde, L.; Hoyer, O.; Krenk, S.
1994-08-01
An optimization problem can be characterized by an object-function, which is maximized, and restrictions, which limit the variation of the variables. A subclass of optimization is Linear Programming (LP), where both the object-function and the restrictions are linear functions of the variables. The traditional solution methods for LP problems are based on the simplex method, and it is customary to allow only non-negative variables. Compared to other optimization routines the LP solvers are more robust and the optimum is reached in a finite number of steps and is not sensitive to the starting point. For structural applications many optimization problems can be linearized and solved by LP routines. However, the structural variables are not always non-negative, and this requires a reformation, where a variable x is substituted by the difference of two non-negative variables, x(sup + ) and x(sup - ). The transformation causes a doubling of the number of variables, and in a computer implementation the memory allocation doubles and for a typical problem the execution time at least doubles. This paper describes a LP solver written in C, which can handle a combination of non-negative variables and unlimited variables. The LP solver also allows restart, and this may reduce the computational costs if the solution to a similar LP problem is known a priori. The algorithm is based on the simplex method, and differs only in the logical choices. Application of the new LP solver will at the same time give both a more direct problem formulation and a more efficient program.
Resolving Neighbourhood Relations in a Parallel Fluid Dynamic Solver
Frisch, Jerome
2012-06-01
Computational Fluid Dynamics simulations require an enormous computational effort if a physically reasonable accuracy should be reached. Therefore, a parallel implementation is inevitable. This paper describes the basics of our implemented fluid solver with a special aspect on the hierarchical data structure, unique cell and grid identification, and the neighbourhood relations in-between grids on different processes. A special server concept keeps track of every grid over all processes while minimising data transfer between the nodes. © 2012 IEEE.
A chemical reaction network solver for the astrophysics code NIRVANA
Ziegler, U.
2016-02-01
Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes
A contribution to the great Riemann solver debate
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
STABLE PROGRAMMED MANIFOLD SOLVER FOR VIRTUAL PROTOTYPING MOTION SIMULATION
无
2006-01-01
Based on constructing programmed constraint and constraint perturbation equation, a kinematics and dynamics numerical simulation model is established for virtual mechanism, in which the difference scheme guarantee precision in simulation procedure and its numerical solutions satisfy programmed manifold stability. A crank-piston mechanism in a car engine, a steering mechanism and a suspension mechanism are simulated in a virtual environment, then comparing the simulation results with those obtained in ADAMS under the same circumstances proved the solver valid.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I.; Wang, Chunguang
2014-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Boundary energy of the open XXX chain with a non-diagonal boundary term
Nepomechie, Rafael I
2013-01-01
We analyze the ground state of the open spin-1/2 isotropic quantum spin chain with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots split evenly into two sets: those that remain finite, and those that become infinite. We argue that the former satisfy conventional Bethe equations, while the latter satisfy a generalization of the Richardson-Gaudin equations. We derive an expression for the leading correction to the boundary energy in terms of the boundary parameters.
Jiang, Tongsong, E-mail: jiangtongsong@sina.com [Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China); Department of Mathematics, Heze University, Heze, Shandong 274015 (China); Jiang, Ziwu; Zhang, Zhaozhong [Department of Mathematics, Linyi University, Linyi, Shandong 276005 (China)
2015-08-15
In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.
Time-dependent renormalized Redfield theory II for off-diagonal transition in reduced density matrix
Kimura, Akihiro
2016-09-01
In our previous letter (Kimura, 2016), we constructed time-dependent renormalized Redfield theory (TRRT) only for diagonal transition in a reduced density matrix. In this letter, we formulate the general expression for off-diagonal transition in the reduced density matrix. We discuss the applicability of TRRT by numerically comparing the dependencies on the energy gap of the exciton relaxation rate by using the TRRT and the modified Redfield theory (MRT). In particular, we roughly show that TRRT improves MRT for the detailed balance about the excitation energy transfer reaction.
Single-Channel Noise Reduction using Unified Joint Diagonalization and Optimal Filtering
Nørholm, Sidsel Marie; Benesty, Jacob; Jensen, Jesper Rindom;
2014-01-01
In this paper, the important problem of single-channel noise reduction is treated from a new perspective. The problem is posed as a filtering problem based on joint diagonalization of the covariance matrices of the desired and noise signals. More specifically, the eigenvectors from the joint...... diagonalization corresponding to the least significant eigenvalues are used to form a filter, which effectively estimates the noise when applied to the observed signal. This estimate is then subtracted from the observed signal to form an estimate of the desired signal, i.e., the speech signal. In doing this, we...
On the Reduction of a Complex Matrix to Triangular or Diagonal by Consimilarity
Tongsong Jiang; Musheng Wei
2006-01-01
Two n × n complex matrices A and B are said to be consimilar if S-1 AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of reducing a given n × n complex matrix A to triangular or diagonal form by consimilarity, not only gives necessary and sufficient conditions for contriangularization and condiagonalization of a complex matrix, but also derives an algebraic technique of reducing a matrix to triangular or diagonal form by consimilarity.
Bias-corrected diagonal discriminant rules for high-dimensional classification.
Huang, Song; Tong, Tiejun; Zhao, Hongyu
2010-12-01
Diagonal discriminant rules have been successfully used for high-dimensional classification problems, but suffer from the serious drawback of biased discriminant scores. In this article, we propose improved diagonal discriminant rules with bias-corrected discriminant scores for high-dimensional classification. We show that the proposed discriminant scores dominate the standard ones under the quadratic loss function. Analytical results on why the bias-corrected rules can potentially improve the predication accuracy are also provided. Finally, we demonstrate the improvement of the proposed rules over the original ones through extensive simulation studies and real case studies.
A Survey of Solver-Related Geometry and Meshing Issues
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
Direct solvers performance on h-adapted grids
Paszynski, Maciej
2015-05-27
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
IGA-ADS: Isogeometric analysis FEM using ADS solver
Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav
2017-08-01
In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
QED multi-dimensional vacuum polarization finite-difference solver
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph
An immersed interface vortex particle-mesh solver
Marichal, Yves; Chatelain, Philippe; Winckelmans, Gregoire
2014-11-01
An immersed interface-enabled vortex particle-mesh (VPM) solver is presented for the simulation of 2-D incompressible viscous flows, in the framework of external aerodynamics. Considering the simulation of free vortical flows, such as wakes and jets, vortex particle-mesh methods already provide a valuable alternative to standard CFD methods, thanks to the interesting numerical properties arising from its Lagrangian nature. Yet, accounting for solid bodies remains challenging, despite the extensive research efforts that have been made for several decades. The present immersed interface approach aims at improving the consistency and the accuracy of one very common technique (based on Lighthill's model) for the enforcement of the no-slip condition at the wall in vortex methods. Targeting a sharp treatment of the wall calls for substantial modifications at all computational levels of the VPM solver. More specifically, the solution of the underlying Poisson equation, the computation of the diffusion term and the particle-mesh interpolation are adapted accordingly and the spatial accuracy is assessed. The immersed interface VPM solver is subsequently validated on the simulation of some challenging impulsively started flows, such as the flow past a cylinder and that past an airfoil. Research Fellow (PhD student) of the F.R.S.-FNRS of Belgium.
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Schneider, T.; Botta, N.; Geratz, K. J.; Klein, R.
1999-11-01
When attempting to compute unsteady, variable density flows at very small or zero Mach number using a standard finite volume compressible flow solver one faces at least the following difficulties: (i) Spatial pressure variations vanish as the Mach number M→0, but they do affect the velocity field at leading order; (ii) the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux; (iii) violations of this constraint crucially affect the transport of mass, preventing a code to properly advect even a constant density distribution. We overcome these difficulties through a new algorithm for constructing numerical fluxes in the context of multi-dimensional finite volume methods in conservation form. The construction of numerical fluxes involves: (1) An explicit upwind step yielding predictions for the nonlinear convective flux components. (2) A first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint. This step requires the solution of a first Poisson-type equation. (3) A second projection step which provides the yet unknown (non-convective) pressure contribution to the total flux of momentum. This second projection requires the solution of another Poisson-type equation and yields the cell centered velocity field at the new time. This velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit. Step (1) can be done by any standard finite volume compressible flow solver. The input to steps (2) and (3) involves solely the fluxes from step (1) and is independent of how these were obtained. Thus, our approach allows any such solver to be extended to compute variable density incompressible flows.
Ferreira, L. A.; Shnir, Ya.
2017-09-01
We introduce a Skyrme type model with the target space being the sphere S3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space-time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.
Fisher, A. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bailey, D. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kaiser, T. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eder, D. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gunney, B. T. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Masters, N. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Koniges, A. E. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Anderson, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-02-01
Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
Zhang, Xin; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2013-01-01
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.
王为忠; 姚凯伦
2002-01-01
Using an exact diagonalization method, we study an extended Hubbard model with an electron-lattice interaction for an organic ferromagnetic chain with radical coupling. The result shows that the ferromagnetic ground state originates from the antiferromagnetic correlation between adjoining sites, which is enhanced by the on-site e-e repulsion. The intersite e-e repulsion induces the inhomogeneous distribution of the charge density. The dimerization is decreased by the e-e interaction and the radical coupling. The electron--lattice interaction and the radical coupling can transfer the spin density and charge density between the main chain and the radicals.
Miller, Gregory H.
2003-08-06
In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in common practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna
2015-06-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Exact Solutions in Modified Gravity Models
Valery V. Obukhov
2012-06-01
Full Text Available We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.
Exact Solutions in Modified Gravity Models
Makarenko, Andrey N
2012-01-01
We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.
Relation between Feynman cycles and off-diagonal long-range order.
Ueltschi, Daniel
2006-10-27
The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.
Off-diagonal long-range order in generalized Hubbard models
Michielsen, Kristel; Raedt, Hans De
1997-01-01
We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the
Cao, Shancheng; Ouyang, Huajiang
2017-01-01
The structural characteristic deflection shapes (CDS’s) such as mode shapes and operational deflection shapes are highly sensitive to structural damage in beam- or plate-type structures. Nevertheless, they are vulnerable to measurement noise and could result in unacceptable identification errors. In order to increase the accuracy and noise robustness of damage identification based on CDS’s using vibration responses of random excitation, joint approximate diagonalization (JAD) technique and gapped smoothing method (GSM) are combined to form a sensitive and robust damage index (DI), which can simultaneously detect the existence of damage and localize its position. In addition, it is possible to apply this approach to damage identification of structures under ambient excitation. First, JAD method which is an essential technique of blind source separation is investigated to simultaneously diagonalize a set of power spectral density matrices corresponding to frequencies near a certain natural frequency to estimate a joint unitary diagonalizer. The columns of this joint diagonalizer contain dominant CDS’s. With the identified dominant CDS’s around different natural frequencies, GSM is used to extract damage features and a robust damage identification index is then proposed. Numerical and experimental examples of beams with cracks are used to verify the validity and noise robustness of JAD based CDS estimation and the proposed DI. Furthermore, damage identification using dominant CDS’s estimated by JAD method is demonstrated to be more accurate and noise robust than by the commonly used singular value decomposition method.
Stability of matrices with sufficiently strong negative-dominant-diagonal submatrices
Nieuwenhuis, H.J.; Schoonbeek, L.
1997-01-01
A well-known sufficient condition for stability of a system of linear first-order differential equations is that the matrix of the homogeneous dynamics has a negative dominant diagonal. However, this condition cannot be applied to systems of second-order differential equations. In this paper we intr
The effects of pelvic diagonal movements and resistance on the lumbar multifidus
Lee, Ji-Yeon; Lee, Dong-Yeop; Hong, Ji-Heon; Yu, Jae-Ho; Kim, Jin Seop
2017-01-01
[Purpose] The purpose of this study was to compare the effects of pelvic diagonal movements, made with and without resistance, on the thickness of lumbar multifidus muscles. [Subjects and Methods] Participants in this study were healthy subjects who had no musculoskeletal disorders or lumbar-related pain. Participants were positioned on their side and instructed to lie with their hip flexor at 40 degrees. Ultrasonography was used for measurement, and the values of two calculations were averaged. [Results] The thickness of ipsilateral lumbar multifidus muscles showed a significant difference following the exercise of pelvic diagonal movements. The results of anterior elevation movements and posterior depression movements also demonstrated significant difference. There was no significant difference in lumbar multifidus muscles thickness between movements made with and without resistance. [Conclusion] These findings suggest that pelvic diagonal movements can be an effective method to promote muscular activation of the ipsilateral multifidus. Furthermore, researchers have concluded that resistance is not required during pelvic diagonal movements to selectively activate the core muscles. PMID:28356650
Off-diagonal Yukawa Couplings in the s-channel Charged Higgs Production at LHC
Hashemi, Majid
2015-01-01
The search for the heavy charged Higgs (mH+ > mtop) has been mainly based on the o?ff-shell top pair production process. However, resonance production in s-channel single top events is an important channel to search for this particle. In a previous work, it was shown that this process, i.e., qq' -> H+ -> tb + h.c., can lead to comparable results to what is already obtained from LHC searches through gb -> tH- process. What was obtained was, however, based on diagonal Yukawa couplings between incoming quarks assuming cs as the main incoming pair due to the CKM matrix element being close to unity. The aim of this paper is to show that off-diagonal couplings, like cb, may lead to substantial contributions to the cross section, even if the corresponding CKM matrix element is two orders of magnitude smaller. For this reason, the cross section is calculated for each initial state including all diagonal and off-diagonal terms, and all is finally added together to get the total cross section which is observed to be ~ ...
Pietracaprina, F.; Gogolin, C.; Goold, J.
2017-03-01
The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics in systems without degeneracies. In analogy to the time average of a classical phase-space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper bound on the multipartite entanglement, it quantifies the combination of both classical and quantum correlations in a mixed state. We generalize the total correlations of the diagonal ensemble to more general α -Renyi entropies and focus on the cases α =1 and α =2 with further numerical extensions in mind. Here we show that the total correlations of the diagonal ensemble is a generic indicator of ergodicity breaking, displaying a subextensive behavior when the system is ergodic. We demonstrate this by investigating its scaling in a range of spin chain models focusing not only on the cases of integrability breaking but also emphasize its role in understanding the transition from an ergodic to a many-body localized phase in systems with disorder or quasiperiodicity.
Yildiz Ulus, Aysegul
2013-01-01
This paper examines experimental and algorithmic contributions of advanced calculators (graphing and computer algebra system, CAS) in teaching the concept of "diagonalization," one of the key topics in Linear Algebra courses taught at the undergraduate level. Specifically, the proposed hypothesis of this study is to assess the effective…
Congestion Control for ATM Networks Based on Diagonal Recurrent Neural Networks
HuangYunxian; YanWei
1997-01-01
An adaptive control model and its algorithms based on simple diagonal recurrent neural networks are presented for the dynamic congestion control in broadband ATM networks.Two simple dynamic queuing models of real networks are used to test the performance of the suggested control scheme.
Zhang, Shuai; Zhao, Kun; Ying, Zhinong
2015-01-01
A diagonal antenna-chassis mode is investigated in long-term evolution multiple-input-multiple-output (LTE MIMO) antennas. The MIMO bandwidth is defined in this paper as the overlap range of the low-envelope correlation coefficient, high total efficiency, and -6-dB impedance matching bandwidths...
Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity
Sergiu I. Vacaru
2016-01-01
Full Text Available Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (inhomogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann–Lamaître–Robertson–Walker (FLRW coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé–Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.
Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity
Vacaru, Sergiu I., E-mail: sergiu.vacaru@uaic.ro [University “Al. I. Cuza” Iaşi, Rector' s Department, 14 Alexandru Lapuşneanu Street, Corpus R, UAIC, Office 323, Iaşi, 700057 (Romania); Max-Planck-Institute for Physics, Werner-Heisenberg-Institute, Foehringer Ring 6, München, D-80805 (Germany); Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover (Germany)
2016-01-10
Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in)homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann–Lamaître–Robertson–Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé–Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.
A discrete Fourier-encoded, diagonal-free experiment to simplify homonuclear 2D NMR correlations
Huang, Zebin; Guan, Quanshuai; Chen, Zhong; Frydman, Lucio; Lin, Yulan
2017-07-01
Nuclear magnetic resonance (NMR) spectroscopy has long served as an irreplaceable, versatile tool in physics, chemistry, biology, and materials sciences, owing to its ability to study molecular structure and dynamics in detail. In particular, the connectivity of chemical sites within molecules, and thereby molecular structure, becomes visible by multi-dimensional NMR. Homonuclear correlation experiments are a powerful tool for identifying coupled spins. Generally, diagonal peaks in these correlation spectra display the strongest intensities and do not offer any new information beyond the standard one-dimensional spectrum, whereas weaker, symmetrically placed cross peaks contain most of the coupling information. The cross peaks near the diagonal are often affected by the tails of strong diagonal peaks or even obscured entirely by the diagonal. In this paper, we demonstrate a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks and combine it with a site-selective sculpting scheme, capable of simplifying the patterns arising in these 2D correlation spectra. The theoretical principles of the new methods are laid out, and experimental observations are rationalized on the basis of theoretical analyses. The ensuing techniques provide a new way to retrieve 2D coupling information within homonuclear spin systems, with enhanced sensitivity, speed, and clarity.
对角方阵的变换群%Transformaion Group of Diagonal Square Matrices
张世德; 李程
2011-01-01
In this paper,we show that the transformaion group of diagonal square matrices is a subgroup of direct product Sn × Sn of symetric groups of order n, if the sets of elements of each row, each column and the two diagonals are kept constant, respectively. The diagonal Latin squares, pair of orthogonal daigonal Latin squares, magic squares, magic squares of high dgree, addition multiplacation magic squares are diagonal square matrices. This paper plays an important role in the study of construction and enumeration of the objects above.%在不改变对角方阵各行、各列、主对角线、次对角线的元素之集的条件下,其变换群是n次对称群Sn的直积Sn×Sn的子群,因对角拉丁方、对角拉丁方正交侣、幻方、高次幻方、加乘幻方均属此类方阵,本文对构作这类对象及研究它们的计数有重要意义.
Mahomed, Ozayr Haroon; Asmall, Shaidah; Freeman, Melvyn
2014-11-01
The integrated chronic disease management model provides a systematic framework for creating a fundamental change in the orientation of the health system. This model adopts a diagonal approach to health system strengthening by establishing a service-linked base to training, supervision, and the opportunity to try out, assess, and implement integrated interventions.
Exact Surface States in Photonic Superlattices
Xie, Qiongtao
2012-01-01
We develop an analytical method to derive exact surface states in photonic superlattices. In a kind of infinite bichromatic superlattices satisfying some certain conditions, we analytically obtain their in-gap states, which are superpositions of finite numbers of unstable Bloch waves. By using the unstable in-gap states, we construct exactly several stable surface states in various photonic superlattices. We analytically explore the parametric dependence of these exact surface states. Our analysis provides an exact demonstration for the existence of surface states and would be also helpful to understand surface states in other lattice systems.
Youdas, James W; Adams, Kady E; Bertucci, John E; Brooks, Koel J; Steiner, Meghan M; Hollman, John H
2015-01-01
The aim of this study was to simultaneously quantify electromyographic (EMG) activation levels (% maximum voluntary isometric contraction [MVIC]) within the gluteus medius muscles on both moving and stance limbs across the performance of four proprioceptive neuromuscular facilitation (PNF) spiral-diagonal patterns in standing using resistance provided by elastic tubing. Differential EMG activity was recorded from the gluteus medius muscle of 26 healthy participants. EMG signals were collected with surface electrodes at a sampling frequency of 1000 Hz during three consecutive repetitions of each spiral-diagonal movement pattern. Significant differences existed among the four-spiral-diagonal movement patterns (F3,75 = 19.8; p < 0.001). The diagonal two flexion [D2F] pattern produced significantly more gluteus medius muscle recruitment (50 SD 29.3% MVIC) than any of the other three patterns and the diagonal one extension [D1E] (39 SD 37% MVIC) and diagonal two extension [D2E] (35 SD 29% MVIC) patterns generated more gluteus medius muscle recruitment than diagonal one flexion [D1F] (22 SD 21% MVIC). From a clinical efficiency standpoint, a fitness professional using the spiral-diagonal movement pattern of D2F and elastic tubing with an average peak tension of about 9% body mass may be able to concurrently strengthen the gluteus medius muscle on both stance and moving lower limbs.
Han, Song; Zhang, Wei; Zhang, Jie
2017-09-01
A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.
Code Verification of the HIGRAD Computational Fluid Dynamics Solver
Van Buren, Kendra L. [Los Alamos National Laboratory; Canfield, Jesse M. [Los Alamos National Laboratory; Hemez, Francois M. [Los Alamos National Laboratory; Sauer, Jeremy A. [Los Alamos National Laboratory
2012-05-04
The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.
Using Solver Interfaced Virtual Reality in PEACER Design Process
Lee, Hyong Won; Nam, Won Chang; Jeong, Seung Ho; Hwang, Il Soon; Shin, Jong Gye; Kim, Chang Hyo [Seoul National University, Seoul (Korea, Republic of)
2006-07-01
The recent research progress in the area of plant design and simulation highlighted the importance of integrating design and analysis models on a unified environment. For currently developed advanced reactors, either for power production or research, this effort has embraced impressive state-of-the-art information and automation technology. The PEACER (Proliferation-resistant, Environment friendly, Accident-tolerant, Continual and Economical Reactor) is one of the conceptual fast reactor system cooled by LBE (Lead Bismuth Eutectic) for nuclear waste transmutation. This reactor system is composed of innovative combination between design process and analysis. To establish an integrated design process by coupling design, analysis, and post-processing technology while minimizing the repetitive and costly manual interactions for design changes, a solver interfaced virtual reality simulation system (SIVR) has been developed for a nuclear transmutation energy system as PEACER. The SIVR was developed using Virtual Reality Modeling Language (VRML) in order to interface a commercial 3D CAD tool with various engineering solvers and to implement virtual reality presentation of results in a neutral format. In this paper, we have shown the SIVR approach viable and effective in the life-cycle management of complex nuclear energy systems, including design, construction and operation. For instance, The HELIOS is a down scaled model of the PEACER prototype to demonstrate the operability and safety as well as preliminary test of PEACER PLM (Product Life-cycle Management) with SIVR (Solver Interfaced Virtual Reality) concepts. Most components are designed by CATIA, which is 3D CAD tool. During the construction, 3D drawing by CATIA was effective to handle and arrange the loop configuration, especially when we changed the design. Most of all, This system shows the transparency of design and operational status of an energy complex to operators and inspectors can help ensure accident
Yu, Hua-Gen
2016-08-01
We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.
Petersen, Christian Leth; Hansen, Ole Per
1996-01-01
We have investigated the AC conductivity elements in the quantum Hall regime of two-dimensional electron gases coupled capacitively to electrodes with Corbino geometry. The samples are GaAlAs/GaAs single heterostructures, and the measurements are made at low frequencies, up to 20 kHz. The diagonal...... conductivity is derived from magnetocapacitance measurements. It increases with increasing frequency according to a power law at integer filling factors. The exponent of the power law depends on both temperature and filling factor. Ratios between Hall conductivities at different filling factors are obtained...
Sebastián B. Lamot
2007-08-01
Full Text Available El surco diagonal es un signo encontrado en el lóbulo de la oreja, que estaría relacionado con la enfermedad arterial coronaria. Nuestro objetivo fue estudiar la utilidad del signo. Se examinaron 104 pacientes (entre 30 y 80 años clasificados por sexo y edad. Cuarenta y nueve tenían enfermedad arterial coronaria diagnosticada por coronariografía (obstrucción > del 70% en una de las grandes arterias y/o gamagrafía de perfusión miocárdica con Talio 201 (defecto fijo. El grupo control estuvo compuesto por 55 pacientes (asintomáticos, con electrocardiograma normal. Los datos obtenidos fueron sensibilidad (61.2%, especificidad (78.2%, valor predictivo positivo de (71.4% y valor predictivo negativo (69.3%.. Observamos una relación significativa entre la presencia de surco diagonal y enfermedad arterial coronaria. Consideramos que este signo podría resultar de utilidad en la práctica clínica, fundamentalmente para los pacientes entre 30 y 60 años.The diagonal earlobe crease is a sign theorically related to coronary artery disease. The purpose of this study was to prove the usefulness of this sign. A total of 104 patients were examined (ages 30 to 80 grouped by age and sex. Forty nine of them were diagnosed of having coronary artery disease by coronary angiography (a 70% obstruction of one of the major arteries, and/or myocardial perfusion imaging with Thallium 201 (fixed defects. The control group included 55 patients (asymptomatic with normal electrocardiogram. Data here obtained included sensitivity (61.2%, specificity (78.2%, positive predictive value (71.4% and negative predictive value (69.3%. We found a significant relation between the presence of the diagonal earlobe crease and coronary artery disease. We consider it a sign that could prove useful in clinical practice, mainly among patients aged between 30 and 60.
Exact Coleman-de Luccia Instantons
Kanno, Sugumi
2011-01-01
We present exact Coleman-de Luccia (CdL) instantons, which describe vacuum decay from Anti de Sitter (AdS) space, de Sitter (dS) space and Minkowski space to AdS space. We systematically obtain these exact solutions by considering deformation of Hawking-Moss (HM) instantons. We analytically calculate decay rates and discuss a subtlety in the interpretation.
Exact Solutions for Einstein's Hyperbolic Geometric Flow
HE Chun-Lei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.
Conjugation-uniqueness of exact Borel subalgebras
张跃辉
1999-01-01
It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.
Exact, almost and delayed fault detection
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.;
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems. Th...
An alternative to exact renormalization equations
Alexandre, Jean
2005-01-01
An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective action, and recovers usual renormalization results.
Reformulation of the Fourier-Bessel steady state mode solver
Gauthier, Robert C.
2016-09-01
The Fourier-Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf
2010-01-01
The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.
A Simple Quantum Integro-Differential Solver (SQuIDS)
Delgado, Carlos Alberto Arguelles; Weaver, Christopher N
2014-01-01
Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.
Turbulent Flow Validation in the Helios Strand Solver
2014-01-07
aerodynamics solution procedure consists of unstructured meshes in the near-body to capture viscous flow around complex geometry , and block structured...on the approximate Riemann solver of Roe,20 F̂ = 1 2 (F (QR)+F (QL))− 1 2 |A(QR,QL)|(QR−QL) , (45) where F = Fjn j is the directed flux at a face with...uniform cartesian mesh that is 16×16×24. The off-body mesh is then adapted to the geometry and flow physics with up to nine levels of isotropic mesh
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S. [Technical Univ. of Vienna (Austria)
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Advances in the hydrodynamics solver of CO5BOLD
Freytag, Bernd
Many features of the Roe solver used in the hydrodynamics module of CO5BOLD have recently been added or overhauled, including the reconstruction methods (by adding the new second-order ``Frankenstein's method''), the treatment of transversal velocities, energy-flux averaging and entropy-wave treatment at small Mach numbers, the CTU scheme to combine the one-dimensional fluxes, and additional safety measures. All this results in a significantly better behavior at low Mach number flows, and an improved stability at larger Mach numbers requiring less (or no) additional tensor viscosity, which then leads to a noticeable increase in effective resolution.
Conjugate gradient solvers on Intel Xeon Phi and NVIDIA GPUs
Kaczmarek, O; Steinbrecher, P; Wagner, M
2014-01-01
Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of the Fermion Matrix. This part is therefore frequently optimized for various HPC architectures. Here we compare the performance of the Intel Xeon Phi to current Kepler-based NVIDIA Tesla GPUs running a conjugate gradient solver. By exposing more parallelism to the accelerator through inverting multiple vectors at the same time, we obtain a performance greater than 300 GFlop/s on both architectures. This more than doubles the performance of the inversions. We also give a short overview of the Knights Corner architecture, discuss some details of the implementation and the effort required to obtain the achieved performance.
Modelo de selección de cartera con Solver
P. Fogués Zornoza
2012-04-01
Full Text Available In this paper, we present an example of linear optimization in the context of degrees in Economics or Business Administration and Management. We show techniques that enable students to go deep and investigate in real problems that have been modelled using the Excel platform. The model shown here has been developed by a student and it consists in minimizing the absolute deviations over the average expected return of a portfolio of securities, using the solver tool that it is included in this software.
EXACT2: the semantics of biomedical protocols.
Soldatova, Larisa N; Nadis, Daniel; King, Ross D; Basu, Piyali S; Haddi, Emma; Baumlé, Véronique; Saunders, Nigel J; Marwan, Wolfgang; Rudkin, Brian B
2014-01-01
The reliability and reproducibility of experimental procedures is a cornerstone of scientific practice. There is a pressing technological need for the better representation of biomedical protocols to enable other agents (human or machine) to better reproduce results. A framework that ensures that all information required for the replication of experimental protocols is essential to achieve reproducibility. To construct EXACT2 we manually inspected hundreds of published and commercial biomedical protocols from several areas of biomedicine. After establishing a clear pattern for extracting the required information we utilized text-mining tools to translate the protocols into a machine amenable format. We have verified the utility of EXACT2 through the successful processing of previously 'unseen' (not used for the construction of EXACT2)protocols. We have developed the ontology EXACT2 (EXperimental ACTions) that is designed to capture the full semantics of biomedical protocols required for their reproducibility. The paper reports on a fundamentally new version EXACT2 that supports the semantically-defined representation of biomedical protocols. The ability of EXACT2 to capture the semantics of biomedical procedures was verified through a text mining use case. In this EXACT2 is used as a reference model for text mining tools to identify terms pertinent to experimental actions, and their properties, in biomedical protocols expressed in natural language. An EXACT2-based framework for the translation of biomedical protocols to a machine amenable format is proposed. The EXACT2 ontology is sufficient to record, in a machine processable form, the essential information about biomedical protocols. EXACT2 defines explicit semantics of experimental actions, and can be used by various computer applications. It can serve as a reference model for for the translation of biomedical protocols in natural language into a semantically-defined format.
On the implicit density based OpenFOAM solver for turbulent compressible flows
Fürst, Jiří
The contribution deals with the development of coupled implicit density based solver for compressible flows in the framework of open source package OpenFOAM. However the standard distribution of OpenFOAM contains several ready-made segregated solvers for compressible flows, the performance of those solvers is rather week in the case of transonic flows. Therefore we extend the work of Shen [15] and we develop an implicit semi-coupled solver. The main flow field variables are updated using lower-upper symmetric Gauss-Seidel method (LU-SGS) whereas the turbulence model variables are updated using implicit Euler method.
On the implicit density based OpenFOAM solver for turbulent compressible flows
Fürst Jiří
2017-01-01
Full Text Available The contribution deals with the development of coupled implicit density based solver for compressible flows in the framework of open source package OpenFOAM. However the standard distribution of OpenFOAM contains several ready-made segregated solvers for compressible flows, the performance of those solvers is rather week in the case of transonic flows. Therefore we extend the work of Shen [15] and we develop an implicit semi-coupled solver. The main flow field variables are updated using lower-upper symmetric Gauss-Seidel method (LU-SGS whereas the turbulence model variables are updated using implicit Euler method.
On the implicit density based OpenFOAM solver for turbulent compressible flows
Fürst, Jiří
2016-11-01
The contribution deals with the development of coupled implicit density based solver for compressible flows in the framework of open source package OpenFOAM. However the standard distribution of OpenFOAM contains several ready-made segregated solvers for compressible flows, the performance of those solvers is rather week in the case of transonic flows. Therefore we extend the work of Shen [15] and we develop an implicit semi-coupled solver. The main flow field variables are updated using lower-upper symmetric Gauss-Seidel method (LU-SGS) whereas the turbulence model variables are updated using implicit Euler method.
The difference between two random mixed quantum states: exact and asymptotic spectral analysis
Mejía, José; Zapata, Camilo; Botero, Alonso
2017-01-01
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.
Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model
Rylands, Colin; Andrei, Natan
2016-09-01
A Luttinger liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a localized transmitting and reflecting impurity. We solve exactly the Hamiltonian by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. A related model, the weak-tunneling model, wherein the impurity is replaced by a tunnel junction, is solved by the same method. The consistency of the construction is established through a generalized Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe ansatz equations are derived by means of the off-diagonal Bethe ansatz approach. We derive the spectrum of the model for all coupling constant regimes and calculate the impurity free energy. We discuss the low energy behavior of the systems for both repulsive and attractive interactions.
Exact integrability in quantum field theory and statistical systems
Thacker, H. B.
1981-04-01
The properties of exactly integrable two-dimensional quantum systems are reviewed and discussed. The nature of exact integrability as a physical phenomenon and various aspects of the mathematical formalism are explored by discussing several examples, including detailed treatments of the nonlinear Schrödinger (delta-function gas) model, the massive Thirring model, and the six-vertex (ice) model. The diagonalization of a Hamiltonian by Bethe's Ansatz is illustrated for the nonlinear Schrödínger model, and the integral equation method of Lieb for obtaining the spectrum of the many-body system from periodic boundary conditions is reviewed. Similar methods are applied to the massive Thirring model, where the fermion-antifermion and bound-state spectrum are obtained explicitly by the integral equation method. After a brief review of the classical inverse scattering method, the quantum inverse method for the nonlinear Schrödinger model is introduced and shown to be an algebraization of the Bethe Ansatz technique. In the quantum inverse method, an auxiliary linear problem is used to define nonlocal operators which are functionals of the original local field on a fixed-time string of arbitrary length. The particular operators for which the string is infinitely long (free boundary conditions) or forms a closed loop around a cylinder (periodic boundary conditions) correspond to the quantized scattering data and have a special significance. One of them creates the Bethe eigenstates, while the other is the generating function for an infinite number of conservation laws. The analogous operators on a lattice are constructed for the symmetric six-vertex model, where the object which corresponds to a solution of the auxiliary linear problem is a string of vertices contracted over horizontal links (arrows). The relationship between the quantum inverse method and the transfer matrix formalism is exhibited. The inverse Gel'fand-Levitan transform which expresses the local field
Application of alternating decision trees in selecting sparse linear solvers
Bhowmick, Sanjukta
2010-01-01
The solution of sparse linear systems, a fundamental and resource-intensive task in scientific computing, can be approached through multiple algorithms. Using an algorithm well adapted to characteristics of the task can significantly enhance the performance, such as reducing the time required for the operation, without compromising the quality of the result. However, the best solution method can vary even across linear systems generated in course of the same PDE-based simulation, thereby making solver selection a very challenging problem. In this paper, we use a machine learning technique, Alternating Decision Trees (ADT), to select efficient solvers based on the properties of sparse linear systems and runtime-dependent features, such as the stages of simulation. We demonstrate the effectiveness of this method through empirical results over linear systems drawn from computational fluid dynamics and magnetohydrodynamics applications. The results also demonstrate that using ADT can resolve the problem of over-fitting, which occurs when limited amount of data is available. © 2010 Springer Science+Business Media LLC.
Riemann solvers and Alfven waves in black hole magnetospheres
Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip
2016-09-01
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Exact Renormalization Group for Point Interactions
Eröncel, Cem
2014-01-01
Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble non-abelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Quaternionic formulation of the exact parity model
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-02-28
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.
EXACT RENORMALIZATION GROUP FOR POINT INTERACTIONS
Osman Teoman Turgut Teoman Turgut
2014-04-01
Full Text Available Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble nonabelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Fundamental Group and Euler Characteristic of Permutation Products and Fat Diagonals
Kallel, Sadok
2010-01-01
Permutation products and their various "fat diagonal" subspaces are studied from the topological and geometric point of view. We first write down an expression for the fundamental group of any permutation product of a connected space $X$, having the homotopy type of a simplicial complex, in terms of $\\pi_1(X)$ and $H_1(X;{\\mathbb Z})$. We then prove that the fundamental group of the configuration space of $n$-points on $X$ of which multiplicities do not exceed $n/2$ coincides with $H_1(X;{\\mathbb Z})$. Useful additivity properties for the Euler characteristic are then spelled out and used to give explicit formulae for the Euler characteristics of various fat diagonals. Several examples and calculations are included.
Li, Yifan; Liang, Xihui; Zuo, Ming J.
2017-02-01
This paper presents a novel signal processing scheme, diagonal slice spectrum assisted optimal scale morphological filter (DSS-OSMF), for rolling element fault diagnosis. In this scheme, the concept of quadratic frequency coupling (QFC) is firstly defined and the ability of diagonal slice spectrum (DSS) in detection QFC is derived. The DSS-OSMF possesses the merits of depressing noise and detecting QFC. It can remove fault independent frequency components and give a clear representation of fault symptoms. A simulated vibration signal and experimental vibration signals collected from a bearing test rig are employed to evaluate the effectiveness of the proposed method. Results show that the proposed method has a superior performance in extracting fault features of defective rolling element bearing. In addition, comparisons are performed between a multi-scale morphological filter (MMF) and a DSS-OSMF. DSS-OSMF outperforms MMF in detection of an outer race fault and a rolling element fault of a rolling element bearing.
Direct current hopping conductance in one-dimensional diagonal disordered systems
Ma Song-Shan; Xu Hui; Liu Xiao-Liang; Xiao Jian-Rong
2006-01-01
Based on a tight-binding disordered model describing a single electron band, we establish a direct current (dc) electronic hopping transport conductance model of one-dimensional diagonal disordered systems, and also derive a dc conductance formula. By calculating the dc conductivity, the relationships between electric field and conductivity and between temperature and conductivity are analysed, and the role played by the degree of disorder in electronic transport is studied. The results indicate the conductivity of systems decreasing with the increase of the degree of disorder, characteristics of negative differential dependence of resistance on temperature at low temperatures in diagonal disordered systems, and the conductivity of systems decreasing with the increase of electric field, featuring the non-Ohm's law conductivity.
Wu, Sheng-Jhih; Chu, Moody T.
2017-08-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.
Ngo, Van A
2013-01-01
We propose a combination between the theory of diagonal entropy representing far-from-equilibrium ensembles and Jarzynski Equality to explore thermalization effects on thermodynamic quantities such as temperature, entropy, mechanical work and free-energy changes. Applying the theory to a quantum harmonic oscillator, we find that diagonal entropy offers a definition of temperature for closed systems far from equilibrium, and a better sampling of reaction pathways than the conventional von Neumann entropy. We also apply the theory to a many-body system of hard-core boson lattice, and discuss the ideas of how to estimate temperature, entropy and measure work distribution functions. The theory suggests a powerful technique to study non-equilibrium dynamics in quantum systems by means of performing work in a series of quenches.
Quasilocal charges and the complete GGE for field theories with non-diagonal scattering
Vernier, Eric
2016-01-01
It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-$\\frac{1}{2}$ XXZ Heisenberg chain. These charges have been proven to be essential for properly describing stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-ocuppation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of quasilocal lattice charge...
Jain, Mamta; Kumar, Anil; Choudhary, Rishabh Charan
2016-09-09
In this article, we have proposed an improved diagonal queue medical image steganography for patient secret medical data transmission using chaotic standard map, linear feedback shift register, and Rabin cryptosystem, for improvement of previous technique (Jain and Lenka in Springer Brain Inform 3:39-51, 2016). The proposed algorithm comprises four stages, generation of pseudo-random sequences (pseudo-random sequences are generated by linear feedback shift register and standard chaotic map), permutation and XORing using pseudo-random sequences, encryption using Rabin cryptosystem, and steganography using the improved diagonal queues. Security analysis has been carried out. Performance analysis is observed using MSE, PSNR, maximum embedding capacity, as well as by histogram analysis between various Brain disease stego and cover images.
A Diagnostic Supportive Sign for the Cause of Death Diagonal Ear Lobe Crease
Birol Demirel
2005-08-01
Full Text Available Coronary artery disease is a major cause of natural death. The high incidence and mortality of these diseases arised a need to investigate possible risk factors beyond well known. Diagonal ear lobe crease (DEC, was the physical sign, described in 1973. We investigated the possibility of DEC as a helpful predictive sign in the postmortem examination of forensic sudden death cases. The angiographic results revealed that whenever the percentages of the stenosis in left descending coronary artery, circumflex artery and right coronary artery increased, the incidence of the DEC did so accordingly. These results were correlated with the previous studies reporting significant correlation between coronary artery disease and the DEC. Particularly, in the absence of supportive medical history and without a physical sign of trauma, the presence of DEC could well be a supportive sign for the physician to consider the coronary artery disease as a cause of death. Key words: Diagonal ear lobe crease, coronary artery disease, death investigation
Identifiability of Complex Blind Source Separation via Non-Unitary Joint Diagonalization
Kleinsteuber, Martin
2011-01-01
Identifiability analysis of complex Blind Source Separation (BSS), i.e. to study under what conditions the BSS problem can be solved, is a long-standing and most critical problem in the community. It serves not only as the indicator to solvability of the BSS problem, but also as the constructive ground for developing efficient algorithms. Various BSS methods are based on jointly diagonalizing a set of matrices, which are generated using second- or higher-order statistics. The present work provides a general result on the uniqueness conditions of matrix joint diagonalization. It unifies all existing results on the identifiability conditions of complex BSS, with respect to non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. Additionally, following the main identifiability result, a solution for complex BSS is proposed. It is given in closed form in terms of an eigenvalue and a singular value decomposition of two matrices.
Self-similar solutions with fat tails for a coagulation equation with diagonal kernel
Niethammer, Barbara
2011-01-01
We consider self-similar solutions of Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $\\gamma < 1$. We show that there exists a family of second-kind self-similar solutions with power-law behavior $x^{-(1+\\rho)}$ as $x \\to \\infty$ with $\\rho \\in (\\gamma,1)$. To our knowledge this is the first example of a non-solvable kernel for which the existence of such a family has been established.
Chulaevsky, Victor, E-mail: victor.tchoulaevski@univ-reims.fr [Universite de Reims, Departement de Mathematiques (France)
2012-12-15
We propose a simplified version of the Multi-Scale Analysis of Anderson models on a lattice and, more generally, on a countable graph with polynomially bounded growth of balls, with diagonal disorder represented by an IID or strongly mixing correlated potential. We apply the new scaling procedure to discrete Schroedinger operators and obtain localization bounds on eigenfunctions and eigenfunction correlators in arbitrarily large finite subsets of the graph which imply the spectral and strong dynamical localization in the entire graph.
王宗国; 覃绍京; 康凯; 王垂林
2012-01-01
We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, arid to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.
Workshop report on large-scale matrix diagonalization methods in chemistry theory institute
Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S. [eds.
1996-10-01
The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems as well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of
A Parallel Algorithm for Solving Block-diagonal Structured Large Linear System
SHEN Jie; ZHANG Zhong-lin; CHENG Ji-lin
2001-01-01
A parallel algorithm for solving block-diagonal structured large linear system is presented.This algorithm is based on the "gradient-simplex" method. It partitions a large linear system into several small linear subsystems so that they can be solved in parallel. The algorithm has the merit of high speed and is suitable for the large linear systems with less coupling constrains. The efficiency and applicability of the method is also analyzed.
Chen, Yang; Zou, Ling; Zhou, Bin
2017-07-01
The high mounting precision of the fiber underwater acoustic array leads to an array manifold without perturbation. Besides, the targets are either static or slowly moving in azimuth in underwater acoustic array signal processing. Therefore, the covariance matrix can be estimated accurately by prolonging the observation time. However, this processing is limited to poor bearing resolution due to small aperture, low SNR and strong interferences. In this paper, diagonal rejection (DR) technology for Minimum Variance Distortionless Response (MVDR) was developed to enhance the resolution performance. The core idea of DR is rejecting the main diagonal elements of the covariance matrix to improve the output signal to interference and noise ratio (SINR). The definition of SINR here implicitly assumes independence between the spatial filter and the received observations at which the SINR is measured. The power of noise converges on the diagonal line in the covariance matrix and then it is integrated into the output beams. With the diagonal noise rejected by a factor smaller than 1, the array weights of MVDR will concentrate on interference suppression, leading to a better resolution capability. The algorithm was theoretically proved with optimal rejecting coefficient derived under both infinite and finite snapshots scenarios. Numerical simulations were conducted with an example of a linear array with eight elements half-wavelength spaced. Both resolution and Direction-of-Arrival (DOA) performances of MVDR and DR-based MVDR (DR-MVDR) were compared under different SNR and snapshot numbers. A conclusion can be drawn that with the covariance matrix accurately estimated, DR-MVDR can provide a lower sidelobe output level and a better bearing resolution capacity than MVDR without harming the DOA performance.
Models with orthogonal block structure, with diagonal blockwise variance-covariance matrices
Carvalho, Francisco; Mexia, João T.; Covas, Ricardo
2017-07-01
We intend to show that in the family of models with orthogonal block structure, OBS, we may single out those with blockwise diagonal variance-covariance matrices, DOBS. Namely we show that for every model with observation vector y with OBS, there is a model y °=P y , with P orthogonal which is DOBS and that the estimation of relevant parameters may be carried out for y ° .
Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries
Ragoucy, E
2011-01-01
We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.
Boundary form factors in the Smirnov--Fateev model with a diagonal boundary $S$ matrix
Lashkevich, Michael
2008-01-01
The boundary conditions with diagonal boundary $S$ matrix and the boundary form factors for the Smirnov--Fateev model on a half line has been considered in the framework of the free field representation. In contrast to the case of the sine-Gordon model, in this case the free field representation is shown to impose severe restrictions on the boundary $S$ matrix, so that a finite number of solutions is only consistent with the free field realization.
Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure
Ling Guo
2013-01-01
Full Text Available The generalized synchronization problem is studied in this paper for different chaotic systems with the aid of the direct design method. Based on Lyapunov stability theory and matrix theory, some sufficient conditions guaranteeing the stability of a nonlinear system with nonnegative off-diagonal structure are obtained. Then the control scheme is designed from the stable system by the direct design method. Finally, two numerical simulations are provided to verify the effectiveness and feasibility of the proposed method.
Generalized cost-criterion-based learning algorithm for diagonal recurrent neural networks
Wang, Yongji; Wang, Hong
2000-05-01
A new generalized cost criterion based learning algorithm for diagonal recurrent neural networks is presented, which is with form of recursive prediction error (RPE) and has second convergent order. A guideline for the choice of the optimal learning rate is derived from convergence analysis. The application of this method to dynamic modeling of typical chemical processes shows that the generalized cost criterion RPE (QRPE) has higher modeling precision than BP trained MLP and quadratic cost criterion trained RPE (QRPE).
DIAGONALLY COMPENSATED REDUCTION AND MULTISPLITTING OF A SYMMETRIC POSITIVE DEFINITE MATRIX
无
2000-01-01
To solve the symmetric positive definite linear system Ax = b on parallel and vector machines, multisplitting methods are considered. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a special form (e.g. the dissection form [11]). The main tool for deriving our methods is the diagonally compensated reduction (cf. [1]). The convergence of such methods is also discussed by using this tool.
Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.
Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai
2011-01-01
Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs.
The decoherence of quantum entanglement and teleportation in Bell-diagonal states
QIN Meng; LI Yan-Biao; WANG Xiao; BAI Zhong
2012-01-01
We study the dynamics of entanglement and teleportation in Bell-diagonal states. Using the concepts of concurrence and fidelity,the analytical expressions of the entanglement,the output entanglement and the average fidelity with decoherence are obtained for this model.We discover a class of initial states in which the output entanglement and the average fidelity are destroyed by decoherence. The quality of teleportation depends on the system parameters and time.
Adaptive PVD Steganography Using Horizontal, Vertical, and Diagonal Edges in Six-Pixel Blocks
Anita Pradhan
2017-01-01
Full Text Available The traditional pixel value differencing (PVD steganographical schemes are easily detected by pixel difference histogram (PDH analysis. This problem could be addressed by adding two tricks: (i utilizing horizontal, vertical, and diagonal edges and (ii using adaptive quantization ranges. This paper presents an adaptive PVD technique using 6-pixel blocks. There are two variants. The proposed adaptive PVD for 2×3-pixel blocks is known as variant 1, and the proposed adaptive PVD for 3×2-pixel blocks is known as variant 2. For every block in variant 1, the four corner pixels are used to hide data bits using the middle column pixels for detecting the horizontal and diagonal edges. Similarly, for every block in variant 2, the four corner pixels are used to hide data bits using the middle row pixels for detecting the vertical and diagonal edges. The quantization ranges are adaptive and are calculated using the correlation of the two middle column/row pixels with the four corner pixels. The technique performs better as compared to the existing adaptive PVD techniques by possessing higher hiding capacity and lesser distortion. Furthermore, it has been proven that the PDH steganalysis and RS steganalysis cannot detect this proposed technique.
Mosayeb Dalvand; Ghanbar Ebrahimi; Mehdi Tajvidi; Mohammad Layeghi
2014-01-01
We investigated bending moment resistance under diagonal compression load of corner doweled joints with plywood members. Joint members were made of 11-ply hardwood plywood of 19 mm thickness. Dowels were fabricated of Beech and Hornbeam species. Their diameters (6, 8 and 10 mm) and depths of penetration (9, 13 and 17 mm) in joint members were chosen variables in our experiment. By increasing the connector’s diameter from 6 to 8 mm, the bending moment resistance under diagonal compressive load was increased, while it decreased when the diameter was increased from 8 to 10 mm. The bending moment re-sistance under diagonal compressive load was increased by increasing the dowel’s depth of penetration. Joints made with dowels of Beech had higher resistance than dowels of Hornbeam. Highest resisting moment (45.18 N·m) was recorded for joints assembled with 8 mm Beech dowels penetrating 17 mm into joint members Lowest resisting moment (13.35 N·m) was recorded for joints assembled with 6 mm Hornbeam dowels and penetrating 9 mm into joint members.
Thermalization away from integrability and the role of operator off-diagonal elements.
Konstantinidis, N P
2015-05-01
We investigate the rate of thermalization of local operators in the one-dimensional anisotropic antiferromagnetic Heisenberg model with next-nearest neighbor interactions that break integrability. This is done by calculating the scaling of the difference of the diagonal and canonical thermal ensemble values as a function of system size, and by directly calculating the time evolution of the expectation values of the operators with the Chebyshev polynomial expansion. Spatial and spin symmetry is exploited and the Hamiltonian is divided into subsectors according to their symmetry. The rate of thermalization depends on the proximity to the integrable limit. When integrability is weakly broken thermalization is slow, and becomes faster the stronger the next-nearest neighbor interaction is. Three different regimes for the rate of thermalization with respect to the strength of the integrability breaking parameter are identified. These are shown to be directly connected with the relative strength of the low and higher energy difference off-diagonal operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close to the integrable limit the off-diagonal matrix elements peak at higher energies and high-frequency fluctuations are important and slow down thermalization. Away from the integrable limit a strong low-energy peak gradually develops that takes over the higher frequency fluctuations and leads to quicker thermalization.
Diagonal-free 3D/4D HN,HN-TROSY-NOESY-TROSY.
Diercks, Tammo; Truffault, Vincent; Coles, Murray; Millet, Oscar
2010-02-24
Structural biology by NMR spectroscopy relies on measuring interproton distances via NOE cross-signals in nuclear Overhauser effect spectroscopy (NOESY) spectra. In proteins, the subset of H(N)-H'(N) NOE contacts is most important for deriving initial structural models and for spectral assignment by "NOE walking". Here we present a fully optimized NMR experiment for measuring these pivotal contacts: diagonal-free 3D/4D HN,HN-TROSY-NOESY-TROSY. It combines all of the critical requirements for extracting the optimal H(N)-H'(N) distance information: the highest resolution by consistent transverse relaxation-optimized spectroscopy (TROSY) evolution, the largest spectral dispersion in two (15)N dimensions, and maximal coverage and purity through specific suppression of the intense diagonal signals that are the main source of overlap, artifacts, and bias in any NOESY spectrum. Most notably, diagonal suppression here comes without compromising the NOE cross-signal intensities. This optimized experiment appears to be ideal for a broad range of structural studies, particularly on large deuterated, partially unfolded, helical, and membrane proteins.
Block-diagonal discriminant analysis and its bias-corrected rules.
Pang, Herbert; Tong, Tiejun; Ng, Michael
2013-06-01
High-throughput expression profiling allows simultaneous measure of tens of thousands of genes at once. These data have motivated the development of reliable biomarkers for disease subtypes identification and diagnosis. Many methods have been developed in the literature for analyzing these data, such as diagonal discriminant analysis, support vector machines, and k-nearest neighbor methods. The diagonal discriminant methods have been shown to perform well for high-dimensional data with small sample sizes. Despite its popularity, the independence assumption is unlikely to be true in practice. Recently, a gene module based linear discriminant analysis strategy has been proposed by utilizing the correlation among genes in discriminant analysis. However, the approach can be underpowered when the samples of the two classes are unbalanced. In this paper, we propose to correct the biases in the discriminant scores of block-diagonal discriminant analysis. In simulation studies, our proposed method outperforms other approaches in various settings. We also illustrate our proposed discriminant analysis method for analyzing microarray data studies.
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Broek, van den Egon; Kittler, J.; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number o
An Exact Black Hole Entropy Bound
Birmingham, Daniel; Birmingham, Danny; Sen, Siddhartha
2001-01-01
We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.
Exact Mappings in Condensed Matter Physics
Lee, Ching Hua
2016-01-01
Condensed matter systems are complex yet simple. Amidst their complexity, one often find order specified by not more than a few parameters. Key to such a reductionistic description is an appropriate choice of basis, two of which I shall describe in this thesis. The first, an exact mapping known as the Wannier State Representation (WSR), provides an exact Hilbert space correspondence between two intensely-studied topological systems, the Fractional Quantum Hall (FQH) and Fractional Chern Insul...