A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

NASA Technical Reports Server (NTRS)

Melbourne, William G.

1986-01-01

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

Recovering hidden diagonal structures via non-negative matrix factorization with multiple constraints.

PubMed

Yang, Xi; Han, Guoqiang; Cai, Hongmin; Song, Yan

2017-03-31

Revealing data with intrinsically diagonal block structures is particularly useful for analyzing groups of highly correlated variables. Earlier researches based on non-negative matrix factorization (NMF) have been shown to be effective in representing such data by decomposing the observed data into two factors, where one factor is considered to be the feature and the other the expansion loading from a linear algebra perspective. If the data are sampled from multiple independent subspaces, the loading factor would possess a diagonal structure under an ideal matrix decomposition. However, the standard NMF method and its variants have not been reported to exploit this type of data via direct estimation. To address this issue, a non-negative matrix factorization with multiple constraints model is proposed in this paper. The constraints include an sparsity norm on the feature matrix and a total variational norm on each column of the loading matrix. The proposed model is shown to be capable of efficiently recovering diagonal block structures hidden in observed samples. An efficient numerical algorithm using the alternating direction method of multipliers model is proposed for optimizing the new model. Compared with several benchmark models, the proposed method performs robustly and effectively for simulated and real biological data.

Minimizing the stochasticity of halos in large-scale structure surveys

NASA Astrophysics Data System (ADS)

Hamaus, Nico; Seljak, Uroš; Desjacques, Vincent; Smith, Robert E.; Baldauf, Tobias

2010-08-01

In recent work (Seljak, Hamaus, and Desjacques 2009) it was found that weighting central halo galaxies by halo mass can significantly suppress their stochasticity relative to the dark matter, well below the Poisson model expectation. This is useful for constraining relations between galaxies and the dark matter, such as the galaxy bias, especially in situations where sampling variance errors can be eliminated. In this paper we extend this study with the goal of finding the optimal mass-dependent halo weighting. We use N-body simulations to perform a general analysis of halo stochasticity and its dependence on halo mass. We investigate the stochasticity matrix, defined as Cij≡⟨(δi-biδm)(δj-bjδm)⟩, where δm is the dark matter overdensity in Fourier space, δi the halo overdensity of the i-th halo mass bin, and bi the corresponding halo bias. In contrast to the Poisson model predictions we detect nonvanishing correlations between different mass bins. We also find the diagonal terms to be sub-Poissonian for the highest-mass halos. The diagonalization of this matrix results in one large and one low eigenvalue, with the remaining eigenvalues close to the Poisson prediction 1/n¯, where n¯ is the mean halo number density. The eigenmode with the lowest eigenvalue contains most of the information and the corresponding eigenvector provides an optimal weighting function to minimize the stochasticity between halos and dark matter. We find this optimal weighting function to match linear mass weighting at high masses, while at the low-mass end the weights approach a constant whose value depends on the low-mass cut in the halo mass function. This weighting further suppresses the stochasticity as compared to the previously explored mass weighting. Finally, we employ the halo model to derive the stochasticity matrix and the scale-dependent bias from an analytical perspective. It is remarkably successful in reproducing our numerical results and predicts that the stochasticity between halos and the dark matter can be reduced further when going to halo masses lower than we can resolve in current simulations.

Long-Range Adiabatic Corrections to the Ground Molecular State of Alkali-Metal Dimers.

NASA Astrophysics Data System (ADS)

Marinescu, M.; Dalgarno, A.

1997-04-01

The structure of the long-range limit of the diagonal adiabatic corrections to the ground molecular state of diatomic molecules, may be expressed as a series of inverse powers of internuclear distance, R. The coefficients of this expansion are proportional to the inverse of the nuclear mass. Thus, they may be interpreted as a nuclear mass-dependent corrections to the dispersion coefficients. Using perturbation theory we have calculated the long-range coefficients of the diagonal adiabatic corrections up to the order of R-10. The final expressions are in terms of integrals over imaginary frequencies of products of atomic matrix elements involving Green's functions of complex energy. Thus, in our approach the molecular problem is reduced to an atomic one. Numerical evaluations have been done for all alkali-metal dimers. We acknowledge the support of the U.S. Dept. of Energy.

Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheid, Robert E.

1989-01-01

The applicability of conjugate gradient algorithms for computation of the manipulator forward dynamics is investigated. The redundancies in the previously proposed conjugate gradient algorithm are analyzed. A new version is developed which, by avoiding these redundancies, achieves a significantly greater efficiency. A preconditioned conjugate gradient algorithm is also presented. A diagonal matrix whose elements are the diagonal elements of the inertia matrix is proposed as the preconditioner. In order to increase the computational efficiency, an algorithm is developed which exploits the synergism between the computation of the diagonal elements of the inertia matrix and that required by the conjugate gradient algorithm.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

NASA Astrophysics Data System (ADS)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

The diagonalization of cubic matrices

NASA Astrophysics Data System (ADS)

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.

Introduction to Computational Chemistry: Teaching Hu¨ckel Molecular Orbital Theory Using an Excel Workbook for Matrix Diagonalization

ERIC Educational Resources Information Center

Litofsky, Joshua; Viswanathan, Rama

2015-01-01

Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…

Baryon asymmetry from leptogenesis with four zero neutrino Yukawa textures

NASA Astrophysics Data System (ADS)

Adhikary, Biswajit; Ghosal, Ambar; Roy, Probir

2011-01-01

The generation of the right amount of baryon asymmetry η of the Universe from supersymmetric leptogenesis is studied within the type-I seesaw framework with three heavy singlet Majorana neutrinos Ni (i = 1,2,3) and their superpartners. We assume the occurrence of four zeroes in the neutrino Yukawa coupling matrix Yν, taken to be μτ symmetric, in the weak basis where Ni (with real masses Mi > 0) and the charged leptons lα (α = e,μ,τ) are mass diagonal. The quadrant of the single nontrivial phase, allowed in the corresponding light neutrino mass matrix mν, gets fixed and additional constraints ensue from the requirement of matching η with its observed value. Special attention is paid to flavor effects in the washout of the lepton asymmetry. We also comment on the role of small departures from high scale μτ symmetry due to RG evolution.

Reduced order feedback control equations for linear time and frequency domain analysis

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1981-01-01

An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized.

RANDOM MATRIX DIAGONALIZATION--A COMPUTER PROGRAM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fuchel, K.; Greibach, R.J.; Porter, C.E.

A computer prograra is described which generates random matrices, diagonalizes them and sorts appropriately the resulting eigenvalues and eigenvector components. FAP and FORTRAN listings for the IBM 7090 computer are included. (auth)

Triple collocation-based estimation of spatially correlated observation error covariance in remote sensing soil moisture data assimilation

NASA Astrophysics Data System (ADS)

Wu, Kai; Shu, Hong; Nie, Lei; Jiao, Zhenhang

2018-01-01

Spatially correlated errors are typically ignored in data assimilation, thus degenerating the observation error covariance R to a diagonal matrix. We argue that a nondiagonal R carries more observation information making assimilation results more accurate. A method, denoted TC_Cov, was proposed for soil moisture data assimilation to estimate spatially correlated observation error covariance based on triple collocation (TC). Assimilation experiments were carried out to test the performance of TC_Cov. AMSR-E soil moisture was assimilated with a diagonal R matrix computed using the TC and assimilated using a nondiagonal R matrix, as estimated by proposed TC_Cov. The ensemble Kalman filter was considered as the assimilation method. Our assimilation results were validated against climate change initiative data and ground-based soil moisture measurements using the Pearson correlation coefficient and unbiased root mean square difference metrics. These experiments confirmed that deterioration of diagonal R assimilation results occurred when model simulation is more accurate than observation data. Furthermore, nondiagonal R achieved higher correlation coefficient and lower ubRMSD values over diagonal R in experiments and demonstrated the effectiveness of TC_Cov to estimate richly structuralized R in data assimilation. In sum, compared with diagonal R, nondiagonal R may relieve the detrimental effects of assimilation when simulated model results outperform observation data.

Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.

PubMed

Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N

2012-11-13

The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.

Workshop report on large-scale matrix diagonalization methods in chemistry theory institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S.

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 asmore » 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« less

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

NASA Astrophysics Data System (ADS)

Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter

2014-06-01

In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.

Breaking Megrelishvili protocol using matrix diagonalization

NASA Astrophysics Data System (ADS)

Arzaki, Muhammad; Triantoro Murdiansyah, Danang; Adi Prabowo, Satrio

2018-03-01

In this article we conduct a theoretical security analysis of Megrelishvili protocol—a linear algebra-based key agreement between two participants. We study the computational complexity of Megrelishvili vector-matrix problem (MVMP) as a mathematical problem that strongly relates to the security of Megrelishvili protocol. In particular, we investigate the asymptotic upper bounds for the running time and memory requirement of the MVMP that involves diagonalizable public matrix. Specifically, we devise a diagonalization method for solving the MVMP that is asymptotically faster than all of the previously existing algorithms. We also found an important counterintuitive result: the utilization of primitive matrix in Megrelishvili protocol makes the protocol more vulnerable to attacks.

On the cross-stream spectral method for the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Zorumski, William E.; Hodge, Steven L.

1993-01-01

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Commander and User Perceptions of the Army’s Intransit Visibility (ITV) Architecture

DTIC Science & Technology

2007-03-01

covariance matrix; (c) Bartlett’s test of Sphericity; and (d) Kaiser-Meyer- Olkin ( KMO ) measure of sampling adequacy. The inter-item correlation matrix...001), and all diagonal terms had a value of 1 while off-diagonal terms were 0. The KMO measure of sampling adequacy reflects the homogeneity...amongst the variables and serves as an index for comparing the magnitudes of correlation coefficients to partial correlation coefficients. KMO values at

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

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 formore » 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 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

Convergence of Transition Probability Matrix in CLVMarkov Models

NASA Astrophysics Data System (ADS)

Permana, D.; Pasaribu, U. S.; Indratno, S. W.; Suprayogi, S.

2018-04-01

A transition probability matrix is an arrangement of transition probability from one states to another in a Markov chain model (MCM). One of interesting study on the MCM is its behavior for a long time in the future. The behavior is derived from one property of transition probabilty matrix for n steps. This term is called the convergence of the n-step transition matrix for n move to infinity. Mathematically, the convergence of the transition probability matrix is finding the limit of the transition matrix which is powered by n where n moves to infinity. The convergence form of the transition probability matrix is very interesting as it will bring the matrix to its stationary form. This form is useful for predicting the probability of transitions between states in the future. The method usually used to find the convergence of transition probability matrix is through the process of limiting the distribution. In this paper, the convergence of the transition probability matrix is searched using a simple concept of linear algebra that is by diagonalizing the matrix.This method has a higher level of complexity because it has to perform the process of diagonalization in its matrix. But this way has the advantage of obtaining a common form of power n of the transition probability matrix. This form is useful to see transition matrix before stationary. For example cases are taken from CLV model using MCM called Model of CLV-Markov. There are several models taken by its transition probability matrix to find its convergence form. The result is that the convergence of the matrix of transition probability through diagonalization has similarity with convergence with commonly used distribution of probability limiting method.

Diagonalization of transfer matrix of supersymmetry U{sub q}(sl-caret(M+1|N+1)) chain with a boundary

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kojima, Takeo

2013-04-15

We study the supersymmetry U{sub q}(sl-caret(M+1|N+1)) analogue of the supersymmetric t-J model with a boundary. Our approach is based on the algebraic analysis method of solvable lattice models. We diagonalize the commuting transfer matrix by using the bosonizations of the vertex operators associated with the quantum affine supersymmetry U{sub q}(sl-caret(M+1|N+1)).

Naval Research Logistics Quarterly. Volume 28, Number 4,

DTIC Science & Technology

1981-12-01

Fan [31 and an observation by Meijerink and van der Vorst [181 guarantee that after pivoting on any diagonal element of a diagonally dominant M- matrix...Science, 3, 255-269 (1957). 1181 Meijerink, J. and H. Van der Vorst, "An Iterative Solution Method for Linear Systems of which the Coefficient Matrix Is a...Hee, K., A. Hordijk and J. Van der Wal, "Successive Approximations for Convergent Dynamic Programming," in Markov Decision Theory, H. Tijms and J

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheld, Robert E.

1989-01-01

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

ASSET: Analysis of Sequences of Synchronous Events in Massively Parallel Spike Trains

PubMed Central

Canova, Carlos; Denker, Michael; Gerstein, George; Helias, Moritz

2016-01-01

With the ability to observe the activity from large numbers of neurons simultaneously using modern recording technologies, the chance to identify sub-networks involved in coordinated processing increases. Sequences of synchronous spike events (SSEs) constitute one type of such coordinated spiking that propagates activity in a temporally precise manner. The synfire chain was proposed as one potential model for such network processing. Previous work introduced a method for visualization of SSEs in massively parallel spike trains, based on an intersection matrix that contains in each entry the degree of overlap of active neurons in two corresponding time bins. Repeated SSEs are reflected in the matrix as diagonal structures of high overlap values. The method as such, however, leaves the task of identifying these diagonal structures to visual inspection rather than to a quantitative analysis. Here we present ASSET (Analysis of Sequences of Synchronous EvenTs), an improved, fully automated method which determines diagonal structures in the intersection matrix by a robust mathematical procedure. The method consists of a sequence of steps that i) assess which entries in the matrix potentially belong to a diagonal structure, ii) cluster these entries into individual diagonal structures and iii) determine the neurons composing the associated SSEs. We employ parallel point processes generated by stochastic simulations as test data to demonstrate the performance of the method under a wide range of realistic scenarios, including different types of non-stationarity of the spiking activity and different correlation structures. Finally, the ability of the method to discover SSEs is demonstrated on complex data from large network simulations with embedded synfire chains. Thus, ASSET represents an effective and efficient tool to analyze massively parallel spike data for temporal sequences of synchronous activity. PMID:27420734

Dynamic Jahn-Teller effect: Calculation of fine structure spectrum, isotope shift and Zeeman behavior at deep center Ni2+ in CdS

NASA Astrophysics Data System (ADS)

Schoepp, Juergen

The internal transition of the deep center Ni2+ in II to IV semiconductor cadmium sulfide is examined with reference to crystal field theory. An algorithm was developed for calculation, in a basis fitted to trigonal symmetry, of fine structure operator matrix which is made of the sum of operators from spin trajectory coupling, trigonal field and electron phonon coupling. The dependence of energy level on the mass was calculated in order to examine the isotropy effect at Ni2+ transition. The mass dependence of phonon energy was estimated in an atomic cluster by using a valence force model from Keating for elastic energy. The Zeeman behavior of Ni2+ transition was examined for magnetic fields; the Zeeman operator was added to the fine structure operator and the resulting matrix was diagonalized. It is noticed that calculations are quantitatively and qualitatively in agreement with experiments.

Transferring elements of a density matrix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allahverdyan, Armen E.; Hovhannisyan, Karen V.; Yerevan State University, A. Manoogian Street 1, Yerevan

2010-01-15

We study restrictions imposed by quantum mechanics on the process of matrix-element transfer. This problem is at the core of quantum measurements and state transfer. Given two systems A and B with initial density matrices lambda and r, respectively, we consider interactions that lead to transferring certain matrix elements of unknown lambda into those of the final state r-tilde of B. We find that this process eliminates the memory on the transferred (or certain other) matrix elements from the final state of A. If one diagonal matrix element is transferred, r(tilde sign){sub aa}=lambda{sub aa}, the memory on each nondiagonal elementmore » lambda{sub an}ot ={sub b} is completely eliminated from the final density operator of A. Consider the following three quantities, Relambda{sub an}ot ={sub b}, Imlambda{sub an}ot ={sub b}, and lambda{sub aa}-lambda{sub bb} (the real and imaginary part of a nondiagonal element and the corresponding difference between diagonal elements). Transferring one of them, e.g., Rer(tilde sign){sub an}ot ={sub b}=Relambda{sub an}ot ={sub b}, erases the memory on two others from the final state of A. Generalization of these setups to a finite-accuracy transfer brings in a trade-off between the accuracy and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations that account for local aspects of the accuracy-disturbance trade-off in quantum measurements. Thus, the general aspect of state disturbance in quantum measurements is elimination of memory on non-diagonal elements, rather than diagonalization.« less

Iterative algorithm for joint zero diagonalization with application in blind source separation.

PubMed

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.

Research on numerical algorithms for large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1981-01-01

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Single-Sided Noinvasive Inspection of Multielement Sample Using Fan-Beam Multiplexed Compton Scatter Tomography

DTIC Science & Technology

2000-05-01

a vector , ρ "# represents the set of voxel densities sorted into a vector , and ( )A ρ $# "# represents a 8 mapping of the voxel densities to...density vector in equation (4) suggests that solving for ρ "# by direct inversion is not possible, calling for an iterative technique beginning with...the vector of measured spectra, and D is the diagonal matrix of the inverse of the variances. The diagonal matrix provides weighting terms, which

The Development and Application of Random Matrix Theory in Adaptive Signal Processing in the Sample Deficient Regime

DTIC Science & Technology

2014-09-01

optimal diagonal loading which minimizes the MSE. The be- havior of optimal diagonal loading when the arrival process is composed of plane waves embedded...observation vectors. The examples of the ensemble correlation matrix corresponding to the input process consisting of a single or multiple plane waves...Y ∗ij is a complex-conjugate of Yij. This result is used in order to evaluate the expectations of different quadratic forms. The Poincare -Nash

Implementing the SU(2) Symmetry for the DMRG

NASA Astrophysics Data System (ADS)

Alvarez, Gonzalo

2010-03-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992), Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This talk will explain how the DMRG++ codefootnotetextarXiv:0902.3185 or Computer Physics Communications 180 (2009) 1572-1578. has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries will be discussed for typical tight-binding models of strongly correlated electronic systems. The computational bottleneck of the algorithm, and the use of shared memory parallelization will also be addressed. Finally, a roadmap for future work on DMRG++ will be presented.

Implementation of the SU(2) Hamiltonian Symmetry for the DMRG Algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alvarez, Gonzalo

2012-01-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) and Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and themore » use of shared memory parallelization are also addressed.« less

Line Interference Effects Using a Refined Robert-Bonamy Formalism: the Test Case of the Isotropic Raman Spectra of Autoperturbed N2

NASA Technical Reports Server (NTRS)

Boulet, Christian; Ma, Qiancheng; Thibault, Franck

2014-01-01

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

An efficient sparse matrix multiplication scheme for the CYBER 205 computer

NASA Technical Reports Server (NTRS)

Lambiotte, Jules J., Jr.

1988-01-01

This paper describes the development of an efficient algorithm for computing the product of a matrix and vector on a CYBER 205 vector computer. The desire to provide software which allows the user to choose between the often conflicting goals of minimizing central processing unit (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of four types of storage is selected for each diagonal. The candidate storage types employed were chosen to be efficient on the CYBER 205 for diagonals which have nonzero structure which is dense, moderately sparse, very sparse and short, or very sparse and long; however, for many densities, no diagonal type is most efficient with respect to both resource requirements, and a trade-off must be made. For each diagonal, an initialization subroutine estimates the CPU time and storage required for each storage type based on results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the two resources. The adjusted resource requirements are then compared to select the most efficient storage and computational scheme.

Characterizing the inverses of block tridiagonal, block Toeplitz matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boffi, Nicholas M.; Hill, Judith C.; Reuter, Matthew G.

2014-12-04

We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix M bius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. There are four symmetry-distinct cases where the blocks of the inverse matrix (i) decay to zero on both sides of the diagonal, (ii) oscillate on both sides, (iii) decay on one side and oscillate on the other and (iv)more » decay on one side and grow on the other. This characterization exposes the necessary conditions for the inverse matrix to be numerically banded and may also aid in the design of preconditioners and fast algorithms. Finally, we present numerical examples of these matrix types.« less

Self-similar solutions for multi-species plasma mixing by gradient driven transport

NASA Astrophysics Data System (ADS)

Vold, E.; Kagan, G.; Simakov, A. N.; Molvig, K.; Yin, L.

2018-05-01

Multi-species transport of plasma ions across an initial interface between DT and CH is shown to exhibit self-similar species density profiles under 1D isobaric conditions. Results using transport theory from recent studies and using a Maxwell–Stephan multi-species approximation are found to be in good agreement for the self-similar mix profiles of the four ions under isothermal and isobaric conditions. The individual ion species mass flux and molar flux profile results through the mixing layer are examined using transport theory. The sum over species mass flux is confirmed to be zero as required, and the sum over species molar flux is related to a local velocity divergence needed to maintain pressure equilibrium during the transport process. The light ion species mass fluxes are dominated by the diagonal coefficients of the diffusion transport matrix, while for the heaviest ion species (C in this case), the ion flux with only the diagonal term is reduced by about a factor two from that using the full diffusion matrix, implying the heavy species moves more by frictional collisions with the lighter species than by its own gradient force. Temperature gradient forces were examined by comparing profile results with and without imposing constant temperature gradients chosen to be of realistic magnitude for ICF experimental conditions at a fuel-capsule interface (10 μm scale length or greater). The temperature gradients clearly modify the relative concentrations of the ions, for example near the fuel center, however the mixing across the fuel-capsule interface appears to be minimally influenced by the temperature gradient forces within the expected compression and burn time. Discussion considers the application of the self-similar profiles to specific conditions in ICF.

Heavy quarkonium in a holographic basis

DOE PAGES

Li, Yang; Maris, Pieter; Zhao, Xingbo; ...

2016-05-04

Here, we study the heavy quarkonium within the basis light-front quantization approach. We implement the one-gluon exchange interaction and a confining potential inspired by light-front holography. We adopt the holographic light-front wavefunction (LFWF) as our basis function and solve the non-perturbative dynamics by diagonalizing the Hamiltonian matrix. We obtain the mass spectrum for charmonium and bottomonium. With the obtained LFWFs, we also compute the decay constants and the charge form factors for selected eigenstates. The results are compared with the experimental measurements and with other established methods.

Relationships between body composition, body dimensions, and peak speed in cross-country sprint skiing.

PubMed

Stoggl, Thomas; Enqvist, Jonas; Muller, Erich; Holmberg, Hans-Christer

2010-01-01

In modern sprint cross-country skiing, strength and maximal speed are major determinants of performance. The aims of this study were to ascertain the anthropometric characteristics of world-class sprint skiers and to evaluate whether a specific body composition and/or body dimension characterizes a successful sprint skier. Our hypothesis was that body height and lean body mass are related to peak speed in double poling and diagonal stride. Fourteen male national and international elite skiers performed two peak speed tests in double poling and diagonal stride roller skiing on a treadmill and were analysed using dual-energy X-ray absorptiometry to determine body composition and body dimensions. Relative pole length was positively correlated with both techniques (double poling: r = 0.77, P < 0.01; diagonal stride: r = 0.60, P < 0.05) and was the only variable that was part of the multiple regression model for both double poling and diagonal stride peak speed. Body height was not correlated with any technique, whereas lean trunk mass (r = 0.75, P < 0.01), body mass index (r = 0.66, P < 0.01), total lean mass (r = 0.69, P < 0.01), and body mass (r = 0.57, P < 0.05) were positively related to double poling peak speed. Total lean mass (absolute: r = 0.58, P < 0.05; relative: r = 0.76, P < 0.001) and relative lean mass of the trunk, arms (both r = 0.72, P < 0.01), and legs (r = 0.54, P < 0.05) were positively related to diagonal stride peak speed. In conclusion, skiers should aim to achieve a body composition with a high percentage of lean mass and low fat mass. A focus on trunk mass through increased muscle mass appears to be important, especially for double poling. The use of longer poles (percent body height) seems to be advantageous for both double poling and diagonal stride peak speed, whereas body dimensions do not appear to be a predictive factor.

US Army Research Laboratory Power-Line UAV Modeling and Simulation (ARL-PLUMS Ver 2.x) Software Tool: User Manual and Technical Report

DTIC Science & Technology

2015-09-01

shown have units of pF/m. This is the capacitance matrix for the 115-kV 3-phase circuit seen in Fig. 24.....................................24 Fig. 29...The window that appears when one clicks “Calculate Lambdas ”. These are the linear charge densities for the 115-kV 3-phase circuit seen in Fig. 24...calculate the capacitance matrix (Fig. 28). The diagonal entries are called the coefficients of capacitance, and the non-diagonal entries are called

Analysis of solar spectra in the middle ultraviolet and visible for atmospheric trace constituents measurements. [hydroxyl radicals

NASA Technical Reports Server (NTRS)

Goldman, A.

1980-01-01

Individual spectral line parameters including line positions, strengths, and intensities were generated for the sq Alpha Sigma - sq Chi Pi (0,0) band of OH, applicable to atmospheric and high temperatures. Energy levels and transition frequencies are calculated by numerically diagonalizing the Hamiltonian. Line strengths are calculated using the dipole matrix and eigenvectors derived from energy matrix diagonalization. The line strengths are compared to those calculated from previously published algebraic line strength formulas. Tables of line parameters are presented for 240 K and 4600 K.

Weak interaction probes of light nuclei

NASA Astrophysics Data System (ADS)

Towner, I. S.

1986-03-01

Experimental evidence for pion enhancement in axial charge transitions as predicted by softpion theorems is reviewed. Corrections from non-soft-pion terms seem to be limited. For transitions involving the space part of the axial-vector current, soft-pion theorems are powerless. Meson-exchange currents then involve a complicated interplay among competing process. Explicit calculations in the hard-pion model for closed-shell-plus (or minus)-one nuclei, A=15 and A= =17, are in reasonable agreement with experiment. Quenching in the off-diagonal spin-flip matrix element is larger than in the diagonal matrix element.

Preliminary results in implementing a model of the world economy on the CYBER 205: A case of large sparse nonsymmetric linear equations

NASA Technical Reports Server (NTRS)

Szyld, D. B.

1984-01-01

A brief description of the Model of the World Economy implemented at the Institute for Economic Analysis is presented, together with our experience in converting the software to vector code. For each time period, the model is reduced to a linear system of over 2000 variables. The matrix of coefficients has a bordered block diagonal structure, and we show how some of the matrix operations can be carried out on all diagonal blocks at once.

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

NASA Astrophysics Data System (ADS)

Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus

2017-10-01

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.

Parallel algorithms for computation of the manipulator inertia matrix

NASA Technical Reports Server (NTRS)

Amin-Javaheri, Masoud; Orin, David E.

1989-01-01

The development of an O(log2N) parallel algorithm for the manipulator inertia matrix is presented. It is based on the most efficient serial algorithm which uses the composite rigid body method. Recursive doubling is used to reformulate the linear recurrence equations which are required to compute the diagonal elements of the matrix. It results in O(log2N) levels of computation. Computation of the off-diagonal elements involves N linear recurrences of varying-size and a new method, which avoids redundant computation of position and orientation transforms for the manipulator, is developed. The O(log2N) algorithm is presented in both equation and graphic forms which clearly show the parallelism inherent in the algorithm.

Embedding A4 into left-right flavor symmetry: Tribimaximal neutrino mixing and fermion hierarchy

NASA Astrophysics Data System (ADS)

Bazzocchi, F.; Morisi, S.; Picariello, M.

2008-01-01

We address two fundamental aspects of flavor physics: the mass hierarchy and the large lepton mixing angles. On one side, left-right flavor symmetry realizes the democratic mass matrix patterns and explains why one family is much heavier than the others. On the other side, discrete flavor symmetry such as A4 leads to the observed tribimaximal mixing for the leptons. We show that, by explicitly breaking the left-right flavor symmetry into the diagonal A4, it is possible to explain both the observed charged fermion mass hierarchies and quark and lepton mixing angles. In particular we predict a heavy 3rd family, the tribimaximal mixing for the leptons, and we suggest a possible origin of the Cabibbo and other mixing angles for the quarks.

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boulet, Christian, E-mail: Christian.boulet@u-psud.fr; Ma, Qiancheng; Thibault, Franck

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N{sub 2} for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While inmore » the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N{sub 2}, opening the way to the analysis of more complex molecular systems.« less

Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Poole, E. L.

1986-01-01

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

E-beam generated holographic masks for optical vector-matrix multiplication

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Case, S. K.

1981-01-01

An optical vector matrix multiplication scheme that encodes the matrix elements as a holographic mask consisting of linear diffraction gratings is proposed. The binary, chrome on glass masks are fabricated by e-beam lithography. This approach results in a fairly simple optical system that promises both large numerical range and high accuracy. A partitioned computer generated hologram mask was fabricated and tested. This hologram was diagonally separated outputs, compact facets and symmetry about the axis. The resultant diffraction pattern at the output plane is shown. Since the grating fringes are written at 45 deg relative to the facet boundaries, the many on-axis sidelobes from each output are seen to be diagonally separated from the adjacent output signals.

Block LU factorization

NASA Technical Reports Server (NTRS)

Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S.

1992-01-01

Many of the currently popular 'block algorithms' are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by columns. Moreover, for a general matrix the level of instability in block LU factorization can be founded in terms of the condition number kappa(A) and the growth factor for Gaussian elimination without pivoting. A consequence is that block LU factorization is stable for a matrix A that is symmetric positive definite or point diagonally dominant by rows or columns as long as A is well-conditioned.

An entropy-variables-based formulation of residual distribution schemes for non-equilibrium flows

NASA Astrophysics Data System (ADS)

Garicano-Mena, Jesús; Lani, Andrea; Degrez, Gérard

2018-06-01

In this paper we present an extension of Residual Distribution techniques for the simulation of compressible flows in non-equilibrium conditions. The latter are modeled by means of a state-of-the-art multi-species and two-temperature model. An entropy-based variable transformation that symmetrizes the projected advective Jacobian for such a thermophysical model is introduced. Moreover, the transformed advection Jacobian matrix presents a block diagonal structure, with mass-species and electronic-vibrational energy being completely decoupled from the momentum and total energy sub-system. The advantageous structure of the transformed advective Jacobian can be exploited by contour-integration-based Residual Distribution techniques: established schemes that operate on dense matrices can be substituted by the same scheme operating on the momentum-energy subsystem matrix and repeated application of scalar scheme to the mass-species and electronic-vibrational energy terms. Finally, the performance gain of the symmetrizing-variables formulation is quantified on a selection of representative testcases, ranging from subsonic to hypersonic, in inviscid or viscous conditions.

Harnessing molecular excited states with Lanczos chains.

PubMed

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains

NASA Astrophysics Data System (ADS)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O.; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

High-efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, J. S.; Centre for Quantum Technologies and Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117542; Wei, L. F.

We propose a high-efficiency scheme to tomographically reconstruct an unknown quantum state by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the stationary transmissions through a driven dispersively coupled resonator. It is shown that only one kind of QND measurement is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining nondiagonal elements can be similarly determined by transferring them to the diagonal locations after a series of unitary operations. Compared with the tomographic reconstructions based on the usual destructive projectivemore » measurements (wherein one such measurement can determine only one diagonal element of the density matrix), the present reconstructive approach exhibits significantly high efficiency. Specifically, our generic proposal is demonstrated by the experimental circuit quantum electrodynamics systems with a few Josephson charge qubits.« less

Fractional charge and emergent mass hierarchy in diagonal two-leg t – J cylinders

DOE PAGES

Jiang, Yi-Fan; Jiang, Hong-Chen; Yao, Hong; ...

2017-06-06

Here, we define a class of “diagonal” tmore » $-$ J ladders rotated by π / 4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group. Here, we focus on the two-leg cylinder with a doped hole concentration near x = $$\\frac{1}{4}$$ . At exactly x = $$\\frac{1}{4}$$, the system forms a period 4 charge density wave and exhibits spin-charge separation. Slightly away from $$\\frac{1}{4}$$ doping, we observe several topologically distinct types of solitons with well-defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.« less

Hierarchical majorana neutrinos from democratic mass matrices

NASA Astrophysics Data System (ADS)

Yang, Masaki J. S.

2016-09-01

In this paper, we obtain the light neutrino masses and mixings consistent with the experiments, in the democratic texture approach. The essential ansatz is that νRi are assumed to transform as ;right-handed fields; 2R +1R under the S3L ×S3R symmetry. The symmetry breaking terms are assumed to be diagonal and hierarchical. This setup only allows the normal hierarchy of the neutrino mass, and excludes both of inverted hierarchical and degenerated neutrinos. Although the neutrino sector has nine free parameters, several predictions are obtained at the leading order. When we neglect the smallest parameters ζν and ζR, all components of the mixing matrix UPMNS are expressed by the masses of light neutrinos and charged leptons. From the consistency between predicted and observed UPMNS, we obtain the lightest neutrino masses m1 = (1.1 → 1.4) meV, and the effective mass for the double beta decay 〈mee 〉 ≃ 4.5 meV.

Exact diagonalization library for quantum electron models

NASA Astrophysics Data System (ADS)

Iskakov, Sergei; Danilov, Michael

2018-04-01

We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.

A parallel algorithm for Hamiltonian matrix construction in electron-molecule collision calculations: MPI-SCATCI

NASA Astrophysics Data System (ADS)

Al-Refaie, Ahmed F.; Tennyson, Jonathan

2017-12-01

Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron - molecule collision calculations. Tennyson (1996) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionization and positron-molecule collisions.

Scattering Matrix for the Interaction between Solar Acoustic Waves and Sunspots. I. Measurements

NASA Astrophysics Data System (ADS)

Yang, Ming-Hsu; Chou, Dean-Yi; Zhao, Hui

2017-01-01

Assessing the interaction between solar acoustic waves and sunspots is a scattering problem. The scattering matrix elements are the most commonly used measured quantities to describe scattering problems. We use the wavefunctions of scattered waves of NOAAs 11084 and 11092 measured in the previous study to compute the scattering matrix elements, with plane waves as the basis. The measured scattered wavefunction is from the incident wave of radial order n to the wave of another radial order n‧, for n=0{--}5. For a time-independent sunspot, there is no mode mixing between different frequencies. An incident mode is scattered into various modes with different wavenumbers but the same frequency. Working in the frequency domain, we have the individual incident plane-wave mode, which is scattered into various plane-wave modes with the same frequency. This allows us to compute the scattering matrix element between two plane-wave modes for each frequency. Each scattering matrix element is a complex number, representing the transition from the incident mode to another mode. The amplitudes of diagonal elements are larger than those of the off-diagonal elements. The amplitude and phase of the off-diagonal elements are detectable only for n-1≤slant n\\prime ≤slant n+1 and -3{{Δ }}k≤slant δ {k}x≤slant 3{{Δ }}k, where δ {k}x is the change in the transverse component of the wavenumber and Δk = 0.035 rad Mm-1.

Numerical radius and zero pattern of matrices

NASA Astrophysics Data System (ADS)

Nikiforov, Vladimir

2008-01-01

Let A be an n×n complex matrix and r be the maximum size of its principal submatrices with no off-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting ||A|| be the Frobenius norm of A, we show that2[less-than-or-equals, slant](1-1/2r-1/2n)||A||2. This inequality is tight within an additive term O(rn-2). If the matrix A is Hermitian, then2[less-than-or-equals, slant](1-1/r)||A||2. This inequality is sharp; moreover, it implies the Turán theorem for graphs.

The g Factors of Ground State of Ruby and Their Pressure-Induced Shifts

NASA Astrophysics Data System (ADS)

Ma, Dongping; Zhang, Hongmei; Chen, Jurong; Liu, Yanyun

1998-12-01

By using the theory of pressure-induced shifts and the eigenfunctions at normal and various pressures obtained from the diagonalization of the complete d3 energy matrix adopting C3v symmetry, g factors of the ground state of ruby and their pressure-induced shifts have been calculated. The results are in very good agreement with the experimental data. For the precise calculation of properties of the ground skate, it is necessary to take into account the effects of all the excited states by the diagonalization of the complete energy matrix. The project (Grant No. 19744001) supported by National Natural Science Foundation of China

Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

NASA Technical Reports Server (NTRS)

Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.

1998-01-01

We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization

NASA Astrophysics Data System (ADS)

Jentschura, Ulrich; Noble, Jonathan

2014-03-01

We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.

Dirac neutrinos with S4 flavor symmetry in warped extra dimensions

NASA Astrophysics Data System (ADS)

Ding, Gui-Jun; Zhou, Ye-Ling

2013-11-01

We present a warped extra dimension model with the custodial symmetry SU(2×SU(2×U(1×PLR based on the flavor symmetry S4×Z2×Z2', and the neutrinos are taken to be Dirac particles. At leading order, the democratic lepton mixing is derived exactly, and the high-dimensional operators introduce corrections of order λc to all the three lepton mixing angles such that agreement with the experimental data can be achieved. The neutrino mass spectrum is predicted to be of the inverted hierarchy and the second octant of θ23 is preferred. We suggest the modified democratic mixing, which is obtained by permuting the second and the third rows of the democratic mixing matrix, should be a good first order approximation to understanding sizable θ13 and the first octant of θ23. The constraints on the model from the electroweak precision measurements are discussed. Furthermore, we investigate the lepton mixing patterns for all the possible residual symmetries Gν and Gl in the neutrino and charged lepton sectors, respectively. For convenience, we work in the base in which m≡mlml† is diagonal, where ml is the charged lepton mass matrix. It is easy to see that the symmetry transformation matrix Gl, which is determined by the condition Gl†mGl=m, is a diagonal and non-degenerate 3×3 phase matrix. In the case that neutrinos are Majorana particles, the light neutrino mass matrix for DC mixing is of the form mνDC=UDC*diag(m1,m2,m3)UDC†. The symmetry transformations Gi, which satisfy GiTmνDCGi=mνDC, are determined to be G1=+u1u1†-u2u2†-u3u3†, G2=-u1u1†+u2u2†-u3u3† and G3=-u1u1†-u2u2†+u3u3† besides the identity transformation, where ui is the ith column of UDC. They satisfy Gi2=1, GiGj=GjGi=Gk(i≠j≠k). Consequently the symmetry group of the neutrino mass matrix mνDC is the Klein four group K4≅Z2×Z2. Denoting the underlying family symmetry group at high energies as G, then the symmetry transformations Gl and Gi should be the elements of G. In the case of G being a finite group, there should be some integers n and mi such that Gln=(=1 with n⩾3 which results from the requirement that Gl is non-degenerate. We have performed a systematic scan of the possible values of n up to n=200, we are unable to find solutions for the integers mi such that (=1, and hence the symmetry groups in these cases are infinite. Therefore we conclude that there is no discrete flavor symmetry group that contains all of the symmetries needed for the DC mixing, although one cannot rule out the possibility of a discrete group with a very large order. This is the reason why the discrete flavor symmetry origin of the DC mixing has not been proposed so far. Note that the S×S symmetry can immediately lead to the so-called democratic mass matrix in which each matrix element has the same value [53], where S and S are symmetric groups of degree three acting on the left-handed and the right-handed fermion fields respectively. However, the DC mixing cannot be uniquely determined by the democratic mass matrix, and in fact only the third row of DC mixing matrix is fixed.

Reflection matrices with U q [osp(2) (2|2m)] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima-Santos, A.

2017-09-01

We propose a classification of the reflection K-matrices (solutions of the boundary Yang-Baxter equation) for the Uq[osp(2)(2\\vert 2m)]=Uq[C(2)(m+1)] vertex-model. We found four families of solutions, namely, the complete solutions, in which no elements of the reflection K-matrix is null, the block-diagonal solutions, the X-shape solutions and the diagonal solutions. We highlight that these diagonal K-matrices also hold for the Uq[osp(2)(2n+2\\vert 2m)]=Uq[D(2)(n+1, m)] vertex-model.

Group Sparse Optimization by Alternating Direction Method

DTIC Science & Technology

2012-11-22

to solving the following linear system: (β1G TG+ β2A TA)x = β1G T z −GTλ1 + β2AT b+ATλ2. (3.5) Note that GTG ∈ Rn×n is a diagonal matrix whose i-th...diagonal entry is the number of repetitions of xi in x̃. When the groups form an complete cover of the solution, the diagonal entries of GTG will be...positive, so GTG is invertible. In the next subsection, we will show that an incomplete cover case can be converted to a complete cover case by

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

PubMed Central

Vitalis, Andreas; Pappu, Rohit V.

2014-01-01

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom. PMID:25053299

An Empirical State Error Covariance Matrix for Batch State Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).

NON-GAUSSIANITIES IN THE LOCAL CURVATURE OF THE FIVE-YEAR WMAP DATA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rudjord, Oeystein; Groeneboom, Nicolaas E.; Hansen, Frode K.

Using the five-year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year WMAP data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the {approx}1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year WMAP data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limitedmore » availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the {chi}{sup 2}-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.« less

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

DOE PAGES

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D.; ...

2015-11-01

Here, we present results for the isovector and flavor diagonal tensor charges g u–d T, g u T, g d T, and g s T needed to probe novel tensor interactions at the TeV scale in neutron and nuclear β-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and three quark masses corresponding to the pionmore » masses M π ≈ 130, 220 and 310 MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the isovector combination is g u–d T = 1.020(76) in the MS¯ scheme at 2 GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find g u T = 0.774(66), g d T = –0.233(28) and g u+d T = 0.541(67). The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio m s/m u,d, is g s T = 0.008(9) in the continuum limit.« less

Improvement of structural models using covariance analysis and nonlinear generalized least squares

NASA Technical Reports Server (NTRS)

Glaser, R. J.; Kuo, C. P.; Wada, B. K.

1992-01-01

The next generation of large, flexible space structures will be too light to support their own weight, requiring a system of structural supports for ground testing. The authors have proposed multiple boundary-condition testing (MBCT), using more than one support condition to reduce uncertainties associated with the supports. MBCT would revise the mass and stiffness matrix, analytically qualifying the structure for operation in space. The same procedure is applicable to other common test conditions, such as empty/loaded tanks and subsystem/system level tests. This paper examines three techniques for constructing the covariance matrix required by nonlinear generalized least squares (NGLS) to update structural models based on modal test data. The methods range from a complicated approach used to generate the simulation data (i.e., the correct answer) to a diagonal matrix based on only two constants. The results show that NGLS is very insensitive to assumptions about the covariance matrix, suggesting that a workable NGLS procedure is possible. The examples also indicate that the multiple boundary condition procedure more accurately reduces errors than individual boundary condition tests alone.

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Sodemann, Inti; Sheng, D. N.; Fu, Liang

2017-05-01

We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n =1 ) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

Entropy of isolated quantum systems after a quench.

PubMed

Santos, Lea F; Polkovnikov, Anatoli; Rigol, Marcos

2011-07-22

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

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.

Nuclear quantum shape-phase transitions in odd-mass systems

NASA Astrophysics Data System (ADS)

Quan, S.; Li, Z. P.; Vretenar, D.; Meng, J.

2018-03-01

Microscopic signatures of nuclear ground-state shape-phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter—the number of nucleons—theoretical low-energy spectra, two-neutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and E 2 reduced transition matrix elements accurately reproduce available data and exhibit more-pronounced discontinuities at neutron number N =90 compared with the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared with the corresponding Sm isotopes.

Measurement of the Spectroscopic Quadrupole Moment for the 2+1 State in 10Be:. Testing AB Initio Calculations

NASA Astrophysics Data System (ADS)

Orce, J. N.; Djongolov, M.; Navratil, P.; Ball, G.; Garnsworthy, A. B.; Hackman, G.; Lassen, J.; Meissner, J.; Pearson, C. J.; Li, R.; Milovanovic, L.; Sjue, S. K. L.; Teigelhoefer, A.; Triambak, S.; Williams, S. J.; Falou, H. Al; Drake, T. E.; Andreoiu, C.; Cross, D.; Kshetri, R.; Finlay, P.; Garrett, P. E.; Leach, K. G.; Rand, E. T.; Sumithrarachchi, C. S.; Svensson, C. E.; Tardiff, E. R.; Wong, J.; Forssen, C.; Hayes, A. B.; Sarazin, F.; Stoyer, M. A.; Wu, C. Y.

2013-03-01

The highly efficient and segmented TIGRESS HPGe γ-ray array at TRIUMF has been used to perform a reorientation effect Coulomb excitation study of the 2+1 state at 3.368 MeV in 10Be. This is the first Coulomb excitation measurement that provides information on diagonal matrix elements for such a high lying first excited state from μ-ray data. With the availability of accurate lifetime data, a restriction on the diagonal < 2+1|M({E}2)|2+1> matrix element is determined. This result is compared to a no core shell model calculation with the CD-Bonn 2000 two nucleon potential.

Efficient, massively parallel eigenvalue computation

NASA Technical Reports Server (NTRS)

Huo, Yan; Schreiber, Robert

1993-01-01

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Decay of correlations between cross-polarized electromagnetic waves in a two-dimensional random medium.

PubMed

Gorodnichev, E E

2018-04-01

The problem of multiple scattering of polarized light in a two-dimensional medium composed of fiberlike inhomogeneities is studied. The attenuation lengths for the density matrix elements are calculated. For a highly absorbing medium it is found that, as the sample thickness increases, the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the sample thickness, the off-diagonal elements which are responsible for correlations between the cross-polarized waves disappear. In the asymptotic limit of very thick samples the scattered light proves to be polarized perpendicular to the fibers. The difference in the attenuation lengths between the density matrix elements results in a nonmonotonic depth dependence of the degree of polarization. In the opposite case of a weakly absorbing medium, the off-diagonal element of the density matrix and, correspondingly, the correlations between the cross-polarized fields are shown to decay faster than the intensity of waves polarized along and perpendicular to the fibers.

Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jonasson, O.; Karimi, F.; Knezevic, I.

2016-08-01

We derive a Markovian master equation for the single-electron density matrix, applicable to quantum cascade lasers (QCLs). The equation conserves the positivity of the density matrix, includes off-diagonal elements (coherences) as well as in-plane dynamics, and accounts for electron scattering with phonons and impurities. We use the model to simulate a terahertz-frequency QCL, and compare the results with both experiment and simulation via nonequilibrium Green's functions (NEGF). We obtain very good agreement with both experiment and NEGF when the QCL is biased for optimal lasing. For the considered device, we show that the magnitude of coherences can be a significantmore » fraction of the diagonal matrix elements, which demonstrates their importance when describing THz QCLs. We show that the in-plane energy distribution can deviate far from a heated Maxwellian distribution, which suggests that the assumption of thermalized subbands in simplified density-matrix models is inadequate. As a result, we also show that the current density and subband occupations relax towards their steady-state values on very different time scales.« less

General design approach and practical realization of decoupling matrices for parallel transmission coils.

PubMed

Mahmood, Zohaib; McDaniel, Patrick; Guérin, Bastien; Keil, Boris; Vester, Markus; Adalsteinsson, Elfar; Wald, Lawrence L; Daniel, Luca

2016-07-01

In a coupled parallel transmit (pTx) array, the power delivered to a channel is partially distributed to other channels because of coupling. This power is dissipated in circulators resulting in a significant reduction in power efficiency. In this study, a technique for designing robust decoupling matrices interfaced between the RF amplifiers and the coils is proposed. The decoupling matrices ensure that most forward power is delivered to the load without loss of encoding capabilities of the pTx array. The decoupling condition requires that the impedance matrix seen by the power amplifiers is a diagonal matrix whose entries match the characteristic impedance of the power amplifiers. In this work, the impedance matrix of the coupled coils is diagonalized by a successive multiplication by its eigenvectors. A general design procedure and software are developed to generate automatically the hardware that implements diagonalization using passive components. The general design method is demonstrated by decoupling two example parallel transmit arrays. Our decoupling matrices achieve better than -20 db decoupling in both cases. A robust framework for designing decoupling matrices for pTx arrays is presented and validated. The proposed decoupling strategy theoretically scales to any arbitrary number of channels. Magn Reson Med 76:329-339, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

A theoretical study of the dissociative recombination of SH+ with electrons through the 2Π states of SH.

PubMed

Kashinski, D O; Talbi, D; Hickman, A P; Di Nallo, O E; Colboc, F; Chakrabarti, K; Schneider, I F; Mezei, J Zs

2017-05-28

A quantitative theoretical study of the dissociative recombination of SH + with electrons has been carried out. Multireference, configuration interaction calculations were used to determine accurate potential energy curves for SH + and SH. The block diagonalization method was used to disentangle strongly interacting SH valence and Rydberg states and to construct a diabatic Hamiltonian whose diagonal matrix elements provide the diabatic potential energy curves. The off-diagonal elements are related to the electronic valence-Rydberg couplings. Cross sections and rate coefficients for the dissociative recombination reaction were calculated with a stepwise version of the multichannel quantum defect theory, using the molecular data provided by the block diagonalization method. The calculated rates are compared with the most recent measurements performed on the ion Test Storage Ring (TSR) in Heidelberg, Germany.

Estimation of a cover-type change matrix from error-prone data

Treesearch

Steen Magnussen

2009-01-01

Coregistration and classification errors seriously compromise per-pixel estimates of land cover change. A more robust estimation of change is proposed in which adjacent pixels are grouped into 3x3 clusters and treated as a unit of observation. A complete change matrix is recovered in a two-step process. The diagonal elements of a change matrix are recovered from...

Inner Space Perturbation Theory in Matrix Product States: Replacing Expensive Iterative Diagonalization.

PubMed

Ren, Jiajun; Yi, Yuanping; Shuai, Zhigang

2016-10-11

We propose an inner space perturbation theory (isPT) to replace the expensive iterative diagonalization in the standard density matrix renormalization group theory (DMRG). The retained reduced density matrix eigenstates are partitioned into the active and secondary space. The first-order wave function and the second- and third-order energies are easily computed by using one step Davidson iteration. Our formulation has several advantages including (i) keeping a balance between the efficiency and accuracy, (ii) capturing more entanglement with the same amount of computational time, (iii) recovery of the standard DMRG when all the basis states belong to the active space. Numerical examples for the polyacenes and periacene show that the efficiency gain is considerable and the accuracy loss due to the perturbation treatment is very small, when half of the total basis states belong to the active space. Moreover, the perturbation calculations converge in all our numerical examples.

Noncommutative mapping from the symplectic formalism

NASA Astrophysics Data System (ADS)

De Andrade, M. A.; Neves, C.

2018-01-01

Bopp's shifts will be generalized through a symplectic formalism. A special procedure, like "diagonalization," which drives the completely deformed symplectic matrix to the standard symplectic form was found as suggested by Faddeev-Jackiw. Consequently, the correspondent transformation matrix guides the mapping from commutative to noncommutative (NC) phase-space coordinates. Bopp's shifts may be directly generalized from this mapping. In this context, all the NC and scale parameters, introduced into the brackets, will be lifted to the Hamiltonian. Well-known results, obtained using ⋆-product, will be reproduced without considering that the NC parameters are small (≪1). Besides, it will be shown that different choices for NC algebra among the symplectic variables generate distinct dynamical systems, in which they may not even connect with each other, and that some of them can preserve, break, or restore the symmetry of the system. Further, we will also discuss the charge and mass rescaling in a simple model.

The effect of Fisher information matrix approximation methods in population optimal design calculations.

PubMed

Strömberg, Eric A; Nyberg, Joakim; Hooker, Andrew C

2016-12-01

With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

An Application of Sylvester's Rank Inequality

ERIC Educational Resources Information Center

Kung, Sidney H.

2011-01-01

Using two well known criteria for the diagonalizability of a square matrix plus an extended form of Sylvester's Rank Inequality, the author presents a new condition for the diagonalization of a real matrix from which one can obtain the eigenvectors by simply multiplying some associated matrices without solving a linear system of simultaneous…

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch; Pappu, Rohit V.

2014-07-21

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear inmore » the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.« less

Parameterized LMI Based Diagonal Dominance Compensator Study for Polynomial Linear Parameter Varying System

NASA Astrophysics Data System (ADS)

Han, Xiaobao; Li, Huacong; Jia, Qiusheng

2017-12-01

For dynamic decoupling of polynomial linear parameter varying(PLPV) system, a robust dominance pre-compensator design method is given. The parameterized precompensator design problem is converted into an optimal problem constrained with parameterized linear matrix inequalities(PLMI) by using the conception of parameterized Lyapunov function(PLF). To solve the PLMI constrained optimal problem, the precompensator design problem is reduced into a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a new constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator is achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation on a turbofan engine PLPV model.

On optimal improvements of classical iterative schemes for Z-matrices

NASA Astrophysics Data System (ADS)

Noutsos, D.; Tzoumas, M.

2006-04-01

Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z- or an M-matrix, that make the associated Jacobi and Gauss-Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161-170], Gunawardena et al. [LAA 154-156 (1991) 123-143]. In this work we generalize the previous preconditioners to obtain optimal methods. "Good" Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.

Negative tunnel magnetoresistance and differential conductance in transport through double quantum dots

NASA Astrophysics Data System (ADS)

Trocha, Piotr; Weymann, Ireneusz; Barnaś, Józef

2009-10-01

Spin-dependent transport through two coupled single-level quantum dots weakly connected to ferromagnetic leads with collinear magnetizations is considered theoretically. Transport characteristics, including the current, linear and nonlinear conductances, and tunnel magnetoresistance are calculated using the real-time diagrammatic technique in the parallel, serial, and intermediate geometries. The effects due to virtual tunneling processes between the two dots via the leads, associated with off-diagonal coupling matrix elements, are also considered. Negative differential conductance and negative tunnel magnetoresistance have been found in the case of serial and intermediate geometries, while no such behavior has been observed for double quantum dots coupled in parallel. It is also shown that transport characteristics strongly depend on the magnitude of the off-diagonal coupling matrix elements.

Off-diagonal Jacobian support for Nodal BCs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peterson, John W.; Andrs, David; Gaston, Derek R.

In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite elementmore » codes in general: 1. The ability to zero out entire Jacobian matrix rows after \

Efficient spares matrix multiplication scheme for the CYBER 203

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.

1984-01-01

This work has been directed toward the development of an efficient algorithm for performing this computation on the CYBER-203. The desire to provide software which gives the user the choice between the often conflicting goals of minimizing central processing (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of three types of storage is selected for each diagonal. For each storage type, an initialization sub-routine estimates the CPU and storage requirements based upon results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the resources. The three storage types employed were chosen to be efficient on the CYBER-203 for diagonals which are sparse, moderately sparse, or dense; however, for many densities, no diagonal type is most efficient with respect to both resource requirements. The user-supplied weights dictate the choice.

On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in SN2 Reactions

PubMed Central

Rosta, Edina; Warshel, Arieh

2012-01-01

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works1,2 and uses the ab initio frozen density functional theory (FDFT) method3 to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of SN2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment. PMID:23329895

The Use of Matrix Training to Promote Generative Language with Children with Autism

ERIC Educational Resources Information Center

Frampton, Sarah E.; Wymer, Sarah C.; Hansen, Bethany; Shillingsburg, M. Alice

2016-01-01

Matrix training consists of planning instruction by arranging components of desired skills across 2 axes. After training with diagonal targets that each combine 2 unique skill components, responses to nondiagonal targets, consisting of novel combinations of the components, may emerge. A multiple-probe design across participants was used to…

An Alternating Least Squares Method for the Weighted Approximation of a Symmetric Matrix.

ERIC Educational Resources Information Center

ten Berge, Jos M. F.; Kiers, Henk A. L.

1993-01-01

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

The ground state magnetic moment and susceptibility of a two electron Gaussian quantum dot

NASA Astrophysics Data System (ADS)

Boda, Aalu; Chatterjee, Ashok

2018-04-01

The problem of two interacting electrons moving in a two-dimensional semiconductor quantum dot with Gaussian confinement under the influence of an external magnetic field is studied by using a method of numerical diagonalization of the Hamiltonian matrix with in the effective-mass approximation. The energy spectrum is calculated as a function of the magnetic field. We find the ground state magnetic moment and the magnetic susceptibility show zero temperature diamagnetic peaks due to exchange induced singlet-triplet oscillations. The position and the number of these peaks depend on the size of the quantum dot and also strength of the electro-electron interaction. The theory is applied to a GaAs quantum dot.

Three flavor neutrino oscillations in matter: Flavor diagonal potentials, the adiabatic basis, and the CP phase

NASA Astrophysics Data System (ADS)

Kneller, James P.; McLaughlin, Gail C.

2009-09-01

We discuss the three neutrino flavor evolution problem with general, flavor-diagonal, matter potentials and a fully parametrized mixing matrix that includes CP violation, and derive expressions for the eigenvalues, mixing angles, and phases. We demonstrate that, in the limit that the mu and tau potentials are equal, the eigenvalues and matter mixing angles θ˜12 and θ˜13 are independent of the CP phase, although θ˜23 does have CP dependence. Since we are interested in developing a framework that can be used for S matrix calculations of neutrino flavor transformation, it is useful to work in a basis that contains only off-diagonal entries in the Hamiltonian. We derive the “nonadiabaticity” parameters that appear in the Hamiltonian in this basis. We then introduce the neutrino S matrix, derive its evolution equation and the integral solution. We find that this new Hamiltonian, and therefore the S matrix, in the limit that the μ and τ neutrino potentials are the same, is independent of both θ˜23 and the CP violating phase. In this limit, any CP violation in the flavor basis can only be introduced via the rotation matrices, and so effects which derive from the CP phase are then straightforward to determine. We then show explicitly that the electron neutrino and electron antineutrino survival probability is independent of the CP phase in this limit. Conversely, if the CP phase is nonzero and mu and tau matter potentials are not equal, then the electron neutrino survival probability cannot be independent of the CP phase.

Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Coupling and Line Mixing Effects on NH3 Lines in the V4 Band

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2017-01-01

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular v4 band. As in the pure rotational and the parallel v1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the v1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 equals K2 equals 0, whose matrix elements require the selection rule delta k equals 0, the formalism is applicable for the v4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

New Priorities for a Changing U.S. Economy

DTIC Science & Technology

1999-01-08

Stockholm, Sweden, 1991. [73] R . Malladi , J. Sethian, B. and Vermuri, "Shape modelling with front propagation: a level set approach," IEEE PAMI17...represented as n x n matrices of operators in £(£), and r (") is represented by a diagonal matrix, with diagonal entries equal to T. Denote by An...also has independent interest. Theorem 1 Assume that A’ is a *-algebra of finite dimension n. Then fa(A) = ^..(Art) for every A 6 £(£)~ r ~ Remark

Large Eddy Simulation of Bubbly Ship Wakes

DTIC Science & Technology

2005-08-01

as, [Cm +BI(p)+ DE (u)+D,(u,)] (2.28) aRm, =-[E,+FE )(p) (229O•., L pe•,z+_tpjj.( F.(]-](2.29) where Ci and EP represent the convective terms, Bi is the...discrete operator for the pressure gradient term, DE and D, (FE and FI) are discrete operators for the explicitly treated off diagonal terms and the...Bashforth scheme is employed for all the other terms. The off diagonal viscous terms ( DE ) are treated explicitly in order to simplify the LHS matrix of the

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Conrady, Florian; Hnybida, Jeff; Department of Physics, University of Waterloo, Waterloo, Ontario

2011-01-15

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states aremore » defined explicitly and related to SU(1,1) and SU(2) matrix elements.« less

Reorientation-effect measurement of the <21+∥E2̂∥21+> matrix element in 10Be

NASA Astrophysics Data System (ADS)

Orce, J. N.; Drake, T. E.; Djongolov, M. K.; Navrátil, P.; Triambak, S.; Ball, G. C.; Al Falou, H.; Churchman, R.; Cross, D. S.; Finlay, P.; Forssén, C.; Garnsworthy, A. B.; Garrett, P. E.; Hackman, G.; Hayes, A. B.; Kshetri, R.; Lassen, J.; Leach, K. G.; Li, R.; Meissner, J.; Pearson, C. J.; Rand, E. T.; Sarazin, F.; Sjue, S. K. L.; Stoyer, M. A.; Sumithrarachchi, C. S.; Svensson, C. E.; Tardiff, E. R.; Teigelhoefer, A.; Williams, S. J.; Wong, J.; Wu, C. Y.

2012-10-01

The highly-efficient and segmented TIGRESS γ-ray spectrometer at TRIUMF has been used to perform a reorientation-effect Coulomb-excitation study of the 21+ state at 3.368 MeV in 10Be. This is the first Coulomb-excitation measurement that enables one to obtain information on diagonal matrix elements for such a high-lying first excited state from γ-ray data. With the availability of accurate lifetime data, a value of -0.110±0.087 eb is determined for the <21+∥E2̂∥21+> diagonal matrix element, which assuming the rotor model, leads to a negative spectroscopic quadrupole moment of QS(21+)=-0.083±0.066 eb. This result is in agreement with both no-core shell-model calculations performed in this work with the CD-Bonn 2000 two-nucleon potential and large shell-model spaces, and Green's function Monte Carlo predictions with two- plus three-nucleon potentials.

Exploiting the Spatio-Temporal Coherence of Ocean Ambient Noise for Passive Tomography

DTIC Science & Technology

2012-09-30

ˆ kfCij and corresponds to the entry (i,j) of cross-covariance matrix for the selected horizontal triangular array, denoted );( ˆ kfC at the...diagonal elements );( ˆ kfCii (i=1..3) of the matrix );( ˆ kfC were set to zero to mitigate the bias due to electronic noise and the large

Inertial sensor and method of use

NASA Technical Reports Server (NTRS)

Gutierrez, Roman C. (Inventor); Tang, Tony K. (Inventor)

2003-01-01

The inertial sensor of the present invention utilizes a proof mass suspended from spring structures forming a nearly degenerate resonant structure into which a perturbation is introduced, causing a split in frequency of the two modes so that the mode shape become uniquely defined, and to the first order, remains orthogonal. The resonator is provided with a mass or inertia tensor with off-diagonal elements. These off-diagonal elements are large enough to change the mode shape of the two nearly degenerate modes from the original coordinate frame. The spring tensor is then provided with a compensating off-diagonal element, such that the mode shape is again defined in the original coordinate frame. The compensating off-diagonal element in the spring tensor is provided by a biasing voltage that softens certain elements in the spring tensor. Acceleration disturbs the compensation and the mode shape again changes from the original coordinate frame. By measuring the change in the mode shape, the acceleration is measured.

Quantum correlation of path-entangled two-photon states in waveguide arrays with defects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dou, Yiling; Xu, Lei; Han, Bin

We study the quantum correlation of path-entangled states of two photons in coupled one-dimensional waveguide arrays with lattice defects. Both off-diagonal and diagonal defects are considered, which show different effects on the quantum correlation of path-entangled two-photon states. Two-photon bunching or anti-bunching effects can be observed and controlled. The two photons are found to have a tendency to bunch at the side lobes with a repulsive off-diagonal defect, and the path-entanglement of the input two-photon state can be preserved during the propagation. We also found that defect modes may play an important role on the two-photon correlation of path-entangled statesmore » in the waveguide arrays. Due to the quantum interference effect, intriguing evolution dynamics of the two-photon correlation matrix elements with oscillation frequencies being either twice of or the same as that of a classical light wave, depending on the position of the correlation matrix element, is observed. Our results show that it is possible to manipulate the two-photon correlation properties of path-entangled states in waveguide arrays with lattice defects.« less

Diagonal dominance for the multivariable Nyquist array using function minimization

NASA Technical Reports Server (NTRS)

Leininger, G. G.

1977-01-01

A new technique for the design of multivariable control systems using the multivariable Nyquist array method was developed. A conjugate direction function minimization algorithm is utilized to achieve a diagonal dominant condition over the extended frequency range of the control system. The minimization is performed on the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal terms of either the inverse or direct open loop transfer function matrix. Several new feedback design concepts were also developed, including: (1) dominance control parameters for each control loop; (2) compensator normalization to evaluate open loop conditions for alternative design configurations; and (3) an interaction index to determine the degree and type of system interaction when all feedback loops are closed simultaneously. This new design capability was implemented on an IBM 360/75 in a batch mode but can be easily adapted to an interactive computer facility. The method was applied to the Pratt and Whitney F100 turbofan engine.

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Tan, Dian

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

A CLT on the SNR of Diagonally Loaded MVDR Filters

NASA Astrophysics Data System (ADS)

Rubio, Francisco; Mestre, Xavier; Hachem, Walid

2012-08-01

This paper studies the fluctuations of the signal-to-noise ratio (SNR) of minimum variance distorsionless response (MVDR) filters implementing diagonal loading in the estimation of the covariance matrix. Previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples. Specifically, a central limit theorem (CLT) is established for the fluctuations of the SNR of the diagonally loaded MVDR filter, under both supervised and unsupervised training settings in adaptive filtering applications. Our second-order analysis is based on the Nash-Poincar\\'e inequality and the integration by parts formula for Gaussian functionals, as well as classical tools from statistical asymptotic theory. Numerical evaluations validating the accuracy of the CLT confirm the asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials.

PubMed

Noel, Yves; D'arco, Philippe; Demichelis, Raffaella; Zicovich-Wilson, Claudio M; Dovesi, Roberto

2010-03-01

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented. (c) 2009 Wiley Periodicals, Inc.

Linear and Nonlinear Optical Properties of Spherical Quantum Dots: Effects of Hydrogenic Impurity and Conduction Band Non-Parabolicity

NASA Astrophysics Data System (ADS)

Rezaei, G.; Vaseghi, B.; Doostimotlagh, N. A.

2012-03-01

Simultaneous effects of an on-center hydrogenic impurity and band edge non-parabolicity on intersubband optical absorption coefficients and refractive index changes of a typical GaAs/AlxGa1-x As spherical quantum dot are theoretically investigated, using the Luttinger—Kohn effective mass equation. So, electronic structure and optical properties of the system are studied by means of the matrix diagonalization technique and compact density matrix approach, respectively. Finally, effects of an impurity, band edge non-parabolicity, incident light intensity and the dot size on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes are investigated. Our results indicate that, the magnitudes of these optical quantities increase and their peaks shift to higher energies as the influences of the impurity and the band edge non-parabolicity are considered. Moreover, incident light intensity and the dot size have considerable effects on the optical absorption coefficients and refractive index changes.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

An improved semi-implicit method for structural dynamics analysis

NASA Technical Reports Server (NTRS)

Park, K. C.

1982-01-01

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.

Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

NASA Astrophysics Data System (ADS)

Lee, Moon Ho; Khan, Md Hashem Ali; Kim, Kyeong Jin

2013-12-01

Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to the identity matrix. Therefore, we mathematically propose a fast block-wise inverse Jacket transform of orders N = 2 k , 3 k , 5 k , and 6 k , where k is a positive integer. Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary matrices, which are obtained from BIJTs, they can be applied in areas such as 3GPP physical layer for ultra mobile broadband permutation matrices design, first-order q-ary Reed-Muller code design, diagonal channel design, diagonal subchannel decompose for interference alignment, and 4G MIMO long-term evolution Alamouti precoding design.

Neutron Multiplicity: LANL W Covariance Matrix for Curve Fitting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wendelberger, James G.

2016-12-08

In neutron multiplicity counting one may fit a curve by minimizing an objective function, χmore » $$2\\atop{n}$$. The objective function includes the inverse of an n by n matrix of covariances, W. The inverse of the W matrix has a closed form solution. In addition W -1 is a tri-diagonal matrix. The closed form and tridiagonal nature allows for a simpler expression of the objective function χ$$2\\atop{n}$$. Minimization of this simpler expression will provide the optimal parameters for the fitted curve.« less

Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2016-01-01

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.

Features of quark and lepton mixing from differential geometry of curves on surfaces

NASA Astrophysics Data System (ADS)

Bordes, José; Hong-Mo, Chan; Pfaudler, Jakov; Sheung Tsun, Tsou

1998-09-01

It is noted that the Cabibbo-Kobayashi-Moskawa (CKM) matrix elements for both quarks and leptons as conceived in the dualized standard model (DSM) can be interpreted as direction cosines obtained by moving the Darboux trihedron (a 3-frame) along a trajectory on a sphere traced out through changing energy scales by a 3-vector factorized from the mass matrix. From the Darboux analogues of the well-known Serret-Frenet formulas for space curves, it is seen that the corner elements (Vub,Vtd for quarks, and Ue3,Uτ1 for leptons) are associated with the (geodesic) torsion, while the other off-diagonal elements (Vus,Vcd and Vcb,Vts for quarks, and Ue2,Uμ1 and Uμ3,Uτ2 for leptons) with the (respectively, geodesic and normal) curvatures of the trajectory. From this it follows that (i) the corner elements in both matrices are much smaller than the other elements, and (ii) the Uμ3,Uτ2 elements for the lepton CKM matrix are much larger than their counterparts in the quark matrix. Both these conclusions are strongly borne out by experiment, for quarks in hadron decays and for leptons in neutrino oscillations, and by previous explicit calculations within the DSM scheme.

Revisiting the comparison between the Shack-Hartmann and the pyramid wavefront sensors via the Fisher information matrix.

PubMed

Plantet, C; Meimon, S; Conan, J-M; Fusco, T

2015-11-02

Exoplanet direct imaging with large ground based telescopes requires eXtreme Adaptive Optics that couples high-order adaptive optics and coronagraphy. A key element of such systems is the high-order wavefront sensor. We study here several high-order wavefront sensing approaches, and more precisely compare their sensitivity to noise. Three techniques are considered: the classical Shack-Hartmann sensor, the pyramid sensor and the recently proposed LIFTed Shack-Hartmann sensor. They are compared in a unified framework based on precise diffractive models and on the Fisher information matrix, which conveys the information present in the data whatever the estimation method. The diagonal elements of the inverse of the Fisher information matrix, which we use as a figure of merit, are similar to noise propagation coefficients. With these diagonal elements, so called "Fisher coefficients", we show that the LIFTed Shack-Hartmann and pyramid sensors outperform the classical Shack-Hartmann sensor. In photon noise regime, the LIFTed Shack-Hartmann and modulated pyramid sensors obtain a similar overall noise propagation. The LIFTed Shack-Hartmann sensor however provides attractive noise properties on high orders.

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

NASA Astrophysics Data System (ADS)

Ma, Q.

2015-12-01

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS and IOS models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

Drude weight of the spin-(1)/(2) XXZ chain: Density matrix renormalization group versus exact diagonalization

NASA Astrophysics Data System (ADS)

Karrasch, C.; Hauschild, J.; Langer, S.; Heidrich-Meisner, F.

2013-06-01

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

Fidelity decay of the two-level bosonic embedded ensembles of random matrices

NASA Astrophysics Data System (ADS)

Benet, Luis; Hernández-Quiroz, Saúl; Seligman, Thomas H.

2010-12-01

We study the fidelity decay of the k-body embedded ensembles of random matrices for bosons distributed over two single-particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one-body term and includes the diagonal of the perturbing k-body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off-diagonal elements of the k-body interaction. This choice mimics the typical mean-field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble-averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = tH = 1, and a freeze in the fidelity decay, during which periodic revivals of period tH are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of tH. These fractional periodic revivals are related to the dominance of specific k-body terms in the perturbation.

Vaidya spacetime in the diagonal coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filinov, A.V.; Golubnychiy, V.O.; Bonitz, M.

Extending our previous work [A.V. Filinov et al., J. Phys. A 36, 5957 (2003)], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the 'exact' quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the 'exact' pair potential in the whole temperature range. The derivedmore » pseudopotentials are then used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.« less

Mass eigenstates in bimetric theory with matter coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se

2015-01-01

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a mattermore » source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.« less

NLTE steady-state response matrix method.

NASA Astrophysics Data System (ADS)

Faussurier, G.; More, R. M.

2000-05-01

A connection between atomic kinetics and non-equilibrium thermodynamics has been recently established by using a collisional-radiative model modified to include line absorption. The calculated net emission can be expressed as a non-local thermodynamic equilibrium (NLTE) symmetric response matrix. In the paper, this connection is extended to both cases of the average-atom model and the Busquet's model (RAdiative-Dependent IOnization Model, RADIOM). The main properties of the response matrix still remain valid. The RADIOM source function found in the literature leads to a diagonal response matrix, stressing the absence of any frequency redistribution among the frequency groups at this order of calculation.

Simple expression for the quantum Fisher information matrix

NASA Astrophysics Data System (ADS)

Šafránek, Dominik

2018-04-01

Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality, quantum phase transitions, coherence, entanglement, and irreversibility. We derive a surprisingly simple formula for this quantity, which, unlike previously known general expression, does not require diagonalization of the density matrix, and is provably at least as efficient. With a minor modification, this formula can be used to compute QFIM for any finite-dimensional density matrix. Because of its simplicity, it could also shed more light on the quantum information geometry in general.

A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory

NASA Astrophysics Data System (ADS)

Nagaoka, Hiroshi

We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization of X, Y when XY = YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.

Convergence to Diagonal Form of Block Jacobi-type Processes

NASA Astrophysics Data System (ADS)

Hari, Vjeran

2008-09-01

The main result of recent research on convergence to diagonal form of block Jacobi-type processes is presented. For this purpose, all notions needed to describe the result are introduced. In particular, elementary block transformation matrices, simple and non-simple algorithms, block pivot strategies together with the appropriate equivalence relations are defined. The general block Jacobi-type process considered here can be specialized to take the form of almost any known Jacobi-type method for solving the ordinary or the generalized matrix eigenvalue and singular value problems. The assumptions used in the result are satisfied by many concrete methods.

A methodology for formulating a minimal uncertainty model for robust control system design and analysis

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.; Chang, B.-C.; Fischl, Robert

1989-01-01

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Spinon excitation spectra of the J1-J2 chain from analytical calculations in the dimer basis and exact diagonalization

NASA Astrophysics Data System (ADS)

Lavarélo, Arthur; Roux, Guillaume

2014-10-01

The excitation spectrum of the frustrated spin-1/2 Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at J 2 = 0.25 J 1 and an onset of incommensurability in the dispersion relation at J 2 = 9/17 J 1 as in [S. Brehmer et al., J. Phys.: Condens. Matter 10, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.

Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.

1988-01-01

This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies.

Boundary Quantum Knizhnik-Zamolodchikov Equations and Bethe Vectors

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart

2015-06-01

Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of is involved. We also consider their rational and classical degenerations.

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

NASA Astrophysics Data System (ADS)

Anastopoulos, C.; Hu, B. L.

2018-02-01

We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.

Singular value decomposition utilizing parallel algorithms on graphical processors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotas, Charlotte W; Barhen, Jacob

2011-01-01

One of the current challenges in underwater acoustic array signal processing is the detection of quiet targets in the presence of noise. In order to enable robust detection, one of the key processing steps requires data and replica whitening. This, in turn, involves the eigen-decomposition of the sample spectral matrix, Cx = 1/K xKX(k)XH(k) where X(k) denotes a single frequency snapshot with an element for each element of the array. By employing the singular value decomposition (SVD) method, the eigenvectors and eigenvalues can be determined directly from the data without computing the sample covariance matrix, reducing the computational requirements formore » a given level of accuracy (van Trees, Optimum Array Processing). (Recall that the SVD of a complex matrix A involves determining V, , and U such that A = U VH where U and V are orthonormal and is a positive, real, diagonal matrix containing the singular values of A. U and V are the eigenvectors of AAH and AHA, respectively, while the singular values are the square roots of the eigenvalues of AAH.) Because it is desirable to be able to compute these quantities in real time, an efficient technique for computing the SVD is vital. In addition, emerging multicore processors like graphical processing units (GPUs) are bringing parallel processing capabilities to an ever increasing number of users. Since the computational tasks involved in array signal processing are well suited for parallelization, it is expected that these computations will be implemented using GPUs as soon as users have the necessary computational tools available to them. Thus, it is important to have an SVD algorithm that is suitable for these processors. This work explores the effectiveness of two different parallel SVD implementations on an NVIDIA Tesla C2050 GPU (14 multiprocessors, 32 cores per multiprocessor, 1.15 GHz clock - peed). The first algorithm is based on a two-step algorithm which bidiagonalizes the matrix using Householder transformations, and then diagonalizes the intermediate bidiagonal matrix through implicit QR shifts. This is similar to that implemented for real matrices by Lahabar and Narayanan ("Singular Value Decomposition on GPU using CUDA", IEEE International Parallel Distributed Processing Symposium 2009). The implementation is done in a hybrid manner, with the bidiagonalization stage done using the GPU while the diagonalization stage is done using the CPU, with the GPU used to update the U and V matrices. The second algorithm is based on a one-sided Jacobi scheme utilizing a sequence of pair-wise column orthogonalizations such that A is replaced by AV until the resulting matrix is sufficiently orthogonal (that is, equal to U ). V is obtained from the sequence of orthogonalizations, while can be found from the square root of the diagonal elements of AH A and, once is known, U can be found from column scaling the resulting matrix. These implementations utilize CUDA Fortran and NVIDIA's CUB LAS library. The primary goal of this study is to quantify the comparative performance of these two techniques against themselves and other standard implementations (for example, MATLAB). Considering that there is significant overhead associated with transferring data to the GPU and with synchronization between the GPU and the host CPU, it is also important to understand when it is worthwhile to use the GPU in terms of the matrix size and number of concurrent SVDs to be calculated.« less

Characterization of Fatigue Damage for Bonded Composite Skin/Stringer Configurations

NASA Technical Reports Server (NTRS)

Paris, Isabelle; Cvitkovich, Michael; Krueger, Ronald

2008-01-01

The fatigue damage was characterized in specimens which consisted of a tapered composite flange bonded onto a composite skin. Quasi-static tension tests were performed first to determine the failure load. Subsequently, tension fatigue tests were performed at 40%, 50%, 60% and 70% of the failure load to evaluate the debonding mechanisms. For four specimens, the cycling loading was stopped at intervals. Photographs of the polished specimen edges were taken under a light microscope to document the damage. At two diagonally opposite corners of the flange, a delamination appeared to initiate at the flange tip from a matrix crack in the top 45deg skin ply and propagated at the top 45deg/-45deg skin ply interface. At the other two diagonally opposite corners, a delamination running in the bondline initiated from a matrix crack in the adhesive pocket. In addition, two specimens were cut longitudinally into several sections. Micrographs revealed a more complex pattern inside the specimen where the two delamination patterns observed at the edges are present simultaneously across most of the width of the specimen. The observations suggest that a more sophisticated nondestructive evaluation technique is required to capture the complex damage pattern of matrix cracking and multi-level delaminations.

Reflectionless CMV Matrices and Scattering Theory

NASA Astrophysics Data System (ADS)

Chu, Sherry; Landon, Benjamin; Panangaden, Jane

2015-04-01

Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient, a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is reflectionless iff the scattering matrix is off-diagonal which in turn provides a short proof of an important result of Breuer et al. (Commun Math Phys 295:531-550, 2010). These developments parallel those recently obtained for Jacobi matrices Jakšić et al. (Commun Math Phys 827-838, 2014).

A multi-state fragment charge difference approach for diabatic states in electron transfer: Extension and automation

NASA Astrophysics Data System (ADS)

Yang, Chou-Hsun; Hsu, Chao-Ping

2013-10-01

The electron transfer (ET) rate prediction requires the electronic coupling values. The Generalized Mulliken-Hush (GMH) and Fragment Charge Difference (FCD) schemes have been useful approaches to calculate ET coupling from an excited state calculation. In their typical form, both methods use two eigenstates in forming the target charge-localized diabatic states. For problems involve three or four states, a direct generalization is possible, but it is necessary to pick and assign the locally excited or charge-transfer states involved. In this work, we generalize the 3-state scheme for a multi-state FCD without the need of manual pick or assignment for the states. In this scheme, the diabatic states are obtained separately in the charge-transfer or neutral excited subspaces, defined by their eigenvalues in the fragment charge-difference matrix. In each subspace, the Hamiltonians are diagonalized, and there exist off-diagonal Hamiltonian matrix elements between different subspaces, particularly the charge-transfer and neutral excited diabatic states. The ET coupling values are obtained as the corresponding off-diagonal Hamiltonian matrix elements. A similar multi-state GMH scheme can also be developed. We test the new multi-state schemes for the performance in systems that have been studied using more than two states with FCD or GMH. We found that the multi-state approach yields much better charge-localized states in these systems. We further test for the dependence on the number of state included in the calculation of ET couplings. The final coupling values are converged when the number of state included is increased. In one system where experimental value is available, the multi-state FCD coupling value agrees better with the previous experimental result. We found that the multi-state GMH and FCD are useful when the original two-state approach fails.

Understanding the determinants of volatility clustering in terms of stationary Markovian processes

NASA Astrophysics Data System (ADS)

Miccichè, S.

2016-11-01

Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ-β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock's volatility is a linear function of the average correlation of such stock's volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts. As a result, the diagonalized volatilities result to share with the original volatilities either the power-law decay of the probability density function and the power-law decay of the autocorrelation function. This would indicate that volatility clustering is already present in the diagonalized un-correlated volatilities. We therefore present a parsimonious univariate model based on a non-linear Langevin equation that well reproduces these two stylized facts of volatility. The model helps us in understanding that the main source of volatility clustering, once volatilities have been diagonalized, is that the economic forces driving volatility can be modeled in terms of a Smoluchowski potential with logarithmic tails.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

PubMed

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-15

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Communication: spin-boson model with diagonal and off-diagonal coupling to two independent baths: ground-state phase transition in the deep sub-Ohmic regime.

PubMed

Zhao, Yang; Yao, Yao; Chernyak, Vladimir; Zhao, Yang

2014-04-28

We investigate a spin-boson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep sub-Ohmic regime there exists a novel second-order phase transition between two types of doubly degenerate states, which is reduced to one of the usual types for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

NASA Astrophysics Data System (ADS)

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-01

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules.

PubMed

Mohallem, José R

2008-04-14

Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).

Condition number estimation of preconditioned matrices.

PubMed

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.

Effect of oscillator strength and intermediate resonance on the performance of resonant phonon-based terahertz quantum cascade lasers

NASA Astrophysics Data System (ADS)

Fathololoumi, S.; Dupont, E.; Wasilewski, Z. R.; Chan, C. W. I.; Razavipour, S. G.; Laframboise, S. R.; Huang, Shengxi; Hu, Q.; Ban, D.; Liu, H. C.

2013-03-01

We experimentally investigated the effect of oscillator strength (radiative transition diagonality) on the performance of resonant phonon-based terahertz quantum cascade lasers that have been optimized using a simplified density matrix formalism. Our results show that the maximum lasing temperature (Tmax) is roughly independent of laser transition diagonality within the lasing frequency range of the devices under test (3.2-3.7 THz) when cavity loss is kept low. Furthermore, the threshold current can be lowered by employing more diagonal transition designs, which can effectively suppress parasitic leakage caused by intermediate resonance between the injection and the downstream extraction levels. Nevertheless, the current carrying capacity through the designed lasing channel in more diagonal designs may sacrifice even more, leading to electrical instability and, potentially, complete inhibition of the device's lasing operation. We propose a hypothesis based on electric-field domain formation and competition/switching of different current-carrying channels to explain observed electrical instability in devices with lower oscillator strengths. The study indicates that not only should designers maximize Tmax during device optimization but also they should always consider the risk of electrical instability in device operation.

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2015-01-01

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS (Energy-Corrected Sudden) and IOS (Infinite-Order Sudden) models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

Diffusion of Conserved Charges in Relativistic Heavy Ion Collisions

NASA Astrophysics Data System (ADS)

Greif, Moritz; Fotakis, Jan. A.; Denicol, Gabriel S.; Greiner, Carsten

2018-06-01

We demonstrate that the diffusion currents do not depend only on gradients of their corresponding charge density, but that the different diffusion charge currents are coupled. This happens in such a way that it is possible for density gradients of a given charge to generate dissipative currents of another charge. Within this scheme, the charge diffusion coefficient is best viewed as a matrix, in which the diagonal terms correspond to the usual charge diffusion coefficients, while the off-diagonal terms describe the coupling between the different currents. In this Letter, we calculate for the first time the complete diffusion matrix for hot and dense nuclear matter, including baryon, electric, and strangeness charges. We find that the baryon diffusion current is strongly affected by baryon charge gradients but also by its coupling to gradients in strangeness. The electric charge diffusion current is found to be strongly affected by electric and strangeness gradients, whereas strangeness currents depend mostly on strange and baryon gradients.

An Unsteady Preconditioning Scheme Based on Convective-Upwind Split-Pressure (CUSP) Artificial Dissipation

DTIC Science & Technology

2014-01-07

this can have a disastrous effect on convergence rate. Even if steady state is obtained for low Mach number flows (after many iterations ), the results...rally lead do a diagonally dominant left-hand-side matrix, which causes stability problems for implicit Gauss - Seidel schemes. For this reason, matrix... convergence at the stagnation point. The iterations for each airfoil is also reported in Fig. 2. Without preconditioning, dramatic efficiency problems are seen

Measurement of spin correlation between top and antitop quarks produced in $$p\\bar{p}$$ collisions at $$\\sqrt{s} = 1.96$$ TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abazov, Victor Mukhamedovich

Here, we present a measurement of the correlation between the spins of t and tbar quarks produced in proton-antiproton collisions at the Tevatron Collider at a center-of-mass energy of 1.96 TeV. We apply a matrix element technique to dilepton and single-lepton+jets final states in data accumulated with the D0 detector that correspond to an integrated luminosity of 9.7 fbmore » $$^{-1}$$. The measured value of the correlation coefficient in the off-diagonal basis, $$O_{off} = 0.89 \\pm 0.22$$ (stat + syst), is in agreement with the standard model prediction, and represents evidence for a top-antitop quark spin correlation difference from zero at a level of 4.2 standard deviations.« less

Measurement of spin correlation between top and antitop quarks produced in $$p\\bar{p}$$ collisions at $$\\sqrt{s} = 1.96$$ TeV

DOE PAGES

Abazov, Victor Mukhamedovich

2016-03-25

Here, we present a measurement of the correlation between the spins of t and tbar quarks produced in proton-antiproton collisions at the Tevatron Collider at a center-of-mass energy of 1.96 TeV. We apply a matrix element technique to dilepton and single-lepton+jets final states in data accumulated with the D0 detector that correspond to an integrated luminosity of 9.7 fbmore » $$^{-1}$$. The measured value of the correlation coefficient in the off-diagonal basis, $$O_{off} = 0.89 \\pm 0.22$$ (stat + syst), is in agreement with the standard model prediction, and represents evidence for a top-antitop quark spin correlation difference from zero at a level of 4.2 standard deviations.« less

An experimental SMI adaptive antenna array simulator for weak interfering signals

NASA Technical Reports Server (NTRS)

Dilsavor, Ronald S.; Gupta, Inder J.

1991-01-01

An experimental sample matrix inversion (SMI) adaptive antenna array for suppressing weak interfering signals is described. The experimental adaptive array uses a modified SMI algorithm to increase the interference suppression. In the modified SMI algorithm, the sample covariance matrix is redefined to reduce the effect of thermal noise on the weights of an adaptive array. This is accomplished by subtracting a fraction of the smallest eigenvalue of the original covariance matrix from its diagonal entries. The test results obtained using the experimental system are compared with theoretical results. The two show a good agreement.

Harmonizing Automatic Test System Assets, Drivers, and Control Methodologies

DTIC Science & Technology

1999-07-18

ORGANIZATION PRINCIPAL AREAS OF INTEREST TO ATS NAME 1394 TA Firewire Trade Association Defining high speed bus protocol Active Group Accelerating ActiveX ...System Assets, Drivers, and Control Methodologies 17 JUL, 1999 component is a diagonal matrix containing scaling values such that when the three

Erratum to Dynamic stresses, Coulomb failure, and remote triggering and to Surface wave potential for triggering tectonic (nonvolcanic) tremor

USGS Publications Warehouse

Hill, David P.

2012-01-01

Hill (2008) and Hill (2010) contain two technical errors: (1) a missing factor of 2 for computed Love‐wave amplitudes, and (2) a sign error in the off‐diagonal elements in the Euler rotation matrix.

Creating a Test-Validated Finite-Element Model of the X-56A Aircraft Structure

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi; Truong, Samson

2014-01-01

Small modeling errors in a finite-element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of the X-56A Multi-Utility Technology Testbed aircraft is the flight demonstration of active flutter suppression and, therefore, in this study, the identification of the primary and secondary modes for the structural model tuning based on the flutter analysis of the X-56A aircraft. The ground-vibration test-validated structural dynamic finite-element model of the X-56A aircraft is created in this study. The structural dynamic finite-element model of the X-56A aircraft is improved using a model-tuning tool. In this study, two different weight configurations of the X-56A aircraft have been improved in a single optimization run. Frequency and the cross-orthogonality (mode shape) matrix were the primary focus for improvement, whereas other properties such as c.g. location, total weight, and off-diagonal terms of the mass orthogonality matrix were used as constraints. The end result was an improved structural dynamic finite-element model configuration for the X-56A aircraft. Improved frequencies and mode shapes in this study increased average flutter speeds of the X-56A aircraft by 7.6% compared to the baseline model.

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

NASA Astrophysics Data System (ADS)

Xing, Zhi-zhong; Zhou, Shun; Zhou, Ye-Ling

2018-05-01

We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter a≡ 2√{2}{G}F{N}_eE to be an arbitrary scale-like variable with N e being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses {\\tilde{m}}_i (for i = 1 , 2 , 3). Given the standard parametrization of V , the RGEs for {{\\tilde{θ}}_{12}, {\\tilde{θ}}_{13}, {\\tilde{θ}}_{23}, \\tilde{δ}} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ- τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.

Strategies for vectorizing the sparse matrix vector product on the CRAY XMP, CRAY 2, and CYBER 205

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry

1987-01-01

Large, randomly sparse matrix vector products are important in a number of applications in computational chemistry, such as matrix diagonalization and the solution of simultaneous equations. Vectorization of this process is considered for the CRAY XMP, CRAY 2, and CYBER 205, using a matrix of dimension of 20,000 with from 1 percent to 6 percent nonzeros. Efficient scatter/gather capabilities add coding flexibility and yield significant improvements in performance. For the CYBER 205, it is shown that minor changes in the IO can reduce the CPU time by a factor of 50. Similar changes in the CRAY codes make a far smaller improvement.

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

NASA Technical Reports Server (NTRS)

Macfarlane, J. J.

1992-01-01

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Extraction-controlled terahertz frequency quantum cascade lasers with a diagonal LO-phonon extraction and injection stage.

PubMed

Han, Y J; Li, L H; Grier, A; Chen, L; Valavanis, A; Zhu, J; Freeman, J R; Isac, N; Colombelli, R; Dean, P; Davies, A G; Linfield, E H

2016-12-12

We report an extraction-controlled terahertz (THz)-frequency quantum cascade laser design in which a diagonal LO-phonon scattering process is used to achieve efficient current injection into the upper laser level of each period and simultaneously extract electrons from the adjacent period. The effects of the diagonality of the radiative transition are investigated, and a design with a scaled oscillator strength of 0.45 is shown experimentally to provide the highest temperature performance. A 3.3 THz device processed into a double-metal waveguide configuration operated up to 123 K in pulsed mode, with a threshold current density of 1.3 kA/cm² at 10 K. The QCL structures are modeled using an extended density matrix approach, and the large threshold current is attributed to parasitic current paths associated with the upper laser levels. The simplicity of this design makes it an ideal platform to investigate the scattering injection process.

Polar and singular value decomposition of 3×3 magic squares

NASA Astrophysics Data System (ADS)

Trenkler, Götz; Schmidt, Karsten; Trenkler, Dietrich

2013-07-01

In this note, we find polar as well as singular value decompositions of a 3×3 magic square, i.e. a 3×3 matrix M with real elements where each row, column and diagonal adds up to the magic sum s of the magic square.

Separability and Entanglement in the Hilbert Space Reference Frames Related Through the Generic Unitary Transform for Four Level System

NASA Astrophysics Data System (ADS)

Man'ko, V. I.; Markovich, L. A.

2018-02-01

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, X-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.

Derivation of a formula for the resonance integral for a nonorthogonal basis set

PubMed Central

Yim, Yung-Chang; Eyring, Henry

1981-01-01

In a self-consistent field calculation, a formula for the off-diagonal matrix elements of the core Hamiltonian is derived for a nonorthogonal basis set by a polyatomic approach. A set of parameters is then introduced for the repulsion integral formula of Mataga-Nishimoto to fit the experimental data. The matrix elements computed for the nonorthogonal basis set in the π-electron approximation are transformed to those for an orthogonal basis set by the Löwdin symmetrical orthogonalization. PMID:16593009

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

NASA Astrophysics Data System (ADS)

Trif, Mircea; Dmytruk, Olesia; Bouchiat, Hélène; Aguado, Ramón; Simon, Pascal

2018-02-01

We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density-matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana state populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, explored, in this Rapid Communication, in the context of Majorana physics, allows probing accurately the presence of Majorana bound states in the junction.

Condition Number Estimation of Preconditioned Matrices

PubMed Central

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager’s method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei’s matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei’s matrix, and matrices generated with the finite element method. PMID:25816331

Optimum modulation and demodulation matrices for solar polarimetry.

PubMed

del Toro Iniesta, J C; Collados, M

2000-04-01

Both temporal and/or spatial modulation are mandatory in current solar polarimetry [Appl. Opt. 24, 3893 (1985); 26, 3838 (1987)]. The modulating and demodulating processes are mathematically described by matrices O and D, respectively, on whose structure the accuracy of Stokes parameter measurements depend. We demonstrate, based on the definition of polarimetric efficiency [Instituto de Astrofísica de Canarias Internal Report (1994); ASP Conf. Ser. 184, 3 (1999)], that the maximum efficiencies of an ideal polarimeter are unity for Stokes I and for (Q(2) + U(2) + V(2))(1/2) and that this occurs if and only if O(T)O is diagonal; given a general (possibly nonideal) modulation matrix O, the optimum demodulation matrix turns out to be D = (O(T)O)(-1)O(T); and the maximum efficiencies in the nonideal case are given by the rms value of the column elements of matrix O and are reached by modulation matrices such that O(T)O is diagonal. From these analytical results we distill two recipes useful in the practical design of polarimeters. Their usefulness is illustrated by discussing cases of currently available solar polarimeters. Although specifically devoted to solar polarimetry, the results here may be applied in practically all other branches of science for which polarimetric measurements are needed.

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.; Chang, B.-C.; Fischl, Robert

1991-01-01

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix

NASA Technical Reports Server (NTRS)

Llama, Eduardo Garcia

2011-01-01

In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.

Bayesian source term determination with unknown covariance of measurements

NASA Astrophysics Data System (ADS)

Belal, Alkomiet; Tichý, Ondřej; Šmídl, Václav

2017-04-01

Determination of a source term of release of a hazardous material into the atmosphere is a very important task for emergency response. We are concerned with the problem of estimation of the source term in the conventional linear inverse problem, y = Mx, where the relationship between the vector of observations y is described using the source-receptor-sensitivity (SRS) matrix M and the unknown source term x. Since the system is typically ill-conditioned, the problem is recast as an optimization problem minR,B(y - Mx)TR-1(y - Mx) + xTB-1x. The first term minimizes the error of the measurements with covariance matrix R, and the second term is a regularization of the source term. There are different types of regularization arising for different choices of matrices R and B, for example, Tikhonov regularization assumes covariance matrix B as the identity matrix multiplied by scalar parameter. In this contribution, we adopt a Bayesian approach to make inference on the unknown source term x as well as unknown R and B. We assume prior on x to be a Gaussian with zero mean and unknown diagonal covariance matrix B. The covariance matrix of the likelihood R is also unknown. We consider two potential choices of the structure of the matrix R. First is the diagonal matrix and the second is a locally correlated structure using information on topology of the measuring network. Since the inference of the model is intractable, iterative variational Bayes algorithm is used for simultaneous estimation of all model parameters. The practical usefulness of our contribution is demonstrated on an application of the resulting algorithm to real data from the European Tracer Experiment (ETEX). This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

Quench action and Rényi entropies in integrable systems

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Calabrese, Pasquale

2017-09-01

Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the nonequilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary thermodynamic entropy is the von Neumann entanglement entropy of a large subsystem embedded in an infinite system. Also motivated by cold-atom experiments, here we consider the generalization to Rényi entropies. We develop a new technique to calculate the diagonal Rényi entropy in the quench action formalism. In the spirit of the replica treatment for the entanglement entropy, the diagonal Rényi entropies are generalized free energies evaluated over a thermodynamic macrostate which depends on the Rényi index and, in particular, is not the same state describing von Neumann entropy. The technical reason for this perhaps surprising result is that the evaluation of the moments of the diagonal density matrix shifts the saddle point of the quench action. An interesting consequence is that different Rényi entropies encode information about different regions of the spectrum of the postquench Hamiltonian. Our approach provides a very simple proof of the long-standing issue that, for integrable systems, the diagonal entropy is half of the thermodynamic one and it allows us to generalize this result to the case of arbitrary Rényi entropy.

First Principle Predictions of Isotopic Shifts in H2O

NASA Technical Reports Server (NTRS)

Schwenke, David W.; Kwak, Dochan (Technical Monitor)

2002-01-01

We compute isotope independent first and second order corrections to the Born-Oppenheimer approximation for water and use them to predict isotopic shifts. For the diagonal correction, we use icMRCI wavefunctions and derivatives with respect to mass dependent, internal coordinates to generate the mass independent correction functions. For the non-adiabatic correction, we use scaled SCF/CIS wave functions and a generalization of the Handy method to obtain mass independent correction functions. We find that including the non-adiabatic correction gives significantly improved results compared to just including the diagonal correction when the Born-Oppenheimer potential energy surface is optimized for H2O-16. The agreement with experimental results for deuterium and tritium containing isotopes is nearly as good as our best empirical correction, however, the present correction is expected to be more reliable for higher, uncharacterized levels.

An attempt to determine the effect of increase of observation correlations on detectability and identifiability of a single gross error

NASA Astrophysics Data System (ADS)

Prószyński, Witold; Kwaśniak, Mieczysław

2016-12-01

The paper presents the results of investigating the effect of increase of observation correlations on detectability and identifiability of a single gross error, the outlier test sensitivity and also the response-based measures of internal reliability of networks. To reduce in a research a practically incomputable number of possible test options when considering all the non-diagonal elements of the correlation matrix as variables, its simplest representation was used being a matrix with all non-diagonal elements of equal values, termed uniform correlation. By raising the common correlation value incrementally, a sequence of matrix configurations could be obtained corresponding to the increasing level of observation correlations. For each of the measures characterizing the above mentioned features of network reliability the effect is presented in a diagram form as a function of the increasing level of observation correlations. The influence of observation correlations on sensitivity of the w-test for correlated observations (Förstner 1983, Teunissen 2006) is investigated in comparison with the original Baarda's w-test designated for uncorrelated observations, to determine the character of expected sensitivity degradation of the latter when used for correlated observations. The correlation effects obtained for different reliability measures exhibit mutual consistency in a satisfactory extent. As a by-product of the analyses, a simple formula valid for any arbitrary correlation matrix is proposed for transforming the Baarda's w-test statistics into the w-test statistics for correlated observations.

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Zubova, N. A.

2017-06-01

This paper presents the results of numerical simulation of the Soret-induced convection of ternary mixture in the rectangular cavity elongated in horizontal direction in gravity field. The cavity has rigid impermeable boundaries. It is heated from the bellow and undergoes translational linearly polarized vibrations of finite amplitude and frequency in the horizontal direction. The problem is solved by finite difference method in the framework of full unsteady non-linear approach. The procedure of diagonalization of the molecular diffusion coefficient matrix is applied, allowing to eliminate cross-diffusion components in the equations and to reduce the number of the governing parameters. The calculations are performed for model ternary mixture with positive separation ratios of the components. The data on the vibration effect on temporal evolution of instantaneous and average fields and integral characteristics of the flow and heat and mass transfer at different levels of gravity are obtained.

Magnon modes and magnon-vortex scattering in two-dimensional easy-plane ferromagnets

NASA Astrophysics Data System (ADS)

Ivanov, B. A.; Schnitzer, H. J.; Mertens, F. G.; Wysin, G. M.

1998-10-01

We calculate the magnon modes in the presence of a vortex on a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasilocal translational modes are identified with the frequencies which appear in the trajectory X-->(t) of the vortex center in recent molecular dynamics simulations of the full many-spin model. Using these quasilocal modes we calculate the two parameters of a third-order equation of motion for X-->(t). This equation was recently derived by a collective variable theory and describes very well the trajectories observed in the simulations. Both parameters, the vortex mass and the factor in front of X-->⃛, depend strongly on the boundary conditions.

Error due to unresolved scales in estimation problems for atmospheric data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana

The error arising due to unresolved scales in data assimilation procedures is examined. The problem of estimating the projection of the state of a passive scalar undergoing advection at a sequence of times is considered. The projection belongs to a finite- dimensional function space and is defined on the continuum. Using the continuum projection of the state of a passive scalar, a mathematical definition is obtained for the error arising due to the presence, in the continuum system, of scales unresolved by the discrete dynamical model. This error affects the estimation procedure through point observations that include the unresolved scales. In this work, two approximate methods for taking into account the error due to unresolved scales and the resulting correlations are developed and employed in the estimation procedure. The resulting formulas resemble the Schmidt-Kalman filter and the usual discrete Kalman filter, respectively. For this reason, the newly developed filters are called the Schmidt-Kalman filter and the traditional filter. In order to test the assimilation methods, a two- dimensional advection model with nonstationary spectrum was developed for passive scalar transport in the atmosphere. An analytical solution on the sphere was found depicting the model dynamics evolution. Using this analytical solution the model error is avoided, and the error due to unresolved scales is the only error left in the estimation problem. It is demonstrated that the traditional and the Schmidt- Kalman filter work well provided the exact covariance function of the unresolved scales is known. However, this requirement is not satisfied in practice, and the covariance function must be modeled. The Schmidt-Kalman filter cannot be computed in practice without further approximations. Therefore, the traditional filter is better suited for practical use. Also, the traditional filter does not require modeling of the full covariance function of the unresolved scales, but only modeling of the covariance matrix obtained by evaluating the covariance function at the observation points. We first assumed that this covariance matrix is stationary and that the unresolved scales are not correlated between the observation points, i.e., the matrix is diagonal, and that the values along the diagonal are constant. Tests with these assumptions were unsuccessful, indicating that a more sophisticated model of the covariance is needed for assimilation of data with nonstationary spectrum. A new method for modeling the covariance matrix based on an extended set of modeling assumptions is proposed. First, it is assumed that the covariance matrix is diagonal, that is, that the unresolved scales are not correlated between the observation points. It is postulated that the values on the diagonal depend on a wavenumber that is characteristic for the unresolved part of the spectrum. It is further postulated that this characteristic wavenumber can be diagnosed from the observations and from the estimate of the projection of the state that is being estimated. It is demonstrated that the new method successfully overcomes previously encountered difficulties.

Golden Matrix Families

ERIC Educational Resources Information Center

Fontaine, Anne; Hurley, Susan

2011-01-01

This student research project explores the properties of a family of matrices of zeros and ones that arises from the study of the diagonal lengths in a regular polygon. There is one family for each n greater than 2. A series of exercises guides the student to discover the eigenvalues and eigenvectors of the matrices, which leads in turn to…

Matrix-product-state method with local basis optimization for nonequilibrium electron-phonon systems

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Brockt, Christoph; Dorfner, Florian; Vidmar, Lev; Jeckelmann, Eric

We present a method for simulating the time evolution of quasi-one-dimensional correlated systems with strongly fluctuating bosonic degrees of freedom (e.g., phonons) using matrix product states. For this purpose we combine the time-evolving block decimation (TEBD) algorithm with a local basis optimization (LBO) approach. We discuss the performance of our approach in comparison to TEBD with a bare boson basis, exact diagonalization, and diagonalization in a limited functional space. TEBD with LBO can reduce the computational cost by orders of magnitude when boson fluctuations are large and thus it allows one to investigate problems that are out of reach of other approaches. First, we test our method on the non-equilibrium dynamics of a Holstein polaron and show that it allows us to study the regime of strong electron-phonon coupling. Second, the method is applied to the scattering of an electronic wave packet off a region with electron-phonon coupling. Our study reveals a rich physics including transient self-trapping and dissipation. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 1807.

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

Reflection K-matrices for a nineteen vertex model with Uq [ osp (2 | 2) (2) ] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima Santos, A.

2017-09-01

We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra Uq [ osp (2 | 2) (2) ]. We found three classes of solutions. The type I solution is characterized by three boundary free-parameters and all elements of the corresponding reflection K-matrix are different from zero. In the type II solution, the reflection K-matrix is even (every element of the K-matrix with an odd parity is null) and it has only one boundary free-parameter. Finally, the type III solution corresponds to a diagonal reflection K-matrix with two boundary free-parameters.

Effect of the magnetic field on the nonlinear optical rectification and second and third harmonic generation in double δ-doped GaAs quantum wells

NASA Astrophysics Data System (ADS)

Martínez-Orozco, J. C.; Rojas-Briseño, J. G.; Rodríguez-Magdaleno, K. A.; Rodríguez-Vargas, I.; Mora-Ramos, M. E.; Restrepo, R. L.; Ungan, F.; Kasapoglu, E.; Duque, C. A.

2017-11-01

In this paper we are reporting the computation for the Nonlinear Optical Rectification (NOR) and the Second and Third Harmonic Generation (SHG and THG) related with electronic states of asymmetric double Si-δ-doped quantum well in a GaAs matrix when this is subjected to an in-plane (x-oriented) constant magnetic field effect. The work is performed in the effective mass and parabolic band approximations in order to compute the electronic structure for the system by a diagonalization procedure. The expressions for the nonlinear optical susceptibilities, χ0(2), χ2ω(2), and χ3ω(3), are those arising from the compact matrix density formulation and stand for the NOR, SHG, and THG, respectively. This asymmetric double δ-doped quantum well potential profile actually exhibits nonzero NOR, SHG, and THG responses which can be easily controlled by the in-plane (x-direction) externally applied magnetic field. In particular we find that for the chosen configuration the harmonic generation is in the far-infrared/THz region, thus and becoming suitable building blocks for photodetectors in this range of the electromagnetic spectra.

Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-01-01

In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.

Baryon interactions from lattice QCD with physical masses — strangeness S = -1 sector —

NASA Astrophysics Data System (ADS)

Nemura, Hidekatsu; Aoki, Sinya; Doi, Takumi; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Sasaki, Kenji

2018-03-01

We present our recent results of baryon interactions with strangeness S = -1 based on Nambu-Bethe-Salpeter (NBS) correlation functions calculated fromlattice QCD with almost physical quark masses corresponding to (mk,mk) ≈ (146, 525) MeV and large volume (La)4 ≈ (96a)4 ≈ (8.1 fm)4. In order to perform a comprehensive study of baryon interactions, a large number of NBS correlation functions from NN to ΞΞ are calculated simultaneously by using large scale computer resources. In this contribution, we focus on the strangeness S = -1 channels of the hyperon interactions by means of HAL QCD method. Four sets of three potentials (the 3S1 - 3 D1 central, 3S1 - 3 D1 tensor, and the 1S0 central potentials) are presented for the ∑N - ∑N (the isospin I = 3/2) diagonal, the ∧N - ∧N diagonal, the ∧N → ∑N transition, and the ∑N - ∑N (I = 1/2) diagonal interactions. Scattering phase shifts for ∑N (I = 3/2) system are presented.

Tuning maps for setpoint changes and load disturbance upsets in a three capacity process under multivariable control

NASA Technical Reports Server (NTRS)

Litt, Jonathan S.; Smith, Ira C.

1991-01-01

Tuning maps are an aid in the controller tuning process because they provide a convenient way for the plant operator to determine the consequences of adjusting different controller parameters. In this application the maps provide a graphical representation of the effect of varying the gains in the state feedback matrix on startup and load disturbance transients for a three capacity process. Nominally, the three tank system, represented in diagonal form, has a Proportional-Integral control on each loop. Cross coupling is then introduced between the loops by using non-zero off-diagonal proportional parameters. Changes in transient behavior due to setpoint and load changes are examined by varying the gains of the cross coupling terms.

Atypicality of Most Few-Body Observables

NASA Astrophysics Data System (ADS)

Hamazaki, Ryusuke; Ueda, Masahito

2018-02-01

The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a major candidate to explain thermalization in isolated quantum systems. According to the typicality argument, the maximum variations of such matrix elements should decrease exponentially with increasing the size of the system, which implies the ETH. We show, however, that the typicality argument does not apply to most few-body observables for few-body Hamiltonians when the width of the energy shell decreases at most polynomially with increasing the size of the system.

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations

NASA Astrophysics Data System (ADS)

Awata, Hidetoshi; Kanno, Hiroaki; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor

2016-10-01

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the Yangian case by A. Smirnov but less general. We investigate the interplay between the R-matrix structure and the structure of DIM algebra intertwiners, i.e. of refined topological vertices and show that the R-matrix is diagonalized by the action of the spectral duality belonging to the SL(2, ℤ) group of DIM algebra automorphisms. We also construct the T-operators satisfying the RTT relations with the R-matrix from refined amplitudes on resolved conifold. We thus show that topological string theories on the toric Calabi-Yau threefolds can be naturally interpreted as lattice integrable models. Integrals of motion for these systems are related to q-deformation of the reflection matrices of the Liouville/Toda theories.

Error Analysis of Deep Sequencing of Phage Libraries: Peptides Censored in Sequencing

PubMed Central

Matochko, Wadim L.; Derda, Ratmir

2013-01-01

Next-generation sequencing techniques empower selection of ligands from phage-display libraries because they can detect low abundant clones and quantify changes in the copy numbers of clones without excessive selection rounds. Identification of errors in deep sequencing data is the most critical step in this process because these techniques have error rates >1%. Mechanisms that yield errors in Illumina and other techniques have been proposed, but no reports to date describe error analysis in phage libraries. Our paper focuses on error analysis of 7-mer peptide libraries sequenced by Illumina method. Low theoretical complexity of this phage library, as compared to complexity of long genetic reads and genomes, allowed us to describe this library using convenient linear vector and operator framework. We describe a phage library as N × 1 frequency vector n = ||ni||, where ni is the copy number of the ith sequence and N is the theoretical diversity, that is, the total number of all possible sequences. Any manipulation to the library is an operator acting on n. Selection, amplification, or sequencing could be described as a product of a N × N matrix and a stochastic sampling operator (S a). The latter is a random diagonal matrix that describes sampling of a library. In this paper, we focus on the properties of S a and use them to define the sequencing operator (S e q). Sequencing without any bias and errors is S e q = S a IN, where IN is a N × N unity matrix. Any bias in sequencing changes IN to a nonunity matrix. We identified a diagonal censorship matrix (C E N), which describes elimination or statistically significant downsampling, of specific reads during the sequencing process. PMID:24416071

Slowest kinetic modes revealed by metabasin renormalization

NASA Astrophysics Data System (ADS)

Okushima, Teruaki; Niiyama, Tomoaki; Ikeda, Kensuke S.; Shimizu, Yasushi

2018-02-01

Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009), 10.1103/PhysRevE.80.036112] and a Jacobi method. We test the method on an illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al., Chem. Phys. Lett. 654, 52 (2016), 10.1016/j.cplett.2016.04.088], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

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.

Methods for Scaling to Doubly Stochastic Form,

DTIC Science & Technology

1981-06-26

Frobenius -Konig Theorem (MARCUS and MINC [1964],p 97) A nonnegative n xn matrix without support contains an s x t zero subma- trix where: s +t =n + -3...that YA(k) has row sums 1. Then normalize the columns by a diagonal similarity transform defined as follows: Let x = (zx , • z,,) be a left Perron vector

Using Least Squares for Error Propagation

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2015-01-01

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

Size Reduction of Hamiltonian Matrix for Large-Scale Energy Band Calculations Using Plane Wave Bases

NASA Astrophysics Data System (ADS)

Morifuji, Masato

2018-01-01

We present a method of reducing the size of a Hamiltonian matrix used in calculations of electronic states. In the electronic states calculations using plane wave basis functions, a large number of plane waves are often required to obtain precise results. Even using state-of-the-art techniques, the Hamiltonian matrix often becomes very large. The large computational time and memory necessary for diagonalization limit the widespread use of band calculations. We show a procedure of deriving a reduced Hamiltonian constructed using a small number of low-energy bases by renormalizing high-energy bases. We demonstrate numerically that the significant speedup of eigenstates evaluation is achieved without losing accuracy.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

DOE PAGES

Miller, William H.; Cotton, Stephen J.

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

PubMed

Miller, William H; Cotton, Stephen J

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Equivalent off-diagonal cosmological models and ekpyrotic scenarios in -modified, massive, and einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2015-04-01

We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and -modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlevé-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed.

SLHAplus: A library for implementing extensions of the standard model

NASA Astrophysics Data System (ADS)

Bélanger, G.; Christensen, Neil D.; Pukhov, A.; Semenov, A.

2011-03-01

We provide a library to facilitate the implementation of new models in codes such as matrix element and event generators or codes for computing dark matter observables. The library contains an SLHA reader routine as well as diagonalisation routines. This library is available in CalcHEP and micrOMEGAs. The implementation of models based on this library is supported by LanHEP and FeynRules. Program summaryProgram title: SLHAplus_1.3 Catalogue identifier: AEHX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6283 No. of bytes in distributed program, including test data, etc.: 52 119 Distribution format: tar.gz Programming language: C Computer: IBM PC, MAC Operating system: UNIX (Linux, Darwin, Cygwin) RAM: 2000 MB Classification: 11.1 Nature of problem: Implementation of extensions of the standard model in matrix element and event generators and codes for dark matter observables. Solution method: For generic extensions of the standard model we provide routines for reading files that adopt the standard format of the SUSY Les Houches Accord (SLHA) file. The procedure has been generalized to take into account an arbitrary number of blocks so that the reader can be used in generic models including non-supersymmetric ones. The library also contains routines to diagonalize real and complex mass matrices with either unitary or bi-unitary transformations as well as routines for evaluating the running strong coupling constant, running quark masses and effective quark masses. Running time: 0.001 sec

Knowledge of damage identification about tensegrities via flexibility disassembly

NASA Astrophysics Data System (ADS)

Jiang, Ge; Feng, Xiaodong; Du, Shigui

2017-12-01

Tensegrity structures composing of continuous cables and discrete struts are under tension and compression, respectively. In order to determine the damage extents of tensegrity structures, a new method for tensegrity structural damage identification is presented based on flexibility disassembly. To decompose a tensegrity structural flexibility matrix into the matrix represention of the connectivity between degress-of-freedoms and the diagonal matrix comprising of magnitude informations. Step 1: Calculate perturbation flexibility; Step 2: Compute the flexibility connectivity matrix and perturbation flexibility parameters; Step 3: Calculate the perturbation stiffness parameters. The efficiency of the proposed method is demonstrated by a numeical example comprising of 12 cables and 4 struts with pretensioned. Accurate identification of local damage depends on the availability of good measured data, an accurate and reasonable algorithm.

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

NASA Astrophysics Data System (ADS)

Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei; Kawashima, Naoki; Sota, Shigetoshi; Tohyama, Takami; Imada, Masatoshi

2017-08-01

We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), 10.1103/PhysRevLett.113.107201], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

Stochastic determination of matrix determinants

NASA Astrophysics Data System (ADS)

Dorn, Sebastian; Enßlin, Torsten A.

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations—matrices—acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Stochastic determination of matrix determinants.

PubMed

Dorn, Sebastian; Ensslin, Torsten A

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations-matrices-acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Isovector and flavor-diagonal charges of the nucleon

NASA Astrophysics Data System (ADS)

Gupta, Rajan; Bhattacharya, Tanmoy; Jang, Yong-Chull; Lin, Huey-Wen; Yoon, Boram

2018-03-01

We present an update on the status of the calculations of isovector and flavor-diagonal charges of the nucleon. The calculations of the isovector charges are being done using ten 2+1+1-flavor HISQ ensembles generated by the MILC collaboration covering the range of lattice spacings a ≈ 0.12, 0.09, 0.06 fm and pion masses Mπ ≈ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and three-states fits to the three-point correlators. The calculations of the disconnected diagrams needed to estimate flavor-diagonal charges are being done on a subset of six ensembles using the stocastic method. Final results are obtained using a simultaneous fit in M2π, the lattice spacing a and the finite volume parameter MπL keeping only the leading order corrections.

Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition

NASA Astrophysics Data System (ADS)

Kumar, Ravi; Bhaduri, Basanta; Nishchal, Naveen K.

2018-01-01

In this study, we propose a quick response (QR) code based nonlinear optical image encryption technique using spiral phase transform (SPT), equal modulus decomposition (EMD) and singular value decomposition (SVD). First, the primary image is converted into a QR code and then multiplied with a spiral phase mask (SPM). Next, the product is spiral phase transformed with particular spiral phase function, and further, the EMD is performed on the output of SPT, which results into two complex images, Z 1 and Z 2. Among these, Z 1 is further Fresnel propagated with distance d, and Z 2 is reserved as a decryption key. Afterwards, SVD is performed on Fresnel propagated output to get three decomposed matrices i.e. one diagonal matrix and two unitary matrices. The two unitary matrices are modulated with two different SPMs and then, the inverse SVD is performed using the diagonal matrix and modulated unitary matrices to get the final encrypted image. Numerical simulation results confirm the validity and effectiveness of the proposed technique. The proposed technique is robust against noise attack, specific attack, and brutal force attack. Simulation results are presented in support of the proposed idea.

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach.

PubMed

Oña, Ofelia B; De Clercq, Olivier; Alcoba, Diego R; Torre, Alicia; Lain, Luis; Van Neck, Dimitri; Bultinck, Patrick

2016-09-19

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thingna, Juzar; Wang, Jian-Sheng; Haenggi, Peter

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correctmore » coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus, allowing to study efficiently large-sized system Hilbert spaces.« less

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of themore » action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, William H.; Cotton, Stephen J.

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

Low-power SXGA active matrix OLED

NASA Astrophysics Data System (ADS)

Wacyk, Ihor; Prache, Olivier; Ghosh, Amal

2009-05-01

This paper presents the design and first evaluation of a full-color 1280×3×1024 pixel, active matrix organic light emitting diode (AMOLED) microdisplay that operates at a low power of 200mW under typical operating conditions of 35fL, and offers a precision 30-bit RGB digital interface in a compact size (0.78-inch diagonal active area). The new system architecture developed by eMagin for the SXGA microdisplay, based on a separate FPGA driver and AMOLED display chip, offers several benefits, including better power efficiency, cost-effectiveness, more features for improved performance, and increased system flexibility.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Decentralized state estimation for a large-scale spatially interconnected system.

PubMed

Liu, Huabo; Yu, Haisheng

2018-03-01

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

PubMed

Cao, Cheng; Akalin Acar, Zeynep; Kreutz-Delgado, Kenneth; Makeig, Scott

2012-01-01

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Propagation of Circularly Polarized Light Through a Two-Dimensional Random Medium

NASA Astrophysics Data System (ADS)

Gorodnichev, E. E.

2017-12-01

The problem of small-angle multiple-scattering of circularly polarized light in a two-dimensional medium with large fiberlike inhomogeneities is studied. The attenuation lengths for elements the density matrix are calculated. It is found that with increasing the sample thickness the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the thickness, the off-diagonal element which is responsible for correlation between the cross-polarized waves dissapears. In the case of very thick samples the scattered field proves to be polarized perpendicular to the fibers. It is shown that the difference in the attenuation lengths of the density matrix elements results in a non-monotonic depth dependence of the degree of polarization.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

NASA Astrophysics Data System (ADS)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.

3DFEMWATER: A three-dimensional finite element model of water flow through saturated-unsaturated media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yeh, G.T.

1987-08-01

The 3DFEMWATER model is designed to treat heterogeneous and anisotropic media consisting of as many geologic formations as desired, consider both distributed and point sources/sinks that are spatially and temporally dependent, accept the prescribed initial conditions or obtain them by simulating a steady state version of the system under consideration, deal with a transient head distributed over the Dirichlet boundary, handle time-dependent fluxes due to pressure gradient varying along the Neumann boundary, treat time-dependent total fluxes distributed over the Cauchy boundary, automatically determine variable boundary conditions of evaporation, infiltration, or seepage on the soil-air interface, include the off-diagonal hydraulic conductivitymore » components in the modified Richards equation for dealing with cases when the coordinate system does not coincide with the principal directions of the hydraulic conductivity tensor, give three options for estimating the nonlinear matrix, include two options (successive subregion block iterations and successive point interactions) for solving the linearized matrix equations, automatically reset time step size when boundary conditions or source/sinks change abruptly, and check the mass balance computation over the entire region for every time step. The model is verified with analytical solutions or other numerical models for three examples.« less

A Hybrid Program for Fitting Rotationally Resolved Spectra of Floppy Molecules with One Large-Amplitude Rotatory Motion and One Large-Amplitude Oscillatory Motion

PubMed Central

Kleiner, Isabelle; Hougen, Jon T.

2015-01-01

A new hybrid-model fitting program for methylamine-like molecules has been developed, based on an effective Hamiltonian in which the ammonia-like inversion motion is treated using a tunneling formalism, while the internal-rotation motion is treated using an explicit kinetic energy operator and potential energy function. The Hamiltonian in the computer program is set up as a 2×2 partitioned matrix, where each diagonal block contains a traditional torsion-rotation Hamiltonian (as in the earlier program BELGI), and the two off-diagonal blocks contain tunneling terms. This hybrid formulation permits the use of the permutation-inversion group G6 (isomorphic to C3v) for terms in the two diagonal blocks, but requires G12 for terms in the off-diagonal blocks. The first application of the new program is to 2-methylmalonaldehyde. Microwave data for this molecule were previously fit using an all-tunneling Hamiltonian formalism to treat both large-amplitude-motions. For 2-methylmalonaldehyde, the hybrid program achieves the same quality of fit as was obtained with the all-tunneling program, but fits with the hybrid program eliminate a large discrepancy between internal rotation barriers in the OH and OD isotopologs of 2-methylmalonaldehyde that arose in fits with the all-tunneling program. This large isotopic shift in internal rotation barrier is thus almost certainly an artifact of the all-tunneling model. Other molecules for application of the hybrid program are mentioned. PMID:26439709

Joint spatial-spectral hyperspectral image clustering using block-diagonal amplified affinity matrix

NASA Astrophysics Data System (ADS)

Fan, Lei; Messinger, David W.

2018-03-01

The large number of spectral channels in a hyperspectral image (HSI) produces a fine spectral resolution to differentiate between materials in a scene. However, difficult classes that have similar spectral signatures are often confused while merely exploiting information in the spectral domain. Therefore, in addition to spectral characteristics, the spatial relationships inherent in HSIs should also be considered for incorporation into classifiers. The growing availability of high spectral and spatial resolution of remote sensors provides rich information for image clustering. Besides the discriminating power in the rich spectrum, contextual information can be extracted from the spatial domain, such as the size and the shape of the structure to which one pixel belongs. In recent years, spectral clustering has gained popularity compared to other clustering methods due to the difficulty of accurate statistical modeling of data in high dimensional space. The joint spatial-spectral information could be effectively incorporated into the proximity graph for spectral clustering approach, which provides a better data representation by discovering the inherent lower dimensionality from the input space. We embedded both spectral and spatial information into our proposed local density adaptive affinity matrix, which is able to handle multiscale data by automatically selecting the scale of analysis for every pixel according to its neighborhood of the correlated pixels. Furthermore, we explored the "conductivity method," which aims at amplifying the block diagonal structure of the affinity matrix to further improve the performance of spectral clustering on HSI datasets.

A minimum drives automatic target definition procedure for multi-axis random control testing

NASA Astrophysics Data System (ADS)

Musella, Umberto; D'Elia, Giacomo; Carrella, Alex; Peeters, Bart; Mucchi, Emiliano; Marulo, Francesco; Guillaume, Patrick

2018-07-01

Multiple-Input Multiple-Output (MIMO) vibration control tests are able to closely replicate, via shakers excitation, the vibration environment that a structure needs to withstand during its operational life. This feature is fundamental to accurately verify the experienced stress state, and ultimately the fatigue life, of the tested structure. In case of MIMO random tests, the control target is a full reference Spectral Density Matrix in the frequency band of interest. The diagonal terms are the Power Spectral Densities (PSDs), representative for the acceleration operational levels, and the off-diagonal terms are the Cross Spectral Densities (CSDs). The specifications of random vibration tests are however often given in terms of PSDs only, coming from a legacy of single axis testing. Information about the CSDs is often missing. An accurate definition of the CSD profiles can further enhance the MIMO random testing practice, as these terms influence both the responses and the shaker's voltages (the so-called drives). The challenges are linked to the algebraic constraint that the full reference matrix must be positive semi-definite in the entire bandwidth, with no flexibility in modifying the given PSDs. This paper proposes a newly developed method that automatically provides the full reference matrix without modifying the PSDs, considered as test specifications. The innovative feature is the capability of minimizing the drives required to match the reference PSDs and, at the same time, to directly guarantee that the obtained full matrix is positive semi-definite. The drives minimization aims on one hand to reach the fixed test specifications without stressing the delicate excitation system; on the other hand it potentially allows to further increase the test levels. The detailed analytic derivation and implementation steps of the proposed method are followed by real-life testing considering different scenarios.

Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation

NASA Astrophysics Data System (ADS)

Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.

2017-04-01

In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No

Inelastic Transitions in Slow Collisions of Anti-Hydrogen with Hydrogen Atoms

NASA Astrophysics Data System (ADS)

Harrison, Robert; Krstic, Predrag

2007-06-01

We calculate excited adiabatic states and nonadiabatic coupling matrix elements of a quasimolecular system containing hydrogen and anti-hydrogen atoms, for a range of internuclear distances from 0.2 to 20 Bohrs. High accuracy is achieved by exact diagonalization of the molecular Hamiltionian in a large Gaussian basis. Nonadiabatic dynamics was calculated by solving MOCC equations. Positronium states are included in the consideration.

The crypto-Hermitian smeared-coordinate representation of wave functions

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2011-08-01

In discrete-coordinate quantum models the kinematical observable of position need not necessarily be chosen local (i.e., diagonal). Its smearing is selected in the nearest-neighbor form of a real asymmetric (i.e., crypto-Hermitian) tridiagonal matrix Qˆ. Via Gauss-Hermite illustrative example we show how such an option restricts the class of admissible dynamical observables (sampled here just by the Hamiltonian).

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

A Note on Parameters of Random Substitutions by γ-Diagonal Matrices

NASA Astrophysics Data System (ADS)

Kang, Ju-Sung

Random substitutions are very useful and practical method for privacy-preserving schemes. In this paper we obtain the exact relationship between the estimation errors and three parameters used in the random substitutions, namely the privacy assurance metric γ, the total number n of data records, and the size N of transition matrix. We also demonstrate some simulations concerning the theoretical result.

On the Assessment of Psychometric Adequacy in Correlation Matrices.

ERIC Educational Resources Information Center

Dziuban, Charles D.; Shirkey, Edwin C.

Three techniques for assessing the adequacy of correlation matrices for factor analysis were applied to four examples from the literature. The methods compared were: (1) inspection of the off diagonal elements of the anti-image covariance matrix S(to the 2nd) R(to the -1) and S(to the 2nd); (2) the Measure of Sampling Adequacy (M.S.A.), and (3)…

A comparison of Fick and Maxwell-Stefan diffusion formulations in PEMFC gas diffusion layers

NASA Astrophysics Data System (ADS)

Lindstrom, Michael; Wetton, Brian

2017-01-01

This paper explores the mathematical formulations of Fick and Maxwell-Stefan diffusion in the context of polymer electrolyte membrane fuel cell cathode gas diffusion layers. The simple Fick law with a diagonal diffusion matrix is an approximation of Maxwell-Stefan. Formulations of diffusion combined with mass-averaged Darcy flow are considered for three component gases. For this application, the formulations can be compared computationally in a simple, one dimensional setting. Despite the models' seemingly different structure, it is observed that the predictions of the formulations are very similar on the cathode when air is used as oxidant. The two formulations give quite different results when the Nitrogen in the air oxidant is replaced by helium (this is often done as a diagnostic for fuel cells designs). The two formulations also give quite different results for the anode with a dilute Hydrogen stream. These results give direction to when Maxwell-Stefan diffusion, which is more complicated to implement computationally in many codes, should be used in fuel cell simulations.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn; Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn; Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate newmore » cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required. - Highlights: • Higher-order cubature points for degrees 7 to 9 are developed. • The effects of quadrature rule on the mass and stiffness matrices has been conducted. • The cubature points have always positive integration weights. • Freeing from the inversion of a wide bandwidth mass matrix. • The accuracy of the TSEM has been improved in about one order of magnitude.« less

Thermal conductivity of an imperfect anharmonic crystal

NASA Astrophysics Data System (ADS)

Sahu, D. N.; Sharma, P. K.

1983-09-01

The thermal conductivity of an anharmonic crystal containing randomly distributed substitutional defects due to impurity-phonon scattering is theoretically investigated with the use of the method of double-time thermal Green's functions and the Kubo formalism considering all the terms, i.e., diagonal, nondiagonal, cubic anharmonic, and imperfection terms in the energy-flux operator as propounded by Hardy. The study uses cubic, quartic anharmonic, and defect terms in the Hamiltonian. Mass changes as well as force-constant changes between impurity and host-lattice atoms are taken into account explicitly. It is shown that the total conductivity can be written as a sum of contributions, namely diagonal, nondiagonal, anharmonic, and imperfection contributions. For phonons of small halfwidth, the diagonal contribution has precisely the same form which is obtained from Boltzmann's transport equation for impurity scattering in the relaxation-time approximation. The present study shows that there is a finite contribution of the nondiagonal term, cubic anharmonic term, and the term due to lattice imperfections in the energy-flux operator to the thermal conductivity although the contribution is small compared with that from the diagonal part. We have also discussed the feasibility of numerical evaluation of the various contributions to the thermal conductivity.

Matrix Formalism of Synchrobetatron Coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Xiaobiao; /SLAC

In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and themore » Courant-Snyder functions. The closed orbit changes due to finite energy gains at rf cavities and radiation energy losses were also studied by the 5 x 5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.« less

Research and simulation of the decoupling transformation in AC motor vector control

NASA Astrophysics Data System (ADS)

He, Jiaojiao; Zhao, Zhongjie; Liu, Ken; Zhang, Yongping; Yao, Tuozhong

2018-04-01

Permanent magnet synchronous motor (PMSM) is a nonlinear, strong coupling, multivariable complex object, and transformation decoupling can solve the coupling problem of permanent magnet synchronous motor. This paper gives a permanent magnet synchronous motor (PMSM) mathematical model, introduces the permanent magnet synchronous motor vector control coordinate transformation in the process of modal matrix inductance matrix transform through the matrix related knowledge of different coordinates of diagonalization, which makes the coupling between the independent, realize the control of motor current and excitation the torque current coupling separation, and derived the coordinate transformation matrix, the thought to solve the coupling problem of AC motor. Finally, in the Matlab/Simulink environment, through the establishment and combination between the PMSM ontology, coordinate conversion module, built the simulation model of permanent magnet synchronous motor vector control, introduces the model of each part, and analyzed the simulation results.

Compound matrices

NASA Astrophysics Data System (ADS)

Kravvaritis, Christos; Mitrouli, Marilena

2009-02-01

This paper studies the possibility to calculate efficiently compounds of real matrices which have a special form or structure. The usefulness of such an effort lies in the fact that the computation of compound matrices, which is generally noneffective due to its high complexity, is encountered in several applications. A new approach for computing the Singular Value Decompositions (SVD's) of the compounds of a matrix is proposed by establishing the equality (up to a permutation) between the compounds of the SVD of a matrix and the SVD's of the compounds of the matrix. The superiority of the new idea over the standard method is demonstrated. Similar approaches with some limitations can be adopted for other matrix factorizations, too. Furthermore, formulas for the n - 1 compounds of Hadamard matrices are derived, which dodge the strenuous computations of the respective numerous large determinants. Finally, a combinatorial counting technique for finding the compounds of diagonal matrices is illustrated.

Stability and stabilisation of a class of networked dynamic systems

NASA Astrophysics Data System (ADS)

Liu, H. B.; Wang, D. Q.

2018-04-01

We investigate the stability and stabilisation of a linear time invariant networked heterogeneous system with arbitrarily connected subsystems. A new linear matrix inequality based sufficient and necessary condition for the stability is derived, based on which the stabilisation is provided. The obtained conditions efficiently utilise the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, a sufficient condition only dependent on each individual subsystem is also presented for the stabilisation of the networked systems with a large scale. Numerical simulations show that these conditions are computationally valid in the analysis and synthesis of a large-scale networked system.

Morphology-Dependent Resonances of Spherical Droplets with Numerous Microscopic Inclusions

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2014-01-01

We use the recently extended superposition T-matrix method to study the behavior of a sharp Lorenz-Mie resonance upon filling a spherical micrometer-sized droplet with tens and hundreds of randomly positioned microscopic inclusions. We show that as the number of inclusions increases, the extinction cross-section peak and the sharp asymmetry-parameter minimum become suppressed, widen, and move toward smaller droplet size parameters, while ratios of diagonal elements of the scattering matrix exhibit sharp angular features indicative of a distinctly nonspherical particle. Our results highlight the limitedness of the concept of an effective refractive index of an inhomogeneous spherical particle.

Entanglement classification with matrix product states

NASA Astrophysics Data System (ADS)

Sanz, M.; Egusquiza, I. L.; di Candia, R.; Saberi, H.; Lamata, L.; Solano, E.

2016-07-01

We propose an entanglement classification for symmetric quantum states based on their diagonal matrix-product-state (MPS) representation. The proposed classification, which preserves the stochastic local operation assisted with classical communication (SLOCC) criterion, relates entanglement families to the interaction length of Hamiltonians. In this manner, we establish a connection between entanglement classification and condensed matter models from a quantum information perspective. Moreover, we introduce a scalable nesting property for the proposed entanglement classification, in which the families for N parties carry over to the N + 1 case. Finally, using techniques from algebraic geometry, we prove that the minimal nontrivial interaction length n for any symmetric state is bounded by .

An invariant asymptotic formula for solutions of second-order linear ODE's

NASA Technical Reports Server (NTRS)

Gingold, H.

1988-01-01

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

UDU/T/ covariance factorization for Kalman filtering

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1980-01-01

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratap, Surender; Sarkar, Niladri, E-mail: niladri@pilani.bits-pilani.ac.in

Self-Consistent Quantum Method using Schrodinger-Poisson equations have been used for determining the Channel electron density of Nano-Scale MOSFETs for 6nm and 9nm thick channels. The 6nm thick MOSFET show the peak of the electron density at the middle where as the 9nm thick MOSFET shows the accumulation of the electrons at the oxide/semiconductor interface. The electron density in the channel is obtained from the diagonal elements of the density matrix; [ρ]=[1/(1+exp(β(H − μ)))] A Tridiagonal Hamiltonian Matrix [H] is constructed for the oxide/channel/oxide 1D structure for the dual gate MOSFET. This structure is discretized and Finite-Difference method is used formore » constructing the matrix equation. The comparison of these results which are obtained by Quantum methods are done with Semi-Classical methods.« less

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken-Hush and block diagonalization methods

NASA Astrophysics Data System (ADS)

Cave, Robert J.; Newton, Marshall D.

1997-06-01

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken-Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene-Cl atom complex and its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn2OH2+. Both methods also yield a natural definition of the effective distance (rDA) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of rDA, generally based on molecular structure data.

Some Correlation Functions in Matrix Product Ground States of One-Dimensional Two-State Chains

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad

2014-04-01

Consider one-dimensional chains with nearest neighbour interactions, for which to each site correspond two independent states (say up and down), and the ground state is a matrix product state. It has been shown [23] that for such systems, the ground states are linear combinations of specific vectors which are essentially direct products of specific numbers of ups and downs, symmetrized in a generalized manner. By a generalized manner, it is meant that the coefficient corresponding to the interchange of states of two sites, in not necessarily plus one or minus one, but a phase which depends on the Hamiltonian and the position of the two sites. Such vectors are characterized by a phase χ, the N-th power of which is one (where N is the number of sites), and an integer. Corresponding to χ, there is another integer M which is the smallest positive integer that χM is one. Two classes of correlation functions for such systems (basically correlation functions for such vectors) are calculated. The first class consists of correlation functions of tensor products of one-site diagonal observables; the second class consists of correlation functions of tensor products of less than M one-site observables (but not necessarily diagonal).

Application of wavelet based MFDFA on Mueller matrix images for cervical pre-cancer detection

NASA Astrophysics Data System (ADS)

Zaffar, Mohammad; Pradhan, Asima

2018-02-01

A systematic study has been conducted on application of wavelet based multifractal de-trended fluctuation analysis (MFDFA) on Mueller matrix (MM) images of cervical tissue sections for early cancer detection. Changes in multiple scattering and orientation of fibers are observed by utilizing a discrete wavelet transform (Daubechies) which identifies fluctuations over polynomial trends. Fluctuation profiles, after 9th level decomposition, for all elements of MM qualitatively establish a demarcation of different grades of cancer from normal tissue. Moreover, applying MFDFA on MM images, Hurst exponent profiles for images of MM qualitatively are seen to display differences. In addition, the values of Hurst exponent increase for the diagonal elements of MM with increasing grades of the cervical cancer, while the value for the elements which correspond to linear polarizance decrease. However, for circular polarizance the value increases with increasing grades. These fluctuation profiles reveal the trend of local variation of refractive -indices and along with Hurst exponent profile, may serve as a useful biological metric in the early detection of cervical cancer. The quantitative measurements of Hurst exponent for diagonal and first column (polarizance governing elements) elements which reflect changes in multiple scattering and structural anisotropy in stroma, may be sensitive indicators of pre-cancer.

Statistical image reconstruction from correlated data with applications to PET

PubMed Central

Alessio, Adam; Sauer, Ken; Kinahan, Paul

2008-01-01

Most statistical reconstruction methods for emission tomography are designed for data modeled as conditionally independent Poisson variates. In reality, due to scanner detectors, electronics and data processing, correlations are introduced into the data resulting in dependent variates. In general, these correlations are ignored because they are difficult to measure and lead to computationally challenging statistical reconstruction algorithms. This work addresses the second concern, seeking to simplify the reconstruction of correlated data and provide a more precise image estimate than the conventional independent methods. In general, correlated variates have a large non-diagonal covariance matrix that is computationally challenging to use as a weighting term in a reconstruction algorithm. This work proposes two methods to simplify the use of a non-diagonal covariance matrix as the weighting term by (a) limiting the number of dimensions in which the correlations are modeled and (b) adopting flexible, yet computationally tractable, models for correlation structure. We apply and test these methods with simple simulated PET data and data processed with the Fourier rebinning algorithm which include the one-dimensional correlations in the axial direction and the two-dimensional correlations in the transaxial directions. The methods are incorporated into a penalized weighted least-squares 2D reconstruction and compared with a conventional maximum a posteriori approach. PMID:17921576

Notes on integrable boundary interactions of open SU(4) alternating spin chains

NASA Astrophysics Data System (ADS)

Wu, JunBao

2018-07-01

Ref. [J. High Energy Phys. 1708, 001 (2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena (ABJM) theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001 (2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.

Weighted Discriminative Dictionary Learning based on Low-rank Representation

NASA Astrophysics Data System (ADS)

Chang, Heyou; Zheng, Hao

2017-01-01

Low-rank representation has been widely used in the field of pattern classification, especially when both training and testing images are corrupted with large noise. Dictionary plays an important role in low-rank representation. With respect to the semantic dictionary, the optimal representation matrix should be block-diagonal. However, traditional low-rank representation based dictionary learning methods cannot effectively exploit the discriminative information between data and dictionary. To address this problem, this paper proposed weighted discriminative dictionary learning based on low-rank representation, where a weighted representation regularization term is constructed. The regularization associates label information of both training samples and dictionary atoms, and encourages to generate a discriminative representation with class-wise block-diagonal structure, which can further improve the classification performance where both training and testing images are corrupted with large noise. Experimental results demonstrate advantages of the proposed method over the state-of-the-art methods.

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

NASA Astrophysics Data System (ADS)

Chandran, A.; Schulz, Marc D.; Burnell, F. J.

2016-12-01

Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

Modeling anomalous radial transport in kinetic transport codes

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S. I.; Cohen, R. H.; Rognlien, T. D.

2009-11-01

Anomalous transport is typically the dominant component of the radial transport in magnetically confined plasmas, where the physical origin of this transport is believed to be plasma turbulence. A model is presented for anomalous transport that can be used in continuum kinetic edge codes like TEMPEST, NEO and the next-generation code being developed by the Edge Simulation Laboratory. The model can also be adapted to particle-based codes. It is demonstrated that the model with a velocity-dependent diffusion and convection terms can match a diagonal gradient-driven transport matrix as found in contemporary fluid codes, but can also include off-diagonal effects. The anomalous transport model is also combined with particle drifts and a particle/energy-conserving Krook collision operator to study possible synergistic effects with neoclassical transport. For the latter study, a velocity-independent anomalous diffusion coefficient is used to mimic the effect of long-wavelength ExB turbulence.

Molecular t-matrices for Low-Energy Electron Diffraction (TMOL v1.1)

NASA Astrophysics Data System (ADS)

Blanco-Rey, Maria; de Andres, Pedro; Held, Georg; King, David A.

2004-08-01

We describe a FORTRAN-90 program that computes scattering t-matrices for a molecule. These can be used in a Low-Energy Electron Diffraction program to solve the molecular structural problem very efficiently. The intramolecular multiple scattering is computed within a Dyson-like approach, using free space Green propagators in a basis of spherical waves. The advantage of this approach is related to exploiting the chemical identity of the molecule, and to the simplicity to translate and rotate these t-matrices without performing a new multiple-scattering calculation for each configuration. FORTRAN-90 routines for rotating the resulting t-matrices using Wigner matrices are also provided. Program summaryTitle of program: TMOL Catalogue number: ADUF Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUF Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland. Computers: Alpha ev6-21264 (700 MHz) and Pentium-IV. Operating systems: Digital UNIX V5.0 and Linux (Red Hat 8.0). Programming language: FORTRAN-90/95 (Compaq True64 compiler, and Intel Fortran Compiler 7.0 for Linux). High-speed storage required for the test run: minimum 64 Mbytes, it can grow to more depending on the system considered. Disk storage required: None. No. of bits in a word: 64 and 32. No. of lines in distributed program, including test data etc.: 5404 No. of bytes in distributed program, including test data etc.: 59 856 Distribution format: tar.gz Nature of problem: We describe the FORTRAN-90 program TMOL (v1.1) for the computation of non-diagonal scattering t-matrices for molecules or any other poly-atomic sub-unit of surface structures. These matrices can be used in an standard Low-Energy Electron Diffraction program, such as LEED90 or CLEED. Method of solution: A general non-diagonal t-matrix is assumed for the atoms or more general scatterers forming the molecule. The molecular t-matrix is solved adding the possible intramolecular multiple scattering events using Green's propagator formalism. The resulting t-matrix is referred to the mass centre of the molecule and can be easily translated with these propagators and rotated applying Wigner matrices. Typical running time: Calculating the t-matrix for a single energy takes a few seconds. Time depends on the maximum angular momentum quantum number, lmax, and the number of scatterers in the molecule, N. Running time scales as lmax6 and N3. References: [1] S. Andersson, J.B. Pendry, J. Phys. C: Solid St. Phys. 13 (1980) 3547. [2] A. Gonis, W.H. Butler, Multiple Scattering in Solids, Springer-Verlag, Berlin/New York, 2000.

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Du; Yang, Weitao

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

DOE PAGES

Zhang, Du; Yang, Weitao

2016-10-13

An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

A combined joint diagonalization-MUSIC algorithm for subsurface targets localization

NASA Astrophysics Data System (ADS)

Wang, Yinlin; Sigman, John B.; Barrowes, Benjamin E.; O'Neill, Kevin; Shubitidze, Fridon

2014-06-01

This paper presents a combined joint diagonalization (JD) and multiple signal classification (MUSIC) algorithm for estimating subsurface objects locations from electromagnetic induction (EMI) sensor data, without solving ill-posed inverse-scattering problems. JD is a numerical technique that finds the common eigenvectors that diagonalize a set of multistatic response (MSR) matrices measured by a time-domain EMI sensor. Eigenvalues from targets of interest (TOI) can be then distinguished automatically from noise-related eigenvalues. Filtering is also carried out in JD to improve the signal-to-noise ratio (SNR) of the data. The MUSIC algorithm utilizes the orthogonality between the signal and noise subspaces in the MSR matrix, which can be separated with information provided by JD. An array of theoreticallycalculated Green's functions are then projected onto the noise subspace, and the location of the target is estimated by the minimum of the projection owing to the orthogonality. This combined method is applied to data from the Time-Domain Electromagnetic Multisensor Towed Array Detection System (TEMTADS). Examples of TEMTADS test stand data and field data collected at Spencer Range, Tennessee are analyzed and presented. Results indicate that due to its noniterative mechanism, the method can be executed fast enough to provide real-time estimation of objects' locations in the field.

Finite and spectral cell method for wave propagation in heterogeneous materials

NASA Astrophysics Data System (ADS)

Joulaian, Meysam; Duczek, Sascha; Gabbert, Ulrich; Düster, Alexander

2014-09-01

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1-3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].

Phase transition and field effect topological quantum transistor made of monolayer MoS2

NASA Astrophysics Data System (ADS)

Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

2018-06-01

We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

G W calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

DOE PAGES

Pham, T. Anh; Nguyen, Huy -Viet; Rocca, Dario; ...

2013-04-26

Inmore » a recent paper we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmon-pole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. Lastly, we demonstrate the efficiency of our approach by carrying out G W calculations for systems with several hundred valence electrons.« less

Forces and mechanical energy fluctuations during diagonal stride roller skiing; running on wheels?

PubMed

Kehler, Alyse L; Hajkova, Eliska; Holmberg, Hans-Christer; Kram, Rodger

2014-11-01

Mechanical energy can be conserved during terrestrial locomotion in two ways: the inverted pendulum mechanism for walking and the spring-mass mechanism for running. Here, we investigated whether diagonal stride cross-country roller skiing (DIA) utilizes similar mechanisms. Based on previous studies, we hypothesized that running and DIA would share similar phase relationships and magnitudes of kinetic energy (KE), and gravitational potential energy (GPE) fluctuations, indicating elastic energy storage and return, as if roller skiing is like 'running on wheels'. Experienced skiers (N=9) walked and ran at 1.25 and 3 m s(-1), respectively, and roller skied with DIA at both speeds on a level dual-belt treadmill that recorded perpendicular and parallel forces. We calculated the KE and GPE of the center of mass from the force recordings. As expected, the KE and GPE fluctuated with an out-of-phase pattern during walking and an in-phase pattern during running. Unlike walking, during DIA, the KE and GPE fluctuations were in phase, as they are in running. However, during the glide phase, KE was dissipated as frictional heat and could not be stored elastically in the tendons, as in running. Elastic energy storage and return epitomize running and thus we reject our hypothesis. Diagonal stride cross-country skiing is a biomechanically unique movement that only superficially resembles walking or running. © 2014. Published by The Company of Biologists Ltd.

Positron collisions with acetylene calculated using the R-matrix with pseudo-states method

NASA Astrophysics Data System (ADS)

Zhang, Rui; Galiatsatos, Pavlos G.; Tennyson, Jonathan

2011-10-01

Eigenphase sums, total cross sections and differential cross sections are calculated for low-energy collisions of positrons with C2H2. The calculations demonstrate that the use of appropriate pseudo-state expansions very significantly improves the representation of this process giving both realistic eigenphases and cross sections. Differential cross sections are strongly forward peaked in agreement with the measurements. These calculations are computationally very demanding; even with improved procedures for matrix diagonalization, fully converged calculations are too expensive with current computer resources. Nonetheless, the calculations show clear evidence for the formation of a virtual state but no indication that acetylene actually binds a positron at its equilibrium geometry.

Analysis of Modified SMI Method for Adaptive Array Weight Control. M.S. Thesis

NASA Technical Reports Server (NTRS)

Dilsavor, Ronald Louis

1989-01-01

An adaptive array is used to receive a desired signal in the presence of weak interference signals which need to be suppressed. A modified sample matrix inversion (SMI) algorithm controls the array weights. The modification leads to increased interference suppression by subtracting a fraction of the noise power from the diagonal elements of the covariance matrix. The modified algorithm maximizes an intuitive power ratio criterion. The expected values and variances of the array weights, output powers, and power ratios as functions of the fraction and the number of snapshots are found and compared to computer simulation and real experimental array performance. Reduced-rank covariance approximations and errors in the estimated covariance are also described.

Cascaded VLSI Chips Help Neural Network To Learn

NASA Technical Reports Server (NTRS)

Duong, Tuan A.; Daud, Taher; Thakoor, Anilkumar P.

1993-01-01

Cascading provides 12-bit resolution needed for learning. Using conventional silicon chip fabrication technology of VLSI, fully connected architecture consisting of 32 wide-range, variable gain, sigmoidal neurons along one diagonal and 7-bit resolution, electrically programmable, synaptic 32 x 31 weight matrix implemented on neuron-synapse chip. To increase weight nominally from 7 to 13 bits, synapses on chip individually cascaded with respective synapses on another 32 x 32 matrix chip with 7-bit resolution synapses only (without neurons). Cascade correlation algorithm varies number of layers effectively connected into network; adds hidden layers one at a time during learning process in such way as to optimize overall number of neurons and complexity and configuration of network.

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions

NASA Astrophysics Data System (ADS)

Dinh, Thanh-Chung; Renger, Thomas

2015-01-01

A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brabec, Jiri; Lin, Lin; Shao, Meiyue

We present two iterative algorithms for approximating the absorption spectrum of molecules within linear response of time-dependent density functional theory (TDDFT) framework. These methods do not attempt to compute eigenvalues or eigenvectors of the linear response matrix. They are designed to approximate the absorption spectrum as a function directly. They take advantage of the special structure of the linear response matrix. Neither method requires the linear response matrix to be constructed explicitly. They only require a procedure that performs the multiplication of the linear response matrix with a vector. These methods can also be easily modified to efficiently estimate themore » density of states (DOS) of the linear response matrix without computing the eigenvalues of this matrix. We show by computational experiments that the methods proposed in this paper can be much more efficient than methods that are based on the exact diagonalization of the linear response matrix. We show that they can also be more efficient than real-time TDDFT simulations. We compare the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost.« less

An alternative section method for casting and posterior laser welding of metallic frameworks for an implant-supported prosthesis.

PubMed

de Aguiar, Fábio Afrânio; Tiossi, Rodrigo; Rodrigues, Renata Cristina Silveira; Mattos, Maria de Gloria Chiarello; Ribeiro, Ricardo Faria

2009-04-01

The aim of this study was to compare the accuracy of fit of three types of implant-supported frameworks cast in Ni-Cr alloy: specifically, a framework cast as one piece compared to frameworks cast separately in sections to the transverse or the diagonal axis, and later laser welded. Three sets of similar implant-supported frameworks were constructed. The first group of six 3-unit implant-supported frameworks were cast as one piece, the second group of six were sectioned in the transverse axis of the pontic region prior to casting, and the last group of six were sectioned in the diagonal axis of the pontic region prior to casting. The sectioned frameworks were positioned in the matrix (10 N.cm torque) and laser welded. To evaluate passive fit, readings were made with an optical microscope with both screws tightened and with only one-screw tightened. Data were submitted to ANOVA and Tukey-Kramer's test (p < 0.05). When both screws were tightened, no differences were found between the three groups (p > 0.05). In the single-screw-tightened test, with readings made opposite to the tightened side, the group cast as one piece (57.02 +/- 33.48 mum) was significantly different (p < 0.05) from the group sectioned diagonally (18.92 +/- 4.75 microm) but no different (p > 0.05) from the group transversally sectioned (31.42 +/- 20.68 microm). On the tightened side, no significant differences were found between the groups (p > 0.05). Results of this study showed that casting diagonally sectioned frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves the levels of passivity to the same frameworks when compared to structures cast as one piece.

Multi-Target Angle Tracking Algorithm for Bistatic MIMO Radar Based on the Elements of the Covariance Matrix

PubMed Central

Zhang, Zhengyan; Zhang, Jianyun; Zhou, Qingsong; Li, Xiaobo

2018-01-01

In this paper, we consider the problem of tracking the direction of arrivals (DOA) and the direction of departure (DOD) of multiple targets for bistatic multiple-input multiple-output (MIMO) radar. A high-precision tracking algorithm for target angle is proposed. First, the linear relationship between the covariance matrix difference and the angle difference of the adjacent moment was obtained through three approximate relations. Then, the proposed algorithm obtained the relationship between the elements in the covariance matrix difference. On this basis, the performance of the algorithm was improved by averaging the covariance matrix element. Finally, the least square method was used to estimate the DOD and DOA. The algorithm realized the automatic correlation of the angle and provided better performance when compared with the adaptive asymmetric joint diagonalization (AAJD) algorithm. The simulation results demonstrated the effectiveness of the proposed algorithm. The algorithm provides the technical support for the practical application of MIMO radar. PMID:29518957

Multi-Target Angle Tracking Algorithm for Bistatic Multiple-Input Multiple-Output (MIMO) Radar Based on the Elements of the Covariance Matrix.

PubMed

Zhang, Zhengyan; Zhang, Jianyun; Zhou, Qingsong; Li, Xiaobo

2018-03-07

In this paper, we consider the problem of tracking the direction of arrivals (DOA) and the direction of departure (DOD) of multiple targets for bistatic multiple-input multiple-output (MIMO) radar. A high-precision tracking algorithm for target angle is proposed. First, the linear relationship between the covariance matrix difference and the angle difference of the adjacent moment was obtained through three approximate relations. Then, the proposed algorithm obtained the relationship between the elements in the covariance matrix difference. On this basis, the performance of the algorithm was improved by averaging the covariance matrix element. Finally, the least square method was used to estimate the DOD and DOA. The algorithm realized the automatic correlation of the angle and provided better performance when compared with the adaptive asymmetric joint diagonalization (AAJD) algorithm. The simulation results demonstrated the effectiveness of the proposed algorithm. The algorithm provides the technical support for the practical application of MIMO radar.

Computer Aided Detection of Microcalcifications Utilizing Texture Analysis

DTIC Science & Technology

1995-12-01

encouraging results using features derived from the first moment of the power spectrum of the region[13]. Chitre, et al. and Kocur have made use of...are largely concentrated around the main diagonal. For the example C matrix in Figure 3.11, the ASM value is 0.0972. Previous work by Kocur [17] and...Patterson AFB OH, 1994. BIB-1 16. Hoffmeister, Jeffery W. Personal interviews, May-Nov 1995. Aerospace Physician. AL/CFHV, Wright-Patterson AFB,OH. 17. Kocur

Tensorial Calibration. 2. Second Order Tensorial Calibration.

DTIC Science & Technology

1987-10-12

index is repeated more than once only in one side of an equation, it implies a summation over the index valid range. 12 To avoid confusion of terms...and higher order tensor, the rank can be higher than the maximum dimensionality. 13 ,ON 6 LINEAR SECOND ORDER TENSORIAL CALIBRATION MODEL From...these equations are valid only if all the elements of the diagonal matrix B3 are non-zero because its inverse (-1) must be computed. This implies that M

Generalized Eigenvalues for pairs on heritian matrices

NASA Technical Reports Server (NTRS)

Rublein, George

1988-01-01

A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.

Minutia Tensor Matrix: A New Strategy for Fingerprint Matching

PubMed Central

Fu, Xiang; Feng, Jufu

2015-01-01

Establishing correspondences between two minutia sets is a fundamental issue in fingerprint recognition. This paper proposes a new tensor matching strategy. First, the concept of minutia tensor matrix (simplified as MTM) is proposed. It describes the first-order features and second-order features of a matching pair. In the MTM, the diagonal elements indicate similarities of minutia pairs and non-diagonal elements indicate pairwise compatibilities between minutia pairs. Correct minutia pairs are likely to establish both large similarities and large compatibilities, so they form a dense sub-block. Minutia matching is then formulated as recovering the dense sub-block in the MTM. This is a new tensor matching strategy for fingerprint recognition. Second, as fingerprint images show both local rigidity and global nonlinearity, we design two different kinds of MTMs: local MTM and global MTM. Meanwhile, a two-level matching algorithm is proposed. For local matching level, the local MTM is constructed and a novel local similarity calculation strategy is proposed. It makes full use of local rigidity in fingerprints. For global matching level, the global MTM is constructed to calculate similarities of entire minutia sets. It makes full use of global compatibility in fingerprints. Proposed method has stronger description ability and better robustness to noise and nonlinearity. Experiments conducted on Fingerprint Verification Competition databases (FVC2002 and FVC2004) demonstrate the effectiveness and the efficiency. PMID:25822489

The Density Matrix for Single-mode Light after k-Photon Absorption

NASA Astrophysics Data System (ADS)

Voigt, H.; Bandilla, A.

In order to continue and generalize the studies of the density matrix of a light field undergoing k-photon absorption, in this paper we put the emphasis on the off-diagonal elements. The solution obtained earlier for the diagonal elements describing the photon statistics can be found as a special case but will not be discussed again. The general solution calculated by recursion shows an asymptotic behaviour if the initial photon number is sufficiently high. Only the initial phase information survives. Illustrating the solution we start with coherent light and a generalized coherent state.Translated AbstractDie Dichtematrix eines Lichtstrahls nach k-Photonen-Absorption aus einer ModeWir führen die Betrachtungen über das Verhalten der Dichtematrix eines Lichtfeldes nach k-Photonen-Absorption aus einer Mode verallgemeinernd weiter und konzentrieren uns auf die Nichtdiagonalelemente. Die im folgenden angegebene allgemeine Lösung, die durch Rekursion gefunden wurde, enthält die schon früher erhaltene, jedoch hier nicht weiter diskutierte Lösung für die Diagonalelemente als Spezialfall. Sie zeigt ferner, daß es einen asymptotischen Zustand gibt, der eine von der Ausgangsintensität unabhängige Information über die Ausgangsphase enthält. Zur Diskussion der Lösung werden verschiedene Anfangsbedingungen betrachtet, so z. B. kohärentes Licht und kohärentes Licht, das ein Medium mit nichtlinearem Brechungsindex durchlaufen hat (Kerr-Effekt).

Factorized three-body S-matrix restrained by the Yang–Baxter equation and quantum entanglements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Li-Wei, E-mail: NKyulw@gmail.com; Zhao, Qing, E-mail: qzhaoyuping@bit.edu.cn; Ge, Mo-Lin, E-mail: geml@nankai.edu.cn

2014-09-15

This paper investigates the physical effects of the Yang–Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix Ř{sub 123}(θ,φ) based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the Ř(θ,φ)-matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed.more » - Highlights: • We give the relation between 3-body S-matrix and 3-qubit entanglement. • The relation between 3-qubit and 2-qubit entanglements is investigated via YBE. • 1D Kitaev toy model is derived by the Type-II solution of YBE. • The condition of YBE kills the “Zero boundary mode” in our chain model.« less

Face verification with balanced thresholds.

PubMed

Yan, Shuicheng; Xu, Dong; Tang, Xiaoou

2007-01-01

The process of face verification is guided by a pre-learned global threshold, which, however, is often inconsistent with class-specific optimal thresholds. It is, hence, beneficial to pursue a balance of the class-specific thresholds in the model-learning stage. In this paper, we present a new dimensionality reduction algorithm tailored to the verification task that ensures threshold balance. This is achieved by the following aspects. First, feasibility is guaranteed by employing an affine transformation matrix, instead of the conventional projection matrix, for dimensionality reduction, and, hence, we call the proposed algorithm threshold balanced transformation (TBT). Then, the affine transformation matrix, constrained as the product of an orthogonal matrix and a diagonal matrix, is optimized to improve the threshold balance and classification capability in an iterative manner. Unlike most algorithms for face verification which are directly transplanted from face identification literature, TBT is specifically designed for face verification and clarifies the intrinsic distinction between these two tasks. Experiments on three benchmark face databases demonstrate that TBT significantly outperforms the state-of-the-art subspace techniques for face verification.

Le Châtelier reciprocal relations and the mechanical analog

NASA Astrophysics Data System (ADS)

Gilmore, Robert

1983-08-01

Le Châtelier's principle is discussed carefully in terms of two sets of simple thermodynamic examples. The principle is then formulated quantitatively for general thermodynamic systems. The formulation is in terms of a perturbation-response matrix, the Le Châtelier matrix [L]. Le Châtelier's principle is contained in the diagonal elements of this matrix, all of which exceed one. These matrix elements describe the response of a system to a perturbation of either its extensive or intensive variables. These response ratios are inverses of each other. The Le Châtelier matrix is symmetric, so that a new set of thermodynamic reciprocal relations is derived. This quantitative formulation is illustrated by a single simple example which includes the original examples and shows the reciprocities among them. The assumptions underlying this new quantitative formulation of Le Châtelier's principle are general and applicable to a wide variety of nonthermodynamic systems. Le Châtelier's principle is formulated quantitatively for mechanical systems in static equilibrium, and mechanical examples of this formulation are given.

Casimir Effect in de Sitter Spacetime

NASA Astrophysics Data System (ADS)

Saharian, A. A.

2011-06-01

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

Exploring the nonequilibrium dynamics of ultracold quantum gases by using numerical tools

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian

Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al., in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis, nonequilibrium mass transport, dynamical fermionization, and transient phenomena such as quantum distillation or dynamical quasicondensation. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems and in determining the asymptotic state after a quantum quench. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 801.

Stiffening of fluid membranes due to thermal undulations: density-matrix renormalization-group study.

PubMed

Nishiyama, Yoshihiro

2002-12-01

It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed the significance of measure factors for the partition sum. Accepting the local curvature as a statistical measure, they found that fluid membranes are stiffened macroscopically. In order to examine this remarkable idea, we performed extensive ab initio simulations for a fluid membrane. We set up a transfer matrix that is diagonalized by means of the density-matrix renormalization group. Our method has an advantage, in that it allows us to survey various statistical measures. As a consequence, we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure. On the contrary, for other measures such as normal displacement and tilt angle, we found a clear tendency toward softening.

The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis

DOE PAGES

Galais, Sebastien; Kneller, James; Volpe, Cristina

2012-01-19

We consider the Hamiltonian for neutrino oscillations in matter in the case of arbitrary potentials including off-diagonal complex terms. We derive the expressions for the corresponding Hamiltonian in the basis of the instantaneous eigenstates in matter, in terms of quantities one can derive from the flavor-basis Hamiltonian and its derivative, for an arbitrary number of neutrino flavors. We make our expressions explicit for the two-neutrino flavor case and apply our results to the neutrino propagation in core-collapse supernovae where the Hamiltonian includes both coupling to matter and to neutrinos. We show that the neutrino flavor evolution depends on the mixingmore » matrix derivatives involving not only the derivative of the matter mixing angles but also of the phases. In particular, we point out the important role of the phase derivatives, that appear due to the neutrino-neutrino interaction, and show how it can cause an oscillating degeneracy between the diagonal elements of the Hamiltonian in the basis of the eigenstates in matter. Lastly, our results also reveal that the end of the synchronization regime is due to a rapid increase of the phase derivative and identify the condition to be fulfilled for the onset of bipolar oscillations involving both the off-diagonal neutrino-neutrino interaction contributions and the vacuum terms.« less

Analysis of modified SMI method for adaptive array weight control

NASA Technical Reports Server (NTRS)

Dilsavor, R. L.; Moses, R. L.

1989-01-01

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

A comparison of SuperLU solvers on the intel MIC architecture

NASA Astrophysics Data System (ADS)

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.

Asymmetric color image encryption based on singular value decomposition

NASA Astrophysics Data System (ADS)

Yao, Lili; Yuan, Caojin; Qiang, Junjie; Feng, Shaotong; Nie, Shouping

2017-02-01

A novel asymmetric color image encryption approach by using singular value decomposition (SVD) is proposed. The original color image is encrypted into a ciphertext shown as an indexed image by using the proposed method. The red, green and blue components of the color image are subsequently encoded into a complex function which is then separated into U, S and V parts by SVD. The data matrix of the ciphertext is obtained by multiplying orthogonal matrices U and V while implementing phase-truncation. Diagonal entries of the three diagonal matrices of the SVD results are abstracted and scrambling combined to construct the colormap of the ciphertext. Thus, the encrypted indexed image covers less space than the original image. For decryption, the original color image cannot be recovered without private keys which are obtained from phase-truncation and the orthogonality of V. Computer simulations are presented to evaluate the performance of the proposed algorithm. We also analyze the security of the proposed system.

R4 terms in supergravities via T -duality constraint

NASA Astrophysics Data System (ADS)

Razaghian, Hamid; Garousi, Mohammad R.

2018-05-01

It has been speculated in the literature that the effective actions of string theories at any order of α' should be invariant under the Buscher rules plus their higher covariant-derivative corrections. This may be used as a constraint to find effective actions at any order of α', in particular, the metric, the B -field, and the dilaton couplings in supergravities at order α'3 up to an overall factor. For the simple case of zero B -field and diagonal metric in which we have done the calculations explicitly, we have found that the constraint fixes almost all of the seven independent Riemann curvature couplings. There is only one term which is not fixed, because when metric is diagonal, the reduction of two R4 terms becomes identical. The Riemann curvature couplings that the T -duality constraint produces for both type II and heterotic theories are fully consistent with the existing couplings in the literature which have been found by the S-matrix and by the sigma-model approaches.

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Performance optimization of spectral amplitude coding OCDMA system using new enhanced multi diagonal code

NASA Astrophysics Data System (ADS)

Imtiaz, Waqas A.; Ilyas, M.; Khan, Yousaf

2016-11-01

This paper propose a new code to optimize the performance of spectral amplitude coding-optical code division multiple access (SAC-OCDMA) system. The unique two-matrix structure of the proposed enhanced multi diagonal (EMD) code and effective correlation properties, between intended and interfering subscribers, significantly elevates the performance of SAC-OCDMA system by negating multiple access interference (MAI) and associated phase induce intensity noise (PIIN). Performance of SAC-OCDMA system based on the proposed code is thoroughly analyzed for two detection techniques through analytic and simulation analysis by referring to bit error rate (BER), signal to noise ratio (SNR) and eye patterns at the receiving end. It is shown that EMD code while using SDD technique provides high transmission capacity, reduces the receiver complexity, and provides better performance as compared to complementary subtraction detection (CSD) technique. Furthermore, analysis shows that, for a minimum acceptable BER of 10-9 , the proposed system supports 64 subscribers at data rates of up to 2 Gbps for both up-down link transmission.

Gravitational collapse and Hawking-like radiation of a shell in AdS spacetime

NASA Astrophysics Data System (ADS)

Saini, Anshul; Stojkovic, Dejan

2018-01-01

In this paper, we study the collapse of a massive shell in 2 +1 and 3 +1 dimensional gravity with anti-de Sitter asymptotics. Using the Gauss-Codazzi method, we derive gravitational equations of motion of the shell. We then use the functional Schrödinger formalism to calculate the spectrum of particles produced during the collapse. At the late time, radiation agrees very well with the standard Hawking results. In 3 +1 dimensions, we reproduce the Hawking-Page transition. We then construct the density matrix of this collapsing system and analyze the information content in the emitted radiation. We find that the off-diagonal elements of the density matrix are very important in preserving the unitarity of the system.

Line mixing in a N2-broadened CO2 Q branch observed with a tunable diode laser

NASA Technical Reports Server (NTRS)

Gentry, Bruce; Strow, L. Larrabee

1987-01-01

Line-mixing effects have been observed in the infrared Q branch of the (11/1/0,03/1/0)I-00/0/0 band of CO2 at 2076/cm. A tunable diode laser spectrometer was used to record spectra of CO2 broadened by N2 and O2 at total pressures ranging from 100 to 720 torr. The observed absorption coefficients are up to 65 percent lower than those calculated using an isolated Lorentzian line approximation. A simple energy gap scaling law is used to determine the off-diagonal relaxation matrix elements from the known pressure-broadening coefficients. The spectra calculated using these matrix elements reproduces the observed absorption coefficients to within several percent.

Enrichment of Cross-Linked Peptides Using Charge-Based Fractional Diagonal Chromatography (ChaFRADIC).

PubMed

Tinnefeld, Verena; Venne, A Saskia; Sickmann, Albert; Zahedi, René P

2017-02-03

Chemical cross-linking of proteins is an emerging field with huge potential for the structural investigation of proteins and protein complexes. Owing to the often relatively low yield of cross-linking products, their identification in complex samples benefits from enrichment procedures prior to mass spectrometry analysis. So far, this is mainly accomplished by using biotin moieties in specific cross-linkers or by applying strong cation exchange chromatography (SCX) for a relatively crude enrichment. We present a novel workflow to enrich cross-linked peptides by utilizing charge-based fractional diagonal chromatography (ChaFRADIC). On the basis of two-dimensional diagonal SCX separation, we could increase the number of identified cross-linked peptides for samples of different complexity: pure cross-linked BSA, cross-linked BSA spiked into a simple protein mixture, and cross-linked BSA spiked into a HeLa lysate. We also compared XL-ChaFRADIC with size exclusion chromatography-based enrichment of cross-linked peptides. The XL-ChaFRADIC approach is straightforward, reproducible, and independent of the cross-linking chemistry and cross-linker properties.

D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations

USGS Publications Warehouse

Kipp, K.L.; Russell, T.F.; Otto, J.S.

1992-01-01

D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

NASA Astrophysics Data System (ADS)

Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

2018-06-01

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

Exceptional point in a simple textbook example

NASA Astrophysics Data System (ADS)

Fernández, Francisco M.

2018-07-01

We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well-known damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.

Special Technology Area Review on Displays. Report of Department of Defense Advisory Group on Electron Devices Working Group C (Electro-Optics)

DTIC Science & Technology

2004-03-01

mirror device ( DMD ) for C4ISR applications, the IBM 9.2 megapixel 22-in. diagonal active matrix liquid crystal display (AMLCD) monitor for data...FED, VFD, OLED and a variety of microdisplays (uD, comprising uLCD, uOLED, DMD and other MEMs) (see glossary). 3 CDT = cathode display tubes (used in...than SVGA, greater battery life and brightness, decreased weight and thickness, electromagnetic interference (EMI), and development of video

Joint Diagonalization Applied to the Detection and Discrimination of Unexploded Ordnance

DTIC Science & Technology

2012-08-01

center (Das et al., 1990; Barrow and Nelson, 2001; Bell et al., 2001; Pasion and Oldenburg , 2001; Zhang et al., 2003; Smith and Mor- rison, 2004; Tarokh et...matrix for the complete transmitter/receiver ar- ray by tiling all the Nr × Nt available samples of expression 5: S ¼ GscUlΛ̇lUTl ðGprÞT...L. R., and D. W. Oldenburg , 2001, A discrimination algorithm for UXO using time-domain electromagnetics: Journal of Environmental and Engineering

Validity of the classical monte carlo method to model the magnetic properties of a large transition-metal cluster: Mn19.

PubMed

Lima, Nicola; Caneschi, Andrea; Gatteschi, Dante; Kritikos, Mikael; Westin, L Gunnar

2006-03-20

The susceptibility of the large transition-metal cluster [Mn19O12(MOE)14(MOEH)10].MOEH (MOE = OC2H2O-CH3) has been fitted through classical Monte Carlo simulation, and an estimation of the exchange coupling constants has been done. With these results, it has been possible to perform a full-matrix diagonalization of the cluster core, which was used to provide information on the nature of the low-lying levels.

Automated Change Detection for Synthetic Aperture Sonar

DTIC Science & Technology

2014-01-01

channels, respectively. The canonical coordinates of x and y are defined as u = FHR−1/2xx x v = GHR−1/2yy y where F and G are the mapping matrices...containing the left and right singular vectors of the coherence matrix C, respectively. The canonical coordinate vectors u and v share the diagonal cross...feature set. The coherent change information between canonical coordinates v and u can be calculated using the residual, v −Ku, owing to the fact that

Theory of an optomechanical quantum heat engine

DTIC Science & Technology

2014-08-12

control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. University of Arizona 888 N . Euclid Ave. Tucson, AZ 85719 -4824 ABSTRACT Theory of an...modes, with a cutoff number state | N 〉 with N n̄a(b), so that the total dimension of the density matrix ρsys is ( N + 1)4. As a result the simulations...become very time consuming even for relatively modest values of N . However, due to the diagonality of thermal states in an energy basis the total

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

NASA Technical Reports Server (NTRS)

Jawerth, Bjoern; Sweldens, Wim

1993-01-01

We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.

Translation invariant time-dependent massive gravity: Hamiltonian analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mourad, Jihad; Steer, Danièle A.; Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr

2014-09-01

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

Comparative test on several forms of background error covariance in 3DVar

NASA Astrophysics Data System (ADS)

Shao, Aimei

2013-04-01

The background error covariance matrix (Hereinafter referred to as B matrix) plays an important role in the three-dimensional variational (3DVar) data assimilation method. However, it is difficult to get B matrix accurately because true atmospheric state is unknown. Therefore, some methods were developed to estimate B matrix (e.g. NMC method, innovation analysis method, recursive filters, and ensemble method such as EnKF). Prior to further development and application of these methods, the function of several B matrixes estimated by these methods in 3Dvar is worth studying and evaluating. For this reason, NCEP reanalysis data and forecast data are used to test the effectiveness of the several B matrixes with VAF (Huang, 1999) method. Here the NCEP analysis is treated as the truth and in this case the forecast error is known. The data from 2006 to 2007 is used as the samples to estimate B matrix and the data in 2008 is used to verify the assimilation effects. The 48h and 24h forecast valid at the same time is used to estimate B matrix with NMC method. B matrix can be represented by a correlation part (a non-diagonal matrix) and a variance part (a diagonal matrix of variances). Gaussian filter function as an approximate approach is used to represent the variation of correlation coefficients with distance in numerous 3DVar systems. On the basis of the assumption, the following several forms of B matrixes are designed and test with VAF in the comparative experiments: (1) error variance and the characteristic lengths are fixed and setted to their mean value averaged over the analysis domain; (2) similar to (1), but the mean characteristic lengths reduce to 50 percent for the height and 60 percent for the temperature of the original; (3) similar to (2), but error variance calculated directly by the historical data is space-dependent; (4) error variance and characteristic lengths are all calculated directly by the historical data; (5) B matrix is estimated directly by the historical data; (6) similar to (5), but a localization process is performed; (7) B matrix is estimated by NMC method but error variance is reduced by 1.7 times in order that the value is close to that calculated from the true forecast error samples; (8) similar to (7), but the localization similar to (6) is performed. Experimental results with the different B matrixes show that for the Gaussian-type B matrix the characteristic lengths calculated from the true error samples don't bring a good analysis results. However, the reduced characteristic lengths (about half of the original one) can lead to a good analysis. If the B matrix estimated directly from the historical data is used in 3DVar, the assimilation effect can not reach to the best. The better assimilation results are generated with the application of reduced characteristic length and localization. Even so, it hasn't obvious advantage compared with Gaussian-type B matrix with the optimal characteristic length. It implies that the Gaussian-type B matrix, widely used for operational 3DVar system, can get a good analysis with the appropriate characteristic lengths. The crucial problem is how to determine the appropriate characteristic lengths. (This work is supported by the National Natural Science Foundation of China (41275102, 40875063), and the Fundamental Research Funds for the Central Universities (lzujbky-2010-9) )

Modeling and simulation of a Stewart platform type parallel structure robot

NASA Technical Reports Server (NTRS)

Lim, Gee Kwang; Freeman, Robert A.; Tesar, Delbert

1989-01-01

The kinematics and dynamics of a Stewart Platform type parallel structure robot (NASA's Dynamic Docking Test System) were modeled using the method of kinematic influence coefficients (KIC) and isomorphic transformations of system dependence from one set of generalized coordinates to another. By specifying the end-effector (platform) time trajectory, the required generalized input forces which would theoretically yield the desired motion were determined. It was found that the relationship between the platform motion and the actuators motion was nonlinear. In addition, the contribution to the total generalized forces, required at the actuators, from the acceleration related terms were found to be more significant than the velocity related terms. Hence, the curve representing the total required actuator force generally resembled the curve for the acceleration related force. Another observation revealed that the acceleration related effective inertia matrix I sub dd had the tendency to decouple, with the elements on the main diagonal of I sub dd being larger than the off-diagonal elements, while the velocity related inertia power array P sub ddd did not show such tendency. This tendency results in the acceleration related force curve of a given actuator resembling the acceleration profile of that particular actuator. Furthermore, it was indicated that the effective inertia matrix for the legs is more decoupled than that for the platform. These observations provide essential information for further research to develop an effective control strategy for real-time control of the Dynamic Docking Test System.

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken{endash}Hush and block diagonalization methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cave, R.J.; Newton, M.D.

1997-06-01

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (H{sub ab}) for electron transfer reactions using {ital ab initio} electronic structure theory. The first is based on the generalized Mulliken{endash}Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn{sub 2}OH{sub 2}{sup +} and (b) the low-lying states of the benzene{endash}Cl atom complex andmore » its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn{sub 2}OH{sub 2}{sup +}. Both methods also yield a natural definition of the effective distance (r{sub DA}) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of r{sub DA}, generally based on molecular structure data. {copyright} {ital 1997 American Institute of Physics.}« less

Diagonal gaits in the feathertail glider Acrobates pygmaeus (Acrobatidae, Diprotodontia): Insights for the evolution of primate quadrupedalism.

PubMed

Karantanis, Nikolaos-Evangelos; Youlatos, Dionisios; Rychlik, Leszek

2015-09-01

Research on primate origins has revolved around arboreality and, more specifically, the adaptations that are linked to safe navigation in the fine-branch niche. To this end, extant non-primate mammals have been used as models to assess the significance of these adaptations. However, the size of these models is larger than that estimated for early primates. In contrast, the feathertail marsupial glider Acrobates pygmaeus, with a body mass of 12 g, a clawless opposable hallux, and terminal branch feeding habits appears more suited to modeling behavioral adaptations to the small branch milieu. Analysis of video recordings of 18 feathertail gliders walking on poles of variable diameter and inclination revealed that they preferentially used diagonal sequence gaits, fast velocities and low duty factors. Diagonal gaits did not correlate to duty factor, but increased as substrate size decreased, and from descending to ascending locomotion. Furthermore, the duty factor index increased in more diagonal gaits and ascending locomotion. Finally, velocities were lower on smaller substrates, and were mainly regulated by stride frequency and, to a lesser degree, stride length. Feathertail glider gaits displayed noteworthy behavioral convergences with primate quadrupedalism, but some of these results need additional investigation. Despite any discrepancies, these features appear to be favorable for quadrupedal progression on small branches, providing a selective advantage for navigating within a fine branch niche and highlighting the importance of small body size in early primate evolution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

NASA Astrophysics Data System (ADS)

Prószyński, W.; Kwaśniak, M.

2018-03-01

A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect.

Recurrence quantity analysis based on matrix eigenvalues

NASA Astrophysics Data System (ADS)

Yang, Pengbo; Shang, Pengjian

2018-06-01

Recurrence plots is a powerful tool for visualization and analysis of dynamical systems. Recurrence quantification analysis (RQA), based on point density and diagonal and vertical line structures in the recurrence plots, is considered to be alternative measures to quantify the complexity of dynamical systems. In this paper, we present a new measure based on recurrence matrix to quantify the dynamical properties of a given system. Matrix eigenvalues can reflect the basic characteristics of the complex systems, so we show the properties of the system by exploring the eigenvalues of the recurrence matrix. Considering that Shannon entropy has been defined as a complexity measure, we propose the definition of entropy of matrix eigenvalues (EOME) as a new RQA measure. We confirm that EOME can be used as a metric to quantify the behavior changes of the system. As a given dynamical system changes from a non-chaotic to a chaotic regime, the EOME will increase as well. The bigger EOME values imply higher complexity and lower predictability. We also study the effect of some factors on EOME,including data length, recurrence threshold, the embedding dimension, and additional noise. Finally, we demonstrate an application in physiology. The advantage of this measure lies in a high sensitivity and simple computation.

ANALYSIS OF A CLASSIFICATION ERROR MATRIX USING CATEGORICAL DATA TECHNIQUES.

USGS Publications Warehouse

Rosenfield, George H.; Fitzpatrick-Lins, Katherine

1984-01-01

Summary form only given. A classification error matrix typically contains tabulation results of an accuracy evaluation of a thematic classification, such as that of a land use and land cover map. The diagonal elements of the matrix represent the counts corrected, and the usual designation of classification accuracy has been the total percent correct. The nondiagonal elements of the matrix have usually been neglected. The classification error matrix is known in statistical terms as a contingency table of categorical data. As an example, an application of these methodologies to a problem of remotely sensed data concerning two photointerpreters and four categories of classification indicated that there is no significant difference in the interpretation between the two photointerpreters, and that there are significant differences among the interpreted category classifications. However, two categories, oak and cottonwood, are not separable in classification in this experiment at the 0. 51 percent probability. A coefficient of agreement is determined for the interpreted map as a whole, and individually for each of the interpreted categories. A conditional coefficient of agreement for the individual categories is compared to other methods for expressing category accuracy which have already been presented in the remote sensing literature.

The feasibility and stability of large complex biological networks: a random matrix approach.

PubMed

Stone, Lewi

2018-05-29

In the 70's, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the "circular law" since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the "circular law" does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the random matrix A is locally stable, the community matrix S = DA will also be locally stable, providing the system is feasible (i.e., all species have positive equilibria D > 0). This helps explain why, unusually, nearly all feasible systems studied here are locally stable. Large complex systems may thus be even more fragile than May predicted, given the difficulty of assembling a feasible system. It was also found that the degree of stability, or resilience of a system, depended on the minimum equilibrium population.

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

NASA Technical Reports Server (NTRS)

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-01-01

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Expendable launch vehicle studies

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reiss, Robert

1995-01-01

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Invariant operators, orthogonal bases and correlators in general tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-07-01

We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry Gd = U (N1) ⊗ ⋯ ⊗ U (Nd). As a continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary Gd and another valid for large rank of Gd. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of Gd diagonalizes the two-point function of the free theory. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood-Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore the parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation.

Rolling Bearing Fault Diagnosis Based on an Improved HTT Transform

PubMed Central

Tang, Guiji; Tian, Tian; Zhou, Chong

2018-01-01

When rolling bearing failure occurs, vibration signals generally contain different signal components, such as impulsive fault feature signals, background noise and harmonic interference signals. One of the most challenging aspects of rolling bearing fault diagnosis is how to inhibit noise and harmonic interference signals, while enhancing impulsive fault feature signals. This paper presents a novel bearing fault diagnosis method, namely an improved Hilbert time–time (IHTT) transform, by combining a Hilbert time–time (HTT) transform with principal component analysis (PCA). Firstly, the HTT transform was performed on vibration signals to derive a HTT transform matrix. Then, PCA was employed to de-noise the HTT transform matrix in order to improve the robustness of the HTT transform. Finally, the diagonal time series of the de-noised HTT transform matrix was extracted as the enhanced impulsive fault feature signal and the contained fault characteristic information was identified through further analyses of amplitude and envelope spectrums. Both simulated and experimental analyses validated the superiority of the presented method for detecting bearing failures. PMID:29662013

Multiresolution texture analysis applied to road surface inspection

NASA Astrophysics Data System (ADS)

Paquis, Stephane; Legeay, Vincent; Konik, Hubert; Charrier, Jean

1999-03-01

Technological advances provide now the opportunity to automate the pavement distress assessment. This paper deals with an approach for achieving an automatic vision system for road surface classification. Road surfaces are composed of aggregates, which have a particular grain size distribution and a mortar matrix. From various physical properties and visual aspects, four road families are generated. We present here a tool using a pyramidal process with the assumption that regions or objects in an image rise up because of their uniform texture. Note that the aim is not to compute another statistical parameter but to include usual criteria in our method. In fact, the road surface classification uses a multiresolution cooccurrence matrix and a hierarchical process through an original intensity pyramid, where a father pixel takes the minimum gray level value of its directly linked children pixels. More precisely, only matrix diagonal is taken into account and analyzed along the pyramidal structure, which allows the classification to be made.

Equations of motion for a spectrum-generating algebra: Lipkin Meshkov Glick model

NASA Astrophysics Data System (ADS)

Rosensteel, G.; Rowe, D. J.; Ho, S. Y.

2008-01-01

For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 106, computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point.

Anisotropic resonator analysis using the Fourier-Bessel mode solver

NASA Astrophysics Data System (ADS)

Gauthier, Robert C.

2018-03-01

A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.

PubMed

Papenbrock, T; Reimann, S M; Kavoulakis, G M

2012-02-17

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

PubMed

Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

2009-11-30

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

Space fabrication: Graphite composite truss welding and cap forming subsystems

NASA Technical Reports Server (NTRS)

Jenkins, L. M.; Browning, D. L.

1980-01-01

An automated beam builder for the fabrication of space structures is described. The beam builder forms a triangular truss 1.3 meters on a side. Flat strips of preconsolidated graphite fiber fabric in a polysulfone matrix are coiled in a storage canister. Heaters raise the material to forming temperature then the structural cap section is formed by a series of rollers. After cooling, cross members and diagonal tension cords are ultrasonically welded in place to complete the truss. The stability of fabricated structures and composite materials is also examined.

Q-operators for the open Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Frassek, Rouven; Szécsényi, István M.

2015-12-01

We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

A Fast Estimation Algorithm for Two-Dimensional Gravity Data (GEOFAST),

DTIC Science & Technology

1979-11-15

to a wide class of problems (Refs. 9 and 17). The major inhibitor to the widespread appli- ( cation of optimal gravity data processing is the severe...extends directly to two dimensions. Define the nln 2xn1 n2 diagonal window matrix W as the Kronecker product of two one-dimensional windows W = W1 0 W2 (B...Inversion of Separable Matrices Consider the linear system y = T x (B.3-1) where T is block Toeplitz of dimension nln 2xnIn 2 . Its fre- quency domain

Three dimensional thermal stresses in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Griffin, O. Hayden, Jr.

1988-01-01

The room temperature stress distributions and shapes of a family of angle ply graphite/epoxy laminates have been obtained using a three-dimensional linear finite element analysis. The sensitivity of the corners to fiber angle variations is examined, in addition to the errors introduced by assuming planes of symmetry which do not exist in angle-ply laminates. The results show that angle ply laminates with 'clustered' plies will tend to delaminate at diagonally opposite corners, and that matrix cracks in this family of laminates will be initiated in the laminate interior.

Asymmetric rotor-like probes to polarized fluorescence study of the macroscopically oriented uniaxial media: Model parameters recognition

NASA Astrophysics Data System (ADS)

Buczkowski, M.; Fisz, J. J.

2008-07-01

In this paper the possibility of the numerical data modelling in the case of angle- and time-resolved fluorescence spectroscopy is investigated. The asymmetric fluorescence probes are assumed to undergo the restricted rotational diffusion in a hosting medium. This process is described quantitatively by the diffusion tensor and the aligning potential. The evolution of the system is expressed in terms of the Smoluchowski equation with an appropriate time-developing operator. A matrix representation of this operator is calculated, then symmetrized and diagonalized. The resulting propagator is used to generate the synthetic noisy data set that imitates results of experimental measurements. The data set serves as a groundwork to the χ2 optimization, performed by the genetic algorithm followed by the gradient search, in order to recover model parameters, which are diagonal elements of the diffusion tensor, aligning potential expansion coefficients and directions of the electronic dipole moments. This whole procedure properly identifies model parameters, showing that the outlined formalism should be taken in the account in the case of analysing real experimental data.

Efficient Numerical Diagonalization of Hermitian 3 × 3 Matrices

NASA Astrophysics Data System (ADS)

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 .

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

2016-01-01

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

2015-03-01

We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Volkas, R. R.; Foot, R.; He, X.

The universal QCD color theory is extended to an SU(3)/sub 1//direct product/SU(3)/sub 2//direct product/SU(3)/sub 3/ gauge theory, where quarks of the /ital i/th generation transform as triplets under SU(3)/sub /ital i// and singlets under the other two factors. The usual color group is then identified with the diagonal subgroup, which remains exact after symmetry breaking. The gauge bosons associated with the 16 broken generators then form two massive octets under ordinary color. The interactions between quarks and these heavy gluonlike particles are explicitly nonuniversal and thus an exploration of their physical implications allows us to shed light on the fundamentalmore » issue of strong-interaction universality. Nonuniversality and weak flavor mixing are shown to generate heavy-gluon-induced flavor-changing neutral currents. The phenomenology of these processes is studied, as they provide the major experimental constraint on the extended theory. Three symmetry-breaking scenarios are presented. The first has color breaking occurring at the weak scale, while the second and third divorce the two scales. The third model has the interesting feature of radiatively induced off-diagonal Kobayashi-Maskawa matrix elements.« less

Empirical Bayes method for reducing false discovery rates of correlation matrices with block diagonal structure.

PubMed

Pacini, Clare; Ajioka, James W; Micklem, Gos

2017-04-12

Correlation matrices are important in inferring relationships and networks between regulatory or signalling elements in biological systems. With currently available technology sample sizes for experiments are typically small, meaning that these correlations can be difficult to estimate. At a genome-wide scale estimation of correlation matrices can also be computationally demanding. We develop an empirical Bayes approach to improve covariance estimates for gene expression, where we assume the covariance matrix takes a block diagonal form. Our method shows lower false discovery rates than existing methods on simulated data. Applied to a real data set from Bacillus subtilis we demonstrate it's ability to detecting known regulatory units and interactions between them. We demonstrate that, compared to existing methods, our method is able to find significant covariances and also to control false discovery rates, even when the sample size is small (n=10). The method can be used to find potential regulatory networks, and it may also be used as a pre-processing step for methods that calculate, for example, partial correlations, so enabling the inference of the causal and hierarchical structure of the networks.

Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors.

PubMed

Peterson, Christine; Vannucci, Marina; Karakas, Cemal; Choi, William; Ma, Lihua; Maletić-Savatić, Mirjana

2013-10-01

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation.

Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors

PubMed Central

PETERSON, CHRISTINE; VANNUCCI, MARINA; KARAKAS, CEMAL; CHOI, WILLIAM; MA, LIHUA; MALETIĆ-SAVATIĆ, MIRJANA

2014-01-01

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation. PMID:24533172

Nonlinear optical response in a zincblende GaN cylindrical quantum dot with donor impurity center

NASA Astrophysics Data System (ADS)

Hoyos, Jaime H.; Correa, J. D.; Mora-Ramos, M. E.; Duque, C. A.

2016-03-01

We calculate the nonlinear optical absorption coefficient of a cylindrical zincblende GaN-based quantum dot. For this purpose, we consider Coulomb interactions between electrons and an impurity ionized donor atom. The electron-donor-impurity spectrum and the associated quantum states are calculated using the effective mass approximation with a parabolic potential energy model describing both the radial and axial electron confinement. We also include the effects of the hydrostatic pressure and external electrostatic fields. The energy spectrum is obtained through an expansion of the eigenstates as a linear combination of Gaussian-type functions which reduces the computational effort since all the matrix elements are obtained analytically. Therefore, the numerical problem is reduced to the direct diagonalization of the Hamiltonian. The obtained energies are used in the evaluation of the dielectric susceptibility and the nonlinear optical absorption coefficient within a modified two-level approach in a rotating wave approximation. This quantity is investigated as a function of the quantum dot dimensions, the impurity position, the external electric field intensity and the hydrostatic pressure. The results of this research could be important in the design and fabrication of zincblende GaN-quantum-dot-based electro-optical devices.

A Green's function formulation of the k→ ·p→ theory in the presence of spin-orbit interaction and magnetic field: Application to the electronic structure and related properties of w-GaN

NASA Astrophysics Data System (ADS)

Shadangi, Subrat K.; Mishra, Sambit R.; Tripathi, Gouri S.

2018-01-01

We use a Green's function perturbation formalism in the presence of an applied magnetic field and spin-orbit effects in the effective mass representation (EMR). The lack of lattice translational symmetry of the vector potential in the presence of the magnetic field is considered by redefining the Green's function in terms of the Peierls' phase factor. The equation of motion of the Green's function as a function of a magnetic wave vector was solved using perturbation theory, leading to expressions for the effective mass and the g-factor. We study the electronic structure of wurtzite GaN theoretically using the resulting k→ ·π→ method, where k→ is the electronic wave vector and π→ is the relativistic momentum operator by considering the conduction band edge and three valence bands. The k→ ·π→ Hamiltonians for the conduction band edge and the valence bands are diagonalized, considering the conduction band and one valence band at a time. We obtain electron and hole dispersions. Effects of other bands are considered by using perturbation theory. Resulting dispersions agree with the results of other calculations. In order to study the effective mass and the g-factor, we use the eigenvalues and eigenfunctions obtained after the diagonalization. Our results for the effective masses and the g-factors agree fairly well with available theoretical and experimental results, Temperature dependence of both the electronic effective mass and g-factor is studied and trends obtained agree with the existing experimental data.

An exploration of the influence of diagonal dissociation and moderate changes in speed on locomotor parameters in trotting horses.

PubMed

Hobbs, Sarah Jane; Bertram, John E A; Clayton, Hilary M

2016-01-01

Background. Although the trot is described as a diagonal gait, contacts of the diagonal pairs of hooves are not usually perfectly synchronized. Although subtle, the timing dissociation between contacts of each diagonal pair could have consequences on gait dynamics and provide insight into the functional strategies employed. This study explores the mechanical effects of different diagonal dissociation patterns when speed was matched between individuals and how these effects link to moderate, natural changes in trotting speed. We anticipate that hind-first diagonal dissociation at contact increases with speed, diagonal dissociation at contact can reduce collision-based energy losses and predominant dissociation patterns will be evident within individuals. Methods. The study was performed in two parts: in the first 17 horses performed speed-matched trotting trials and in the second, five horses each performed 10 trotting trials that represented a range of individually preferred speeds. Standard motion capture provided kinematic data that were synchronized with ground reaction force (GRF) data from a series of force plates. The data were analyzed further to determine temporal, speed, GRF, postural, mass distribution, moment, and collision dynamics parameters. Results. Fore-first, synchronous, and hind-first dissociations were found in horses trotting at (3.3 m/s ± 10%). In these speed-matched trials, mean centre of pressure (COP) cranio-caudal location differed significantly between the three dissociation categories. The COP moved systematically and significantly (P = .001) from being more caudally located in hind-first dissociation (mean location = 0.41 ± 0.04) through synchronous (0.36 ± 0.02) to a more cranial location in fore-first dissociation (0.32 ± 0.02). Dissociation patterns were found to influence function, posture, and balance parameters. Over a moderate speed range, peak vertical forelimb GRF had a strong relationship with dissociation time (R = .594; P < .01) and speed (R = .789; P < .01), but peak vertical hindlimb GRF did not have a significant relationship with dissociation time (R = .085; P > 0.05) or speed (R = .223; P = .023). Discussion. The results indicate that at moderate speeds individual horses use dissociation patterns that allow them to maintain trunk pitch stability through management of the cranio-caudal location of the COP. During the hoof-ground collisions, reduced mechanical energy losses were found in hind-first dissociations compared to fully synchronous contacts. As speed increased, only forelimb vertical peak force increased so dissociations tended towards hind-first, which shifted the net COP caudally and balanced trunk pitching moments.

Dynamic simulation of concentrated macromolecular solutions with screened long-range hydrodynamic interactions: Algorithm and limitations

PubMed Central

Ando, Tadashi; Chow, Edmond; Skolnick, Jeffrey

2013-01-01

Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N3) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions. PMID:24089734

Study of modal coupling procedures for the shuttle: A matrix method for damping synthesis

NASA Technical Reports Server (NTRS)

Hasselman, T. K.

1972-01-01

The damping method was applied successfully to real structures as well as analytical models. It depends on the ability to determine an appropriate modal damping matrix for each substructure. In the past, modal damping matrices were assumed diagonal for lack of being able to determine the coupling terms which are significant in the general case of nonproportional damping. This problem was overcome by formulating the damped equations of motion as a linear perturbation of the undamped equations for light structural damping. Damped modes are defined as complex vectors derived from the complex frequency response vectors of each substructure and are obtained directly from sinusoidal vibration tests. The damped modes are used to compute first order approximations to the modal damping matrices. The perturbation approach avoids ever having to solve a complex eigenvalue problem.

Propagation of polarised light in bent hi-bi spun fibres

NASA Astrophysics Data System (ADS)

Przhiyalkovsky, Ya V.; Morshnev, S. K.; Starostin, N. I.; Gubin, V. P.

2015-11-01

The evolution of polarisation states (PS's) of broadband light propagating through a bent optical fibre with a helical structure of its refractive index anisotropy (hi-bi spun fibre) has been studied theoretically and experimentally. It has been shown that there exists a coordinate system of PS's in which the differential Jones matrix can be replaced by a diagonal matrix, which allows the polarisation parameters of the output broadband light to be readily calculated with sufficient accuracy. We have derived a formula for evaluating the magneto-optical sensitivity of a bent spun fibre. An approach has been proposed for restoring the degree of polarisation of light in a bent hi-bi spun fibre and, as a consequence, the visibility (contrast) of the interferometer in a current sensor with a sensing element based on the fibre under consideration.

A comparative study of methods for describing non-adiabatic coupling: diabatic representation of the 1Sigma +/1Pi HOH and HHO conical intersections

NASA Astrophysics Data System (ADS)

Dobbyn, Abigail J.; Knowles, Peter J.

A number of established techniques for obtaining diabatic electronic states in small molecules are critically compared for the example of the X and B states in the water molecule, which contribute to the two lowest-energy conical intersections. Integration of the coupling matrix elements and analysis of configuration mixing coefficients both produce reliable diabatic states globally. Methods relying on diagonalization of dipole moment and angular momentum operators are shown to fail in large regions of coordinate space. However, the use of transition angular momentum matrix elements involving the A state, which is degenerate with B at the conical intersections, is successful globally, provided that an appropriate choice of coordinates is made. Long range damping of non-adiabatic coupling to give correct asymptotic mixing angles also is investigated.

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

NASA Astrophysics Data System (ADS)

Alazzawi, Sabina; Lechner, Gandalf

2017-09-01

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.

Magneto-photonic crystal microcavities based on magnetic nanoparticles embedded in Silica matrix

NASA Astrophysics Data System (ADS)

Hocini, Abdesselam; Moukhtari, Riad; Khedrouche, Djamel; Kahlouche, Ahmed; Zamani, Mehdi

2017-02-01

Using the three-dimensional finite difference time domain method (3D FDTD) with perfectly matched layers (PML), optical and magneto-optical properties of two-dimensional magneto-photonic crystals micro-cavity is studied. This micro-cavity is fabricated by SiO2/ZrO2 or SiO2/TiO2 matrix doped with magnetic nanoparticles, in which the refractive index varied in the range of 1.51-1.58. We demonstrate that the Q factor for the designed cavity increases as the refractive index increases, and we find that the Q factor decreases as the volume fraction VF% due to off-diagonal elements increases. These magnetic microcavities may serve as a fundamental structure in a variety of ultra compact magneto photonic devices such as optical isolators, circulators and modulators in the future.

Predictions for the Dirac C P -violating phase from sum rules

NASA Astrophysics Data System (ADS)

Delgadillo, Luis A.; Everett, Lisa L.; Ramos, Raymundo; Stuart, Alexander J.

2018-05-01

We explore the implications of recent results relating the Dirac C P -violating phase to predicted and measured leptonic mixing angles within a standard set of theoretical scenarios in which charged lepton corrections are responsible for generating a nonzero value of the reactor mixing angle. We employ a full set of leptonic sum rules as required by the unitarity of the lepton mixing matrix, which can be reduced to predictions for the observable mixing angles and the Dirac C P -violating phase in terms of model parameters. These sum rules are investigated within a given set of theoretical scenarios for the neutrino sector diagonalization matrix for several known classes of charged lepton corrections. The results provide explicit maps of the allowed model parameter space within each given scenario and assumed form of charged lepton perturbations.

Eigenvalue computations with the QUAD4 consistent-mass matrix

NASA Technical Reports Server (NTRS)

Butler, Thomas A.

1990-01-01

The NASTRAN user has the option of using either a lumped-mass matrix or a consistent- (coupled-) mass matrix with the QUAD4 shell finite element. At the Sixteenth NASTRAN Users' Colloquium (1988), Melvyn Marcus and associates of the David Taylor Research Center summarized a study comparing the results of the QUAD4 element with results of other NASTRAN shell elements for a cylindrical-shell modal analysis. Results of this study, in which both the lumped-and consistent-mass matrix formulations were used, implied that the consistent-mass matrix yielded poor results. In an effort to further evaluate the consistent-mass matrix, a study was performed using both a cylindrical-shell geometry and a flat-plate geometry. Modal parameters were extracted for several modes for both geometries leading to some significant conclusions. First, there do not appear to be any fundamental errors associated with the consistent-mass matrix. However, its accuracy is quite different for the two different geometries studied. The consistent-mass matrix yields better results for the flat-plate geometry and the lumped-mass matrix seems to be the better choice for cylindrical-shell geometries.

The Quantum-to-Classical Transition in Strongly Interacting Nanoscale Systems

NASA Astrophysics Data System (ADS)

Benatov, Latchezar Latchezarov

This thesis comprises two separate but related studies, dealing with two strongly interacting nanoscale systems on the border between the quantum and classical domains. In Part 1, we use a Born-Markov approximated master equation approach to study the symmetrized-in-frequency current noise spectrum and the oscillator steady state of a nanoelectromechanical system where a nanoscale resonator is coupled linearly via its momentum to a quantum point contact (QPC). Our current noise spectra exhibit clear signatures of the quantum correlations between the QPC current and the back-action force on the oscillator at a value of the relative tunneling phase where such correlations are expected to be maximized. We also show that the steady state of the oscillator obeys a classical Fokker-Planck equation, but can experience thermomechanical noise squeezing in the presence of a momentum-coupled detector bath and a position-coupled environmental bath. Besides, the full master equation clearly shows that half of the detector back-action is correlated with electron tunneling, indicating a departure from the model of the detector as an effective bath and suggesting that a future calculation valid at lower bias voltage, stronger tunneling and/or stronger coupling might reveal interesting quantum effects in the oscillator dynamics. In the second part of the thesis, we study the subsystem dynamics and thermalization of an oscillator-spin star model, where a nanomechanical resonator is coupled to a few two-level systems (TLS's). We use a fourth-order Runge-Kutta numerical algorithm to integrate the Schrodinger equation for the system and obtain our results. We find that the oscillator reaches a Boltzmann steady state when the TLS bath is initially in a thermal state at a temperature higher than the oscillator phonon energy. This occurs in both chaotic and integrable systems, and despite the small number of spins (only six) and the lack of couplings between them. At the same time, pure initial states do not thermalize well in our system, indicating that mixed state thermalization stems from the thermal nature of the initial bath state. Under the influence of a thermal TLS bath, oscillator Fock states decay in an approximately exponential manner, but there is also a concave-down trend at very early times, possibly indicative of Gaussian decay. In the case of initial Fock state superpositions, the diagonal density matrix element behaves very similarly to single initial Fock states, while the off-diagonal matrix element decays sinusoidally with an exponentially decreasing amplitude. The off-diagonal decay time is much smaller then the diagonal one, indicating that superposition states decohere much faster than they decay. Both decay times decrease with increasing Fock state number, but more slowly than the 1/n dependence seen in the presence of an external ohmic bath.

Low-rank matrix decomposition and spatio-temporal sparse recovery for STAP radar

DOE PAGES

Sen, Satyabrata

2015-08-04

We develop space-time adaptive processing (STAP) methods by leveraging the advantages of sparse signal processing techniques in order to detect a slowly-moving target. We observe that the inherent sparse characteristics of a STAP problem can be formulated as the low-rankness of clutter covariance matrix when compared to the total adaptive degrees-of-freedom, and also as the sparse interference spectrum on the spatio-temporal domain. By exploiting these sparse properties, we propose two approaches for estimating the interference covariance matrix. In the first approach, we consider a constrained matrix rank minimization problem (RMP) to decompose the sample covariance matrix into a low-rank positivemore » semidefinite and a diagonal matrix. The solution of RMP is obtained by applying the trace minimization technique and the singular value decomposition with matrix shrinkage operator. Our second approach deals with the atomic norm minimization problem to recover the clutter response-vector that has a sparse support on the spatio-temporal plane. We use convex relaxation based standard sparse-recovery techniques to find the solutions. With extensive numerical examples, we demonstrate the performances of proposed STAP approaches with respect to both the ideal and practical scenarios, involving Doppler-ambiguous clutter ridges, spatial and temporal decorrelation effects. As a result, the low-rank matrix decomposition based solution requires secondary measurements as many as twice the clutter rank to attain a near-ideal STAP performance; whereas the spatio-temporal sparsity based approach needs a considerably small number of secondary data.« less

Diffusion of multi-isotopic chemical species in molten silicates

NASA Astrophysics Data System (ADS)

Watkins, James M.; Liang, Yan; Richter, Frank; Ryerson, Frederick J.; DePaolo, Donald J.

2014-08-01

Diffusion experiments in a simplified Na2O-CaO-SiO2 liquid system are used to develop a general formulation for the fractionation of Ca isotopes during liquid-phase diffusion. Although chemical diffusion is a well-studied process, the mathematical description of the effects of diffusion on the separate isotopes of a chemical element is surprisingly underdeveloped and uncertain. Kinetic theory predicts a mass dependence on isotopic mobility, but it is unknown how this translates into a mass dependence on effective binary diffusion coefficients, or more generally, the chemical diffusion coefficients that are housed in a multicomponent diffusion matrix. Our experiments are designed to measure Ca mobility, effective binary diffusion coefficients, the multicomponent diffusion matrix, and the effects of chemical diffusion on Ca isotopes in a liquid of single composition. We carried out two chemical diffusion experiments and one self-diffusion experiment, all at 1250 °C and 0.7 GPa and using a bulk composition for which other information is available from the literature. The self-diffusion experiment is used to determine the mobility of Ca in the absence of diffusive fluxes of other liquid components. The chemical diffusion experiments are designed to determine the effect on Ca isotope fractionation of changing the counter-diffusing component from fast-diffusing Na2O to slow-diffusing SiO2. When Na2O is the main counter-diffusing species, CaO diffusion is fast and larger Ca isotopic effects are generated. When SiO2 is the main counter-diffusing species, CaO diffusion is slow and smaller Ca isotopic effects are observed. In both experiments, the liquid is initially isotopically homogeneous, and during the experiment Ca isotopes become fractionated by diffusion. The results are used as a test of a new general expression for the diffusion of isotopes in a multicomponent liquid system that accounts for both self diffusion and the effects of counter-diffusing species. Our results show that (1) diffusive isotopic fractionations depend on the direction of diffusion in composition space, (2) diffusive isotopic fractionations scale with effective binary diffusion coefficient, as previously noted by Watkins et al. (2011), (3) self-diffusion is not decoupled from chemical diffusion, (4) self diffusion can be faster than or slower than chemical diffusion and (5) off-diagonal terms in the chemical diffusion matrix have isotopic mass-dependence. The results imply that relatively large isotopic fractionations can be generated by multicomponent diffusion even in the absence of large concentration gradients of the diffusing element. The new formulations for isotope diffusion can be tested with further experimentation and provide an improved framework for interpreting mass-dependent isotopic variations in natural liquids.

On the Maximum Storage Capacity of the Hopfield Model

PubMed Central

Folli, Viola; Leonetti, Marco; Ruocco, Giancarlo

2017-01-01

Recurrent neural networks (RNN) have traditionally been of great interest for their capacity to store memories. In past years, several works have been devoted to determine the maximum storage capacity of RNN, especially for the case of the Hopfield network, the most popular kind of RNN. Analyzing the thermodynamic limit of the statistical properties of the Hamiltonian corresponding to the Hopfield neural network, it has been shown in the literature that the retrieval errors diverge when the number of stored memory patterns (P) exceeds a fraction (≈ 14%) of the network size N. In this paper, we study the storage performance of a generalized Hopfield model, where the diagonal elements of the connection matrix are allowed to be different from zero. We investigate this model at finite N. We give an analytical expression for the number of retrieval errors and show that, by increasing the number of stored patterns over a certain threshold, the errors start to decrease and reach values below unit for P ≫ N. We demonstrate that the strongest trade-off between efficiency and effectiveness relies on the number of patterns (P) that are stored in the network by appropriately fixing the connection weights. When P≫N and the diagonal elements of the adjacency matrix are not forced to be zero, the optimal storage capacity is obtained with a number of stored memories much larger than previously reported. This theory paves the way to the design of RNN with high storage capacity and able to retrieve the desired pattern without distortions. PMID:28119595

The case for mixed dark matter from sterile neutrinos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lello, Louis; Boyanovsky, Daniel, E-mail: lal81@pitt.edu, E-mail: boyan@pitt.edu

2016-06-01

Sterile neutrinos are SU(2) singlets that mix with active neutrinos via a mass matrix, its diagonalization leads to mass eigenstates that couple via standard model vertices. We study the cosmological production of heavy neutrinos via standard model charged and neutral current vertices under a minimal set of assumptions: i) the mass basis contains a hierarchy of heavy neutrinos , ii) these have very small mixing angles with the active (flavor) neutrinos, iii) standard model particles, including light (active-like) neutrinos are in thermal equilibrium. If kinematically allowed, the same weak interaction processes that produce active-like neutrinos also produce the heavier species.more » We introduce the quantum kinetic equations that describe their production, freeze out and decay and discuss the various processes that lead to their production in a wide range of temperatures assessing their feasibility as dark matter candidates. The final distribution function at freeze-out is a mixture of the result of the various production processes. We identify processes in which finite temperature collective excitations may lead to the production of the heavy species. As a specific example, we consider the production of heavy neutrinos in the mass range M {sub h} ∼< 140 MeV from pion decay shortly after the QCD crossover including finite temperature corrections to the pion form factors and mass. We consider the different decay channels that allow for the production of heavy neutrinos showing that their frozen distribution functions exhibit effects from ''kinematic entanglement'' and argue for their viability as mixed dark matter candidates. We discuss abundance, phase space density and stability constraints and argue that heavy neutrinos with lifetime τ> 1/ H {sub 0} freeze out of local thermal equilibrium, and conjecture that those with lifetimes τ || 1/ H {sub 0} may undergo cascade decay into lighter DM candidates and/or inject non-LTE neutrinos into the cosmic neutrino background. We provide a comparison with non-resonant production via active-sterile mixing.« less

The Reverse Time Migration technique coupled with Interior Penalty Discontinuous Galerkin method.

NASA Astrophysics Data System (ADS)

Baldassari, C.; Barucq, H.; Calandra, H.; Denel, B.; Diaz, J.

2009-04-01

Seismic imaging is based on the seismic reflection method which produces an image of the subsurface from reflected waves recordings by using a tomography process and seismic migration is the industrial standard to improve the quality of the images. The migration process consists in replacing the recorded wavefields at their actual place by using various mathematical and numerical methods but each of them follows the same schedule, according to the pioneering idea of Claerbout: numerical propagation of the source function (propagation) and of the recorded wavefields (retropropagation) and next, construction of the image by applying an imaging condition. The retropropagation step can be realized accouting for the time reversibility of the wave equation and the resulting algorithm is currently called Reverse Time Migration (RTM). To be efficient, especially in three dimensional domain, the RTM requires the solution of the full wave equation by fast numerical methods. Finite element methods are considered as the best discretization method for solving the wave equation, even if they lead to the solution of huge systems with several millions of degrees of freedom, since they use meshes adapted to the domain topography and the boundary conditions are naturally taken into account in the variational formulation. Among the different finite element families, the spectral element one (SEM) is very interesting because it leads to a diagonal mass matrix which dramatically reduces the cost of the numerical computation. Moreover this method is very accurate since it allows the use of high order finite elements. However, SEM uses meshes of the domain made of quadrangles in 2D or hexaedra in 3D which are difficult to compute and not always suitable for complex topographies. Recently, Grote et al. applied the IPDG (Interior Penalty Discontinuous Galerkin) method to the wave equation. This approach is very interesting since it relies on meshes with triangles in 2D or tetrahedra in 3D, which allows to handle the topography of the domain very accurately. Moreover, the fact that the resulting mass matrix is block-diagonal and that IPDG is compatible with the use of high-order finite element may let us suppose that its performances are similar to the ones of the SEM. In this presentation, we study the performances of IDPG through numerical comparisons with the SEM in 1D and 2D. We compare in particular the accuracy of the solutions obtained by the two methods with various order of approximation and the computational burden of the algorithms. The conclusion is IPDG and SEM perform similarly when considering low order finite elements while IPDG outperforms SEM in case of high order finite elements. Next we illustrate the impact of IPDG on the RTM, first through a simple configuration test (two-layered medium), then through realistic industrial applications in 2D.

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

DOE PAGES

Negre, Christian F. A; Mniszewski, Susan M.; Cawkwell, Marc Jon; ...

2016-06-06

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance ismore » obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.« less

Thouless energy and multifractality across the many-body localization transition

NASA Astrophysics Data System (ADS)

Serbyn, Maksym; Papić, Z.; Abanin, Dmitry A.

2017-09-01

Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across this transition in two different models of disordered spin chains. We show that the behavior of matrix elements can be used to characterize the breakdown of thermalization and to extract the many-body Thouless energy. We find that upon increasing the disorder strength the system enters a critical region around the many-body localization transition. The properties of the system in this region are: (i) the Thouless energy becomes smaller than the level spacing, (ii) the matrix elements show critical dependence on the energy difference, and (iii) the matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. This critical region decreases with the system size, which we interpret as evidence for a diverging correlation length at the many-body localization transition. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values and shed light on the critical behavior near the many-body localization transition.

A similarity measure for partially folded proteins: application to unfolded and native-like conformational fluctuations

NASA Astrophysics Data System (ADS)

Larios, Edgar; Yang, Wei Y.; Schulten, K.; Gruebele, M.

2004-12-01

Computing the root-mean-square deviation (RMSD) of a partially folded protein structure from the folded state requires the two structures to be translationally and rotationally aligned. We examine the constraint matrix L that preserves orthogonality of the rotation matrix during minimization of the RMSD. L is proportional to the sensitivity of the RMSD to the rotational alignment matrix. Its trace yields an isotropic reaction coordinate, while its off-diagonal matrix elements are related to the moment of inertia derivative tensor that encodes anisotropic information about the structure. We use L to compare λ-repressor fragment 6-85 (λ 6-85) to several partially folded structures obtained from molecular dynamics simulation (MD), and find that L as a reaction coordinate indeed encodes some information about protein topology. We also apply C α RMSD, L and tryptophan sidechain mobility as criteria for native state structural fluctuations of several λ 6-85 mutants. The mutants' denaturation curves and fluorescence quenching are measured experimentally for comparison. The results are in accord with a recent proposal that structural fluctuations near the chromophore can induce increased native state fluorescence or hyperfluorescence during unfolding of proteins.

A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities

NASA Astrophysics Data System (ADS)

Bosela, P. A.; Fertis, D. G.; Shaker, F. J.

1992-09-01

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.

An efficient basis set representation for calculating electrons in molecules

DOE PAGES

Jones, Jeremiah R.; Rouet, Francois -Henry; Lawler, Keith V.; ...

2016-04-27

The method of McCurdy, Baertschy, and Rescigno, is generalised to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. Themore » calculation of contracted two-electron matrix elements among orbitals requires only O( Nlog (N)) multiplication operations, not O( N 4), where N is the number of basis functions; N = n 3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionisation potentials are reported for 1- (He +, H + 2), 2- (H 2, He), 10- (CH 4), and 56-electron (C 8H 8) systems.« less

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

NASA Astrophysics Data System (ADS)

Mascarenhas, Eduardo; Flayac, Hugo; Savona, Vincenzo

2015-08-01

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Determining Diagonal Branches in Mine Ventilation Networks

NASA Astrophysics Data System (ADS)

Krach, Andrzej

2014-12-01

The present paper discusses determining diagonal branches in a mine ventilation network by means of a method based on the relationship A⊗ PT(k, l) = M, which states that the nodal-branch incidence matrix A, modulo-2 multiplied by the transposed path matrix PT(k, l ) from node no. k to node no. l, yields the matrix M where all the elements in rows k and l - corresponding to the start and the end node - are 1, and where the elements in the remaining rows are 0, exclusively. If a row of the matrix M is to contain only "0" elements, the following condition has to be fulfilled: after multiplying the elements of a row of the matrix A by the elements of a column of the matrix PT(k, l), i.e. by the elements of a proper row of the matrix P(k, l ), the result row must display only "0" elements or an even number of "1" entries, as only such a number of "1" entries yields 0 when modulo-2 added - and since the rows of the matrix A correspond to the graph nodes, and the path nodes level is 2 (apart from the nodes k and l, whose level is 1), then the number of "1" elements in a row has to be 0 or 2. If, in turn, the rows k and l of the matrix M are to contain only "1" elements, the following condition has to be fulfilled: after multiplying the elements of the row k or l of the matrix A by the elements of a column of the matrix PT(k, l), the result row must display an uneven number of "1" entries, as only such a number of "1" entries yields 1 when modulo-2 added - and since the rows of the matrix A correspond to the graph nodes, and the level of the i and j path nodes is 1, then the number of "1" elements in a row has to be 1. The process of determining diagonal branches by means of this method was demonstrated using the example of a simple ventilation network with two upcast shafts and one downcast shaft. W artykule przedstawiono metodę wyznaczania bocznic przekątnych w sieci wentylacyjnej kopalni metodą bazującą na zależności A⊗PT(k, l) = M, która podaje, że macierz incydencji węzłowo bocznicowej A pomnożona modulo 2 przez transponowaną macierz ścieżek PT(k, l) od węzła nr k do węzła nr l daje w wyniku macierz M o takich własnościach że ma same jedynki w wierszach k i l, odpowiadającym węzłom początkowemu i końcowemu i same zera w pozostałych wierszach. Warunkiem na to, aby w wierszu macierzy M były same zera jest aby po pomnożeniu elementów wiersza macierzy A przez elementy kolumny macierzy PT(k, l), czyli przez elementy odpowiedniego wiersza macierzy P(k, l), w wierszu wynikowym były same zera lub parzysta liczba jedynek, ponieważ tylko taka liczba jedynek zsumowana modulo 2 daje w wyniku 0, a ponieważ wiersze macierzy A odpowiadają węzłom grafu, a węzły ścieżki są stopnia 2 (oprócz węzłów k i l, które są stopnia 1), to liczba jedynek w wierszu musi być równa 0 lub 2. Natomiast warunkiem na to, aby w wierszach k i l macierzy M były same jedynki jest aby po pomnożeniu elementów wiersza k lub l macierzy A przez elementy kolumny macierzy PT(k, l) w wierszu wynikowym była nieparzysta liczba jedynek, ponieważ tylko taka liczba jedynek zsumowana modulo 2 daje w wyniku 1, a ponieważ wiersze macierzy A odpowiadają węzłom grafu, a węzły k i j ścieżki są stopnia 1, to liczba jedynek w wierszu musi być równa 1. Wyznaczanie bocznic przekątnych tą metodą pokazano na przykładzie prostej sieci wentylacyjnej z dwoma szybami wydechowymi i jednym wdechowym.

Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: Correlated neutrino trajectories

NASA Astrophysics Data System (ADS)

Duan, Huaiyu; Fuller, George M.; Carlson, J.; Qian, Yong-Zhong

2006-11-01

We present results of large-scale numerical simulations of the evolution of neutrino and antineutrino flavors in the region above the late-time post-supernova-explosion proto-neutron star. Our calculations are the first to allow explicit flavor evolution histories on different neutrino trajectories and to self-consistently couple flavor development on these trajectories through forward scattering-induced quantum coupling. Employing the atmospheric-scale neutrino mass-squared difference (|δm2|≃3×10-3eV2) and values of θ13 allowed by current bounds, we find transformation of neutrino and antineutrino flavors over broad ranges of energy and luminosity in roughly the “bi-polar” collective mode. We find that this large-scale flavor conversion, largely driven by the flavor off-diagonal neutrino-neutrino forward scattering potential, sets in much closer to the proto-neutron star than simple estimates based on flavor-diagonal potentials and Mikheyev-Smirnov-Wolfenstein evolution would indicate. In turn, this suggests that models of r-process nucleosynthesis sited in the neutrino-driven wind could be affected substantially by active-active neutrino flavor mixing, even with the small measured neutrino mass-squared differences.

Probing coherence aspects of adiabatic quantum computation and control.

PubMed

Goswami, Debabrata

2007-09-28

Quantum interference between multiple excitation pathways can be used to cancel the couplings to the unwanted, nonradiative channels resulting in robustly controlling decoherence through adiabatic coherent control approaches. We propose a useful quantification of the two-level character in a multilevel system by considering the evolution of the coherent character in the quantum system as represented by the off-diagonal density matrix elements, which switches from real to imaginary as the excitation process changes from being resonant to completely adiabatic. Such counterintuitive results can be explained in terms of continuous population exchange in comparison to no population exchange under the adiabatic condition.

Investigating decoherence in a simple system

NASA Technical Reports Server (NTRS)

Albrecht, Andreas

1991-01-01

The results of some simple calculations designed to study quantum decoherence are presented. The physics of quantum decoherence are briefly reviewed, and a very simple 'toy' model is analyzed. Exact solutions are found using numerical techniques. The type of incoherence exhibited by the model can be changed by varying a coupling strength. The author explains why the conventional approach to studying decoherence by checking the diagonality of the density matrix is not always adequate. Two other approaches, the decoherence functional and the Schmidt paths approach, are applied to the toy model and contrasted to each other. Possible problems with each are discussed.

Application of Financial Risk-reward Theory to Link and Network Optimization

DTIC Science & Technology

2011-10-01

OFDM systems the matrices V k and U k are Fourier matrices which diagonalize a circulant or block-circulant matrix Hk [18]. In multi-antenna systems...probability α=Pr(η r <=t) Figure 13: Mean link spectral efficiency as a function of target link spectral efficiency ηt and outage probability ζ in a MIMO ...in a MIMO channel. Distribution A: Approved for public release; distribution is unlimited. 41 (75) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8

Orthogonal bases of invariants in tensor models

NASA Astrophysics Data System (ADS)

Diaz, Pablo; Rey, Soo-Jong

2018-02-01

Representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry G d = U( N 1) ⊗ · · · ⊗ U( N d ) . We show that there are two natural ways of counting invariants, one for arbitrary G d and another valid for large rank of G d . We construct basis of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of G d diagonalizes two-point function. It is analogous to the restricted Schur basis used in matrix models. We comment on future directions for investigation.

Z H η vertex in the simplest little Higgs model

NASA Astrophysics Data System (ADS)

He, Shi-Ping; Mao, Ying-nan; Zhang, Chen; Zhu, Shou-hua

2018-04-01

The issue of deriving Z H η vertex in the simplest little Higgs (SLH) model is revisited. Special attention is paid to the treatment of noncanonically-normalized scalar kinetic matrix and vector-scalar two-point transitions. We elucidate a general procedure to diagonalize a general vector-scalar system in gauge theories and apply it to the case of SLH. The resultant Z H η vertex is found to be different from those which have already existed in the literature for a long time. We also present an understanding of this issue from an effective field theory viewpoint.

Fetal ECG extraction using independent component analysis by Jade approach

NASA Astrophysics Data System (ADS)

Giraldo-Guzmán, Jader; Contreras-Ortiz, Sonia H.; Lasprilla, Gloria Isabel Bautista; Kotas, Marian

2017-11-01

Fetal ECG monitoring is a useful method to assess the fetus health and detect abnormal conditions. In this paper we propose an approach to extract fetal ECG from abdomen and chest signals using independent component analysis based on the joint approximate diagonalization of eigenmatrices approach. The JADE approach avoids redundancy, what reduces matrix dimension and computational costs. Signals were filtered with a high pass filter to eliminate low frequency noise. Several levels of decomposition were tested until the fetal ECG was recognized in one of the separated sources output. The proposed method shows fast and good performance.

The Masked Sample Covariance Estimator: An Analysis via the Matrix Laplace Transform

DTIC Science & Technology

2012-02-01

Variables: Suppose that we divide the stock market into disjoint sectors, and we would like to study the interactions among the monthly returns for...vector to conform with the market sectors, and we estimate only the entries in the diagonal blocks. Spatial or Temporal Localization: A simple random model...eαW1A c ] ≤ 4p e−B/2κ 2 = 1 n . Introduce this expression into (4.11) to conclude that E[exp(2θεM xx∗)1A c ] 4 1 n · I. (4.17) 20 RICHARD Y. CHEN

Diagonal Born-Oppenheimer correction for coupled-cluster wave-functions

NASA Astrophysics Data System (ADS)

Shamasundar, K. R.

2018-06-01

We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. This is shown to lead to a biorthogonal version of SOS formula with similar properties. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. One of this agrees with the formula used in the current literature. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified.

CPsuperH2.0: An improved computational tool for Higgs phenomenology in the MSSM with explicit CP violation

NASA Astrophysics Data System (ADS)

Lee, J. S.; Carena, M.; Ellis, J.; Pilaftsis, A.; Wagner, C. E. M.

2009-02-01

We describe the Fortran code CPsuperH2.0, which contains several improvements and extensions of its predecessor CPsuperH. It implements improved calculations of the Higgs-boson pole masses, notably a full treatment of the 4×4 neutral Higgs propagator matrix including the Goldstone boson and a more complete treatment of threshold effects in self-energies and Yukawa couplings, improved treatments of two-body Higgs decays, some important three-body decays, and two-loop Higgs-mediated contributions to electric dipole moments. CPsuperH2.0 also implements an integrated treatment of several B-meson observables, including the branching ratios of B→μμ, B→ττ, B→τν, B→Xγ and the latter's CP-violating asymmetry A, and the supersymmetric contributions to the Bs,d0-B¯s,d0 mass differences. These additions make CPsuperH2.0 an attractive integrated tool for analyzing supersymmetric CP and flavour physics as well as searches for new physics at high-energy colliders such as the Tevatron, LHC and linear colliders. Program summaryProgram title: CPsuperH2.0 Catalogue identifier: ADSR_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 13 290 No. of bytes in distributed program, including test data, etc.: 89 540 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC running under Linux and computers in Unix environment Operating system: Linux RAM: 32 Mbytes Classification: 11.1 Catalogue identifier of the previous version: ADSR_v1_0 Journal reference of the previous version: CPC 156 (2004) 283 Does the new version supersede the previous version?: Yes Nature of problem: The calculations of mass spectrum, decay widths and branching ratios of the neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model with explicit CP violation have been improved. The program is based on recent renormalization-group-improved diagrammatic calculations that include dominant higher-order logarithmic and threshold corrections, b-quark Yukawa-coupling resummation effects and improved treatment of Higgs-boson pole-mass shifts. The couplings of the Higgs bosons to the Standard Model gauge bosons and fermions, to their supersymmetric partners and all the trilinear and quartic Higgs-boson self-couplings are also calculated. The new implementations include a full treatment of the 4×4(2×2) neutral (charged) Higgs propagator matrix together with the center-of-mass dependent Higgs-boson couplings to gluons and photons, two-loop Higgs-mediated contributions to electric dipole moments, and an integrated treatment of several B-meson observables. Solution method: One-dimensional numerical integration for several Higgs-decay modes, iterative treatment of the threshold corrections and Higgs-boson pole masses, and the numerical diagonalization of the neutralino mass matrix. Reasons for new version: Mainly to provide a coherent numerical framework which calculates consistently observables for both low- and high-energy experiments. Summary of revisions: Improved treatment of Higgs-boson masses and propagators. Improved treatment of Higgs-boson couplings and decays. Higgs-mediated two-loop electric dipole moments. B-meson observables. Running time: Less than 0.1 seconds. The program may be obtained from http://www.hep.man.ac.uk/u/jslee/CPsuperH.html.

Tunneling splitting in double-proton transfer: direct diagonalization results for porphycene.

PubMed

Smedarchina, Zorka; Siebrand, Willem; Fernández-Ramos, Antonio

2014-11-07

Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans - trans path; a corresponding cis - cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian.

Propagation of polarised light in bent hi-bi spun fibres

DOE Office of Scientific and Technical Information (OSTI.GOV)

Przhiyalkovsky, Ya V; Morshnev, S K; Starostin, N I

The evolution of polarisation states (PS's) of broadband light propagating through a bent optical fibre with a helical structure of its refractive index anisotropy (hi-bi spun fibre) has been studied theoretically and experimentally. It has been shown that there exists a coordinate system of PS's in which the differential Jones matrix can be replaced by a diagonal matrix, which allows the polarisation parameters of the output broadband light to be readily calculated with sufficient accuracy. We have derived a formula for evaluating the magneto-optical sensitivity of a bent spun fibre. An approach has been proposed for restoring the degree ofmore » polarisation of light in a bent hi-bi spun fibre and, as a consequence, the visibility (contrast) of the interferometer in a current sensor with a sensing element based on the fibre under consideration. (optical fibres)« less

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

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.

Low-temperature anomalies in the dynamic elastic moduli of cubic AIIBVI crystals with 3d-transition metal impurities

NASA Astrophysics Data System (ADS)

Lonchakov, A. T.

2011-04-01

A negative paramagnetic contribution to the dynamic elastic moduli is identified in AIIBVI:3d wide band-gap compounds for the first time. It appears as a paramagnetic elastic, or, briefly, paraelastic, susceptibility. These compounds are found to have a linear temperature dependence for the inverse paraelastic susceptibility. This is explained by a contribution from the diagonal matrix elements of the orbit-lattice interaction operators in the energy of the spin-orbital states of the 3d-ion as a function of applied stress (by analogy with the Curie contribution to the magnetic susceptibility). The inverse paraelastic susceptibility of AIIBVI crystals containing non-Kramers 3d-ions is found to deviate from linearity with decreasing temperature and reaches saturation. This effect is explained by a contribution from nondiagonal matrix elements (analogous to the well known van Vleck contribution to the magnetic susceptibility of paramagnets).

Design of three-well indirect pumping terahertz quantum cascade lasers for high optical gain based on nonequilibrium Green's function analysis

NASA Astrophysics Data System (ADS)

Liu, Tao; Kubis, Tillmann; Jie Wang, Qi; Klimeck, Gerhard

2012-03-01

The nonequilibrium Green's function approach is applied to the design of three-well indirect pumping terahertz (THz) quantum cascade lasers (QCLs) based on a resonant phonon depopulation scheme. The effects of the anticrossing of the injector states and the dipole matrix element of the laser levels on the optical gain of THz QCLs are studied. The results show that a design that results in a more pronounced anticrossing of the injector states will achieve a higher optical gain in the indirect pumping scheme compared to the traditional resonant-tunneling injection scheme. This offers in general a more efficient coherent resonant-tunneling transport of electrons in the indirect pumping scheme. It is also shown that, for operating temperatures below 200 K and low lasing frequencies, larger dipole matrix elements, i.e., vertical optical transitions, offer a higher optical gain. In contrast, in the case of high lasing frequencies, smaller dipole matrix elements, i.e., diagonal optical transitions are better for achieving a higher optical gain.

Quadrupole collectivity in 42Ca from low-energy Coulomb excitation with AGATA

NASA Astrophysics Data System (ADS)

Hadyńska-Klęk, K.; Napiorkowski, P. J.; Zielińska, M.; Srebrny, J.; Maj, A.; Azaiez, F.; Valiente Dobón, J. J.; Kicińska-Habior, M.; Nowacki, F.; Naïdja, H.; Bounthong, B.; Rodríguez, T. R.; de Angelis, G.; Abraham, T.; Anil Kumar, G.; Bazzacco, D.; Bellato, M.; Bortolato, D.; Bednarczyk, P.; Benzoni, G.; Berti, L.; Birkenbach, B.; Bruyneel, B.; Brambilla, S.; Camera, F.; Chavas, J.; Cederwall, B.; Charles, L.; Ciemała, M.; Cocconi, P.; Coleman-Smith, P.; Colombo, A.; Corsi, A.; Crespi, F. C. L.; Cullen, D. M.; Czermak, A.; Désesquelles, P.; Doherty, D. T.; Dulny, B.; Eberth, J.; Farnea, E.; Fornal, B.; Franchoo, S.; Gadea, A.; Giaz, A.; Gottardo, A.; Grave, X.; Grębosz, J.; Görgen, A.; Gulmini, M.; Habermann, T.; Hess, H.; Isocrate, R.; Iwanicki, J.; Jaworski, G.; Judson, D. S.; Jungclaus, A.; Karkour, N.; Kmiecik, M.; Karpiński, D.; Kisieliński, M.; Kondratyev, N.; Korichi, A.; Komorowska, M.; Kowalczyk, M.; Korten, W.; Krzysiek, M.; Lehaut, G.; Leoni, S.; Ljungvall, J.; Lopez-Martens, A.; Lunardi, S.; Maron, G.; Mazurek, K.; Menegazzo, R.; Mengoni, D.; Merchán, E.; Męczyński, W.; Michelagnoli, C.; Million, B.; Myalski, S.; Napoli, D. R.; Niikura, M.; Obertelli, A.; Özmen, S. F.; Palacz, M.; Próchniak, L.; Pullia, A.; Quintana, B.; Rampazzo, G.; Recchia, F.; Redon, N.; Reiter, P.; Rosso, D.; Rusek, K.; Sahin, E.; Salsac, M.-D.; Söderström, P.-A.; Stefan, I.; Stézowski, O.; Styczeń, J.; Theisen, Ch.; Toniolo, N.; Ur, C. A.; Wadsworth, R.; Wasilewska, B.; Wiens, A.; Wood, J. L.; Wrzosek-Lipska, K.; Ziębliński, M.

2018-02-01

A Coulomb-excitation experiment to study electromagnetic properties of 42Ca was performed using a 170-MeV calcium beam from the TANDEM XPU facility at INFN Laboratori Nazionali di Legnaro. γ rays from excited states in 42Ca were measured with the AGATA spectrometer. The magnitudes and relative signs of ten E 2 matrix elements coupling six low-lying states in 42Ca, including the diagonal E 2 matrix elements of 21+ and 22+ states, were determined using the least-squares code gosia. The obtained set of reduced E 2 matrix elements was analyzed using the quadrupole sum rule method and yielded overall quadrupole deformation for 01,2 + and 21,2 + states, as well as triaxiality for 01,2 + states, establishing the coexistence of a weakly deformed ground-state band and highly deformed slightly triaxial sideband in 42Ca. The experimental results were compared with the state-of-the-art large-scale shell-model and beyond-mean-field calculations, which reproduce well the general picture of shape coexistence in 42Ca.

Reduced-Density-Matrix Description of Decoherence and Relaxation Processes for Electron-Spin Systems

NASA Astrophysics Data System (ADS)

Jacobs, Verne

2017-04-01

Electron-spin systems are investigated using a reduced-density-matrix description. Applications of interest include trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are self-consistently developed. The general non-perturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. Particular attention is given to decoherence and relaxation processes, as well as spectral-line broadening phenomena, that are induced by interactions with photons, phonons, nuclear spins, and external electric and magnetic fields. These processes are treated either as coherent interactions or as environmental interactions. The environmental interactions are incorporated by means of the general expressions derived for the time-domain and frequency-domain Liouville-space self-energy operators, for which the tetradic-matrix elements are explicitly evaluated in the diagonal-resolvent, lowest-order, and Markov (short-memory time) approximations. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.

Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Alaghband, Gita; Jordan, Harry F.

1989-01-01

It is shown that in sparse matrices arising from electronic circuits, it is possible to do computations on many diagonal elements simultaneously. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A novel heuristic algorithm is presented that combines the idea of an order-compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set for reducing the matrix is generated and selected on the basis of a minimum Markowitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Thus, it is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices using the HEP multiprocessor (Kowalik, 1985) are presented and analyzed.

Effective vortex mass from microscopic theory

NASA Astrophysics Data System (ADS)

Han, Jung Hoon; Kim, June Seo; Kim, Min Jae; Ao, Ping

2005-03-01

We calculate the effective mass of a single quantized vortex in the Bardeen-Cooper-Schrieffer superconductor at finite temperature. Based on effective action approach, we arrive at the effective mass of a vortex as integral of the spectral function J(ω) divided by ω3 over frequency. The spectral function is given in terms of the quantum-mechanical transition elements of the gradient of the Hamiltonian between two Bogoliubov-deGennes (BdG) eigenstates. Based on self-consistent numerical diagonalization of the BdG equation we find that the effective mass per unit length of vortex at zero temperature is of order m(kfξ0)2 ( kf=Fermi momentum, ξ0=coherence length), essentially equaling the electron mass displaced within the coherence length from the vortex core. Transitions between the core states are responsible for most of the mass. The mass reaches a maximum value at T≈0.5Tc and decreases continuously to zero at Tc .

Atomistic absorption spectra and non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model

NASA Astrophysics Data System (ADS)

Glowacki, David

Recently, we outlined an efficient multi-tiered parallel excitonic framework that utilizes time dependent density functional theory (TDDFT) to calculate ground/excited state energies and gradients of large supramolecular complexes in atomistic detail. In this paper, we apply our ab initioexciton framework to the 27 coupled bacteriocholorophyll-a chromophores which make up the LH2 complex, using it to compute linear absorption spectra and short-time, on-the-fly nonadiabatic surface-hopping (SH) dynamics of electronically excited LH2. Our ab initio exciton model includes two key parameters whose values are determined by fitting to experiment: d, which is added to the diagonal elements, corrects for the error in TDDFT vertical excitation energies on a single chromophore; and e, which occurs on the off-diagonal matrix elements, describes the average dielectric screening of the inter-chromophore transition-dipole coupling. Using snapshots obtained from equilibrium molecular dynamics simulations (MD) of LH2, best-fit values of both d and e were obtained by fitting to the thermally broadened experimental absorption spectrum within the Frank-Condon approximation, providing a linear absorption spectrum that agrees reasonably well with the experimental observations. We follow the nonadiabatic dynamics using surface hopping to construct time-resolved visualizations of the EET dynamics in the sub-picosecond regime following photoexcitation. This provides some qualitative insight into the excitonic energy transfer (EET) that results from atomically resolved vibrational fluctuations of the chromophores. The dynamical picture that emerges is one of rapidly fluctuating eigenstates that are delocalized over multiple chromophores and undergo frequent crossing on a femtosecond timescale as a result of the underlying chromophore vibrational dynamics. The eigenstate fluctuations arise from disorder in both the diagonal chromophore site energies and the off-diagonal inter-chromophore couplings. The scalability of our excitonic computational framework across massively parallel architectures opens up the possibility of addressing a wide range of questions, including how specific dynamical motions impact both the pathways and efficiency of electronic energy-transfer within large supramolecular systems.

Optimization of super-resolution processing using incomplete image sets in PET imaging.

PubMed

Chang, Guoping; Pan, Tinsu; Clark, John W; Mawlawi, Osama R

2008-12-01

Super-resolution (SR) techniques are used in PET imaging to generate a high-resolution image by combining multiple low-resolution images that have been acquired from different points of view (POVs). The number of low-resolution images used defines the processing time and memory storage necessary to generate the SR image. In this paper, the authors propose two optimized SR implementations (ISR-1 and ISR-2) that require only a subset of the low-resolution images (two sides and diagonal of the image matrix, respectively), thereby reducing the overall processing time and memory storage. In an N x N matrix of low-resolution images, ISR-1 would be generated using images from the two sides of the N x N matrix, while ISR-2 would be generated from images across the diagonal of the image matrix. The objective of this paper is to investigate whether the two proposed SR methods can achieve similar performance in contrast and signal-to-noise ratio (SNR) as the SR image generated from a complete set of low-resolution images (CSR) using simulation and experimental studies. A simulation, a point source, and a NEMA/IEC phantom study were conducted for this investigation. In each study, 4 (2 x 2) or 16 (4 x 4) low-resolution images were reconstructed from the same acquired data set while shifting the reconstruction grid to generate images from different POVs. SR processing was then applied in each study to combine all as well as two different subsets of the low-resolution images to generate the CSR, ISR-1, and ISR-2 images, respectively. For reference purpose, a native reconstruction (NR) image using the same matrix size as the three SR images was also generated. The resultant images (CSR, ISR-1, ISR-2, and NR) were then analyzed using visual inspection, line profiles, SNR plots, and background noise spectra. The simulation study showed that the contrast and the SNR difference between the two ISR images and the CSR image were on average 0.4% and 0.3%, respectively. Line profiles of the point source study showed that the three SR images exhibited similar signal amplitudes and FWHM. The NEMA/IEC study showed that the average difference in SNR among the three SR images was 2.1% with respect to one another and they contained similar noise structure. ISR-1 and ISR-2 can be used to replace CSR, thereby reducing the total SR processing time and memory storage while maintaining similar contrast, resolution, SNR, and noise structure.

The symmetries of the system matrix and propagator matrix for anisotropic media and of the system matrix forperiodically layered media

NASA Astrophysics Data System (ADS)

Xu, Guo-Ming; Ni, Si-Dao

1998-11-01

The `auxiliary' symmetry properties of the system matrix (symmetry with respect to the trailing diagonal) for a general anisotropic dissipative medium and the special form for a monoclinic medium are revealed by rearranging the motion-stress vector. The propagator matrix of a single-layer general anisotropic dissipative medium is also shown to have auxiliary symmetry. For the multilayered case, a relatively simple matrix method is utilized to obtain the inverse of the propagator matrix. Further, Woodhouse's inverse of the propagator matrix for a transversely isotropic medium is extended in a clearer form to handle the monoclinic symmetric medium. The properties of a periodic layer system are studied through its system matrix Aly , which is computed from the propagator matrix P. The matrix Aly is then compared with Aeq , the system matrix for the long-wavelength equivalent medium of the periodic isotropic layers. Then we can find how the periodic layered medium departs from its long-wavelength equivalent medium when the wavelength decreases. In our numerical example, the results show that, when λ/D decreases to 6-8, the components of the two matrices will depart from each other. The component ratio of these two matrices increases to its maximum (more than 15 in our numerical test) when λ/D is reduced to 2.3, and then oscillates with λ/D when it is further reduced. The eigenvalues of the system matrix Aly show that the velocities of P and S waves decrease when λ/D is reduced from 6-8 and reach their minimum values when λ/D is reduced to 2.3 and then oscillate afterwards. We compute the time shifts between the peaks of the transmitted waves and the incident waves. The resulting velocity curves show a similar variation to those computed from the eigenvalues of the system matrix Aly , but on a smaller scale. This can be explained by the spectrum width of the incident waves.

Thermodynamic framework for the ground state of a simple quantum system

NASA Astrophysics Data System (ADS)

Souza, Andre M. C.; Nobre, Fernando D.

2017-01-01

The ground state of a two-level system (associated with probabilities p and 1 -p , respectively) defined by a general Hamiltonian H ̂=Ĥ0+λ V ̂ is studied. The simple case characterized by λ =0 , whose Hamiltonian Ĥ0 is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (SBG=0 ) at zero temperature (T =0 ). Herein it is shown that the introduction of a perturbation λ V ̂ (λ >0 ) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S [p ] (with S [p ] ≠SBG[p ] ), if the Hermitian operator V ̂ is represented by a 2 ×2 matrix, defined by nonzero off-diagonal elements V12=V21=-z , where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V12≠0 , may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ ∝λ z ), which is shown to be a parameter conjugated to the entropy S . Based on this, one introduces an infinitesimal heatlike quantity, δ Q =θ d S , leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T ↔θ , and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S →0 , when θ →0 .

Sensitivity of coronal loop sausage mode frequencies and decay rates to radial and longitudinal density inhomogeneities: a spectral approach

NASA Astrophysics Data System (ADS)

Cally, Paul S.; Xiong, Ming

2018-01-01

Fast sausage modes in solar magnetic coronal loops are only fully contained in unrealistically short dense loops. Otherwise they are leaky, losing energy to their surrounds as outgoing waves. This causes any oscillation to decay exponentially in time. Simultaneous observations of both period and decay rate therefore reveal the eigenfrequency of the observed mode, and potentially insight into the tubes’ nonuniform internal structure. In this article, a global spectral description of the oscillations is presented that results in an implicit matrix eigenvalue equation where the eigenvalues are associated predominantly with the diagonal terms of the matrix. The off-diagonal terms vanish identically if the tube is uniform. A linearized perturbation approach, applied with respect to a uniform reference model, is developed that makes the eigenvalues explicit. The implicit eigenvalue problem is easily solved numerically though, and it is shown that knowledge of the real and imaginary parts of the eigenfrequency is sufficient to determine the width and density contrast of a boundary layer over which the tubes’ enhanced internal densities drop to ambient values. Linearized density kernels are developed that show sensitivity only to the extreme outside of the loops for radial fundamental modes, especially for small density enhancements, with no sensitivity to the core. Higher radial harmonics do show some internal sensitivity, but these will be more difficult to observe. Only kink modes are sensitive to the tube centres. Variation in internal and external Alfvén speed along the loop is shown to have little effect on the fundamental dimensionless eigenfrequency, though the associated eigenfunction becomes more compact at the loop apex as stratification increases, or may even displace from the apex.

Thermodynamic framework for the ground state of a simple quantum system.

PubMed

Souza, Andre M C; Nobre, Fernando D

2017-01-01

The ground state of a two-level system (associated with probabilities p and 1-p, respectively) defined by a general Hamiltonian H[over ̂]=H[over ̂]_{0}+λV[over ̂] is studied. The simple case characterized by λ=0, whose Hamiltonian H[over ̂]_{0} is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (S_{BG}=0) at zero temperature (T=0). Herein it is shown that the introduction of a perturbation λV[over ̂] (λ>0) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S[p] (with S[p]≠S_{BG}[p]), if the Hermitian operator V[over ̂] is represented by a 2×2 matrix, defined by nonzero off-diagonal elements V_{12}=V_{21}=-z, where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V_{12}≠0, may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ∝λz), which is shown to be a parameter conjugated to the entropy S. Based on this, one introduces an infinitesimal heatlike quantity, δQ=θdS, leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T↔θ, and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S→0, when θ→0.

Frequency-domain elastic full waveform inversion using encoded simultaneous sources

NASA Astrophysics Data System (ADS)

Jeong, W.; Son, W.; Pyun, S.; Min, D.

2011-12-01

Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results provided by the approximate Hessian matrix, it is noted that the latter are better than the former for deeper parts of the model. This work was financially supported by the Brain Korea 21 project of Energy System Engineering, by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0006155), by the Energy Efficiency & Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 2010T100200133).

Modified section method for laser-welding of ill-fitting cp Ti and Ni-Cr alloy one-piece cast implant-supported frameworks.

PubMed

Tiossi, R; Falcão-Filho, H; Aguiar Júnior, F A; Rodrigues, R C; Mattos, M da G; Ribeiro, R F

2010-05-01

This study aimed to verify the effect of modified section method and laser-welding on the accuracy of fit of ill-fitting commercially pure titanium (cp Ti) and Ni-Cr alloy one-piece cast frameworks. Two sets of similar implant-supported frameworks were constructed. Both groups of six 3-unit implant-supported fixed partial dentures were cast as one-piece [I: Ni-Cr (control) and II: cp Ti] and evaluated for passive fitting in an optical microscope with both screws tightened and with only one screw tightened. All frameworks were then sectioned in the diagonal axis at the pontic region (III: Ni-Cr and IV: cp Ti). Sectioned frameworks were positioned in the matrix (10-Ncm torque) and laser-welded. Passive fitting was evaluated for the second time. Data were submitted to anova and Tukey-Kramer honestly significant difference tests (P < 0.05). With both screws tightened, one-piece cp Ti group II showed significantly higher misfit values (27.57 +/- 5.06 microm) than other groups (I: 11.19 +/- 2.54 microm, III: 12.88 +/- 2.93 microm, IV: 13.77 +/- 1.51 microm) (P < 0.05). In the single-screw-tightened test, with readings on the opposite side to the tightened side, Ni-Cr cast as one-piece (I: 58.66 +/- 14.30 microm) was significantly different from cp Ti group after diagonal section (IV: 27.51 +/- 8.28 microm) (P < 0.05). On the tightened side, no significant differences were found between groups (P > 0.05). Results showed that diagonally sectioning ill-fitting cp Ti frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves passivity levels of the same frameworks when compared to one-piece cast structures.

Electrophoresis for genotyping: microtiter array diagonal gel electrophoresis on horizontal polyacrylamide gels, hydrolink, or agarose.

PubMed

Day, I N; Humphries, S E

1994-11-01

Electrophoresis of DNA has been performed traditionally in either an agarose or acrylamide gel matrix. Considerable effort has been directed to improved quality agaroses capable of high resolution, but for small fragments, such as those from polymerase chain reaction (PCR) and post-PCR digests, acrylamide still offers the highest resolution. Although agarose gels can easily be prepared in an open-faced format to gain the conveniences of horizontal electrophoresis, acrylamide does not polymerize in the presence of air and the usual configurations for gel preparation lead to electrophoresis in the vertical dimension. We describe here a very simple device and method to prepare and manipulate horizontal polyacrylamide gels (H-PAGE). In addition, the open-faced horizontal arrangement enables loading of arrays of wells. Since many procedures are undertaken in standard 96-well microtiter plates, we have also designed a device which preserves the exact configuration of the 8 x 12 array and enables electrophoresis in tracks following a 71.6 degrees diagonal between wells (MADGE, microtiter array diagonal gel electrophoresis), using either acrylamide or agarose. This eliminates almost all of the staff time taken in setup, loading, and recordkeeping and offers high resolution for genotyping pattern recognition. The nature and size of the gels allow direct stacking of gels in one tank, so that a tank used typically to analyze 30-60 samples can readily be used to analyze 1000-2000 samples. The gels would also enable robotic loading. Electrophoresis allows analysis of size and charge, parameters inaccessible to liquid-phase methods: thus, genotyping size patterns, variable length repeats, and haplotypes is possible, as well as adaptability to typing of point variations using protocols which create a difference detectable by electrophoresis.

Scenarios of physics beyond the standard model

NASA Astrophysics Data System (ADS)

Fok, Ricky

This dissertation discusses three topics on scenarios beyond the Standard Model. Topic one is the effects from a fourth generation of quarks and leptons on electroweak baryogenesis in the early universe. The Standard Model is incapable of electroweak baryogenesis due to an insufficiently strong enough electroweak phase transition (EWPT) as well as insufficient CP violation. We show that the presence of heavy fourth generation fermions solves the first problem but requires additional bosons to be included to stabilize the electroweak vacuum. Introducing supersymmetric partners of the heavy fermions, we find that the EWPT can be made strong enough and new sources of CP violation are present. Topic two relates to the lepton avor problem in supersymmetry. In the Minimal Supersymmetric Standard Model (MSSM), the off-diagonal elements in the slepton mass matrix must be suppressed at the 10-3 level to avoid experimental bounds from lepton avor changing processes. This dissertation shows that an enlarged R-parity can alleviate the lepton avor problem. An analysis of all sensitive parameters was performed in the mass range below 1 TeV, and we find that slepton maximal mixing is possible without violating bounds from the lepton avor changing processes: mu → egamma; mu → e conversion, and mu → 3e. Topic three is the collider phenomenology of quirky dark matter. In this model, quirks are particles that are gauged under the electroweak group, as well as a dark" color SU(2) group. The hadronization scale of this color group is well below the quirk masses. As a result, the dark color strings never break. Quirk and anti-quirk pairs can be produced at the LHC. Once produced, they immediately form a bound state of high angular momentum. The quirk pair rapidly shed angular momentum by emitting soft radiation before they annihilate into observable signals. This dissertation presents the decay branching ratios of quirkonia where quirks obtain their masses through electroweak symmetry breaking. This dissertation includes previously published and unpublished co-authored material.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

A theory for modeling ground-water flow in heterogeneous media

USGS Publications Warehouse

Cooley, Richard L.

2004-01-01

Construction of a ground-water model for a field area is not a straightforward process. Data are virtually never complete or detailed enough to allow substitution into the model equations and direct computation of the results of interest. Formal model calibration through optimization, statistical, and geostatistical methods is being applied to an increasing extent to deal with this problem and provide for quantitative evaluation and uncertainty analysis of the model. However, these approaches are hampered by two pervasive problems: 1) nonlinearity of the solution of the model equations with respect to some of the model (or hydrogeologic) input variables (termed in this report system characteristics) and 2) detailed and generally unknown spatial variability (heterogeneity) of some of the system characteristics such as log hydraulic conductivity, specific storage, recharge and discharge, and boundary conditions. A theory is developed in this report to address these problems. The theory allows construction and analysis of a ground-water model of flow (and, by extension, transport) in heterogeneous media using a small number of lumped or smoothed system characteristics (termed parameters). The theory fully addresses both nonlinearity and heterogeneity in such a way that the parameters are not assumed to be effective values. The ground-water flow system is assumed to be adequately characterized by a set of spatially and temporally distributed discrete values, ?, of the system characteristics. This set contains both small-scale variability that cannot be described in a model and large-scale variability that can. The spatial and temporal variability in ? are accounted for by imagining ? to be generated by a stochastic process wherein ? is normally distributed, although normality is not essential. Because ? has too large a dimension to be estimated using the data normally available, for modeling purposes ? is replaced by a smoothed or lumped approximation y?. (where y is a spatial and temporal interpolation matrix). Set y?. has the same form as the expected value of ?, y 'line' ? , where 'line' ? is the set of drift parameters of the stochastic process; ?. is a best-fit vector to ?. A model function f(?), such as a computed hydraulic head or flux, is assumed to accurately represent an actual field quantity, but the same function written using y?., f(y?.), contains error from lumping or smoothing of ? using y?.. Thus, the replacement of ? by y?. yields nonzero mean model errors of the form E(f(?)-f(y?.)) throughout the model and covariances between model errors at points throughout the model. These nonzero means and covariances are evaluated through third and fifth-order accuracy, respectively, using Taylor series expansions. They can have a significant effect on construction and interpretation of a model that is calibrated by estimating ?.. Vector ?.. is estimated as 'hat' ? using weighted nonlinear least squares techniques to fit a set of model functions f(y'hat' ?) to a. corresponding set of observations of f(?), Y. These observations are assumed to be corrupted by zero-mean, normally distributed observation errors, although, as for ?, normality is not essential. An analytical approximation of the nonlinear least squares solution is obtained using Taylor series expansions and perturbation techniques that assume model and observation errors to be small. This solution is used to evaluate biases and other results to second-order accuracy in the errors. The correct weight matrix to use in the analysis is shown to be the inverse of the second-moment matrix E(Y-f(y?.))(Y-f(y?.))', but the weight matrix is assumed to be arbitrary in most developments. The best diagonal approximation is the inverse of the matrix of diagonal elements of E(Y-f(y?.))(Y-f(y?.))', and a method of estimating this diagonal matrix when it is unknown is developed using a special objective function to compute 'hat' ?. When considered to be an estimate of f

Master Lovas-Andai and equivalent formulas verifying the 8/33 two-qubit Hilbert-Schmidt separability probability and companion rational-valued conjectures

NASA Astrophysics Data System (ADS)

Slater, Paul B.

2018-04-01

We begin by investigating relationships between two forms of Hilbert-Schmidt two-rebit and two-qubit "separability functions"—those recently advanced by Lovas and Andai (J Phys A Math Theor 50(29):295303, 2017), and those earlier presented by Slater (J Phys A 40(47):14279, 2007). In the Lovas-Andai framework, the independent variable ɛ \\in [0,1] is the ratio σ (V) of the singular values of the 2 × 2 matrix V=D_2^{1/2} D_1^{-1/2} formed from the two 2 × 2 diagonal blocks (D_1, D_2) of a 4 × 4 density matrix D= ||ρ _{ij}||. In the Slater setting, the independent variable μ is the diagonal-entry ratio √{ρ _{11} ρ _ {44}/ρ _ {22 ρ _ {33}}}—with, of central importance, μ =ɛ or μ =1/ɛ when both D_1 and D_2 are themselves diagonal. Lovas and Andai established that their two-rebit "separability function" \\tilde{χ }_1 (ɛ ) (≈ ɛ ) yields the previously conjectured Hilbert-Schmidt separability probability of 29/64. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we newly find its two-qubit, two-quater[nionic]-bit and "two-octo[nionic]-bit" counterparts, \\tilde{χ _2}(ɛ ) =1/3 ɛ ^2 ( 4-ɛ ^2) , \\tilde{χ _4}(ɛ ) =1/35 ɛ ^4 ( 15 ɛ ^4-64 ɛ ^2+84) and \\tilde{χ _8} (ɛ )= 1/1287ɛ ^8 ( 1155 ɛ ^8-7680 ɛ ^6+20160 ɛ ^4-25088 ɛ ^2+12740) . These immediately lead to predictions of Hilbert-Schmidt separability/PPT-probabilities of 8/33, 26/323 and 44482/4091349, in full agreement with those of the "concise formula" (Slater in J Phys A 46:445302, 2013), and, additionally, of a "specialized induced measure" formula. Then, we find a Lovas-Andai "master formula," \\tilde{χ _d}(ɛ )= ɛ ^d Γ (d+1)^3 _3\\tilde{F}_2( -{d/2,d/2,d;d/2+1,3 d/2+1;ɛ ^2) }/{Γ ( d/2+1) ^2}, encompassing both even and odd values of d. Remarkably, we are able to obtain the \\tilde{χ _d}(ɛ ) formulas, d=1,2,4, applicable to full (9-, 15-, 27-) dimensional sets of density matrices, by analyzing (6-, 9, 15-) dimensional sets, with not only diagonal D_1 and D_2, but also an additional pair of nullified entries. Nullification of a further pair still leads to X-matrices, for which a distinctly different, simple Dyson-index phenomenon is noted. C. Koutschan, then, using his HolonomicFunctions program, develops an order-4 recurrence satisfied by the predictions of the several formulas, establishing their equivalence. A two-qubit separability probability of 1-256/27 π ^2 is obtained based on the operator monotone function √{x}, with the use of \\tilde{χ _2}(ɛ ).

``Diagonalization'' of a compound Atwood machine

NASA Astrophysics Data System (ADS)

Crawford, Frank S.

1987-06-01

We consider a simple Atwood machine consisting of a massless frictionless pulley no. 0 supporting two masses m1 and m2 connected by a massless flexible string. We show that the string that supports massless pulley no. 0 ``thinks'' it is simply supporting a mass m0, with m0=4m1m2/(m1+m2). This result, together with Einstein's equivalence principle, allows us to solve easily those compound Atwood machines created by replacing one or both of m1 and m2 in machine no. 0 by an Atwood machine. We may then replacing the masses in these new machines by machines, etc. The complete solution can be written down immediately, without solving simultaneous equations. Finally we give the effective mass of an Atwood machine whose pulley has nonzero mass and moment of inertia.

Design and application of quadrature compensation patterns in bulk silicon micro-gyroscopes.

PubMed

Ni, Yunfang; Li, Hongsheng; Huang, Libin

2014-10-29

This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose.

Design Spectrum Analysis in NASTRAN

NASA Technical Reports Server (NTRS)

Butler, T. G.

1984-01-01

The utility of Design Spectrum Analysis is to give a mode by mode characterization of the behavior of a design under a given loading. The theory of design spectrum is discussed after operations are explained. User instructions are taken up here in three parts: Transient Preface, Maximum Envelope Spectrum, and RMS Average Spectrum followed by a Summary Table. A single DMAP ALTER packet will provide for all parts of the design spectrum operations. The starting point for getting a modal break-down of the response to acceleration loading is the Modal Transient rigid format. After eigenvalue extraction, modal vectors need to be isolated in the full set of physical coordinates (P-sized as opposed to the D-sized vectors in RF 12). After integration for transient response the results are scanned over the solution time interval for the peak values and for the times that they occur. A module called SCAN was written to do this job, that organizes these maxima into a diagonal output matrix. The maximum amplifier in each mode is applied to the eigenvector of each mode which then reveals the maximum displacements, stresses, forces and boundary reactions that the structure will experience for a load history, mode by mode. The standard NASTRAN output processors have been modified for this task. It is required that modes be normalized to mass.

Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations

NASA Astrophysics Data System (ADS)

Abdi, Daniel S.; Giraldo, Francis X.

2016-09-01

A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods, namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine how classical CG that uses a global storage scheme can be constructed within the DG framework using constraint imposition techniques commonly used in the finite element literature. Then, we implement and test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the case of explicit time integration and a diagonal mass matrix. Constructing CG within the DG framework allows CG to benefit from the desirable properties of DG such as, easier hp-refinement, better stability etc. Moreover, this representation allows for regional mixing of CG and DG depending on the flow regime in an area. The different flavors of CG and DG in the unified implementation are then tested for accuracy and performance using a suite of benchmark problems representative of cloud-resolving scale, meso-scale and global-scale atmospheric dynamics. The value of our unified approach is that we are able to show how to carry both CG and DG methods within the same code and also offer a simple recipe for modifying an existing CG code to DG and vice versa.

Optimized detection of shear peaks in weak lensing maps

NASA Astrophysics Data System (ADS)

Marian, Laura; Smith, Robert E.; Hilbert, Stefan; Schneider, Peter

2012-06-01

We present a new method to extract cosmological constraints from weak lensing (WL) peak counts, which we denote as ‘the hierarchical algorithm’. The idea of this method is to combine information from WL maps sequentially smoothed with a series of filters of different size, from the largest down to the smallest, thus increasing the cosmological sensitivity of the resulting peak function. We compare the cosmological constraints resulting from the peak abundance measured in this way and the abundance obtained by using a filter of fixed size, which is the standard practice in WL peak studies. For this purpose, we employ a large set of WL maps generated by ray tracing through N-body simulations, and the Fisher matrix formalism. We find that if low signal-to-noise ratio (?) peaks are included in the analysis (?), the hierarchical method yields constraints significantly better than the single-sized filtering. For a large future survey such as Euclid or Large Synoptic Survey Telescope, combined with information from a cosmic microwave background experiment like Planck, the results for the hierarchical (single-sized) method are Δns= 0.0039 (0.004), ΔΩm= 0.002 (0.0045), Δσ8= 0.003 (0.006) and Δw= 0.019 (0.0525). This forecast is conservative, as we assume no knowledge of the redshifts of the lenses, and consider a single broad bin for the redshifts of the sources. If only peaks with ? are considered, then there is little difference between the results of the two methods. We also examine the statistical properties of the hierarchical peak function: Its covariance matrix has off-diagonal terms for bins with ? and aperture mass of M < 3 × 1014 h-1 M⊙, the higher bins being largely uncorrelated and therefore well described by a Poisson distribution.

Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states

NASA Astrophysics Data System (ADS)

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.

Tensor models, Kronecker coefficients and permutation centralizer algebras

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Ramgoolam, Sanjaye

2017-11-01

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.

More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares.

PubMed

Yuan, Ke-Hai; Jiang, Ge; Cheng, Ying

2017-11-01

Data in psychology are often collected using Likert-type scales, and it has been shown that factor analysis of Likert-type data is better performed on the polychoric correlation matrix than on the product-moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice. In either LS or DWLS, the associations among the polychoric correlation coefficients are completely ignored. To mend such a gap between statistical theory and empirical work, this paper proposes new methods, called ridge GLS, for factor analysis of ordinal data. Monte Carlo results show that, for a wide range of sample sizes, ridge GLS methods yield uniformly more accurate parameter estimates than existing methods (LS, DWLS, AGLS). A real-data example indicates that estimates by ridge GLS are 9-20% more efficient than those by existing methods. Rescaled and adjusted test statistics as well as sandwich-type standard errors following the ridge GLS methods also perform reasonably well. © 2017 The British Psychological Society.

Biomechanical analysis of knee and trunk in badminton players with and without knee pain during backhand diagonal lunges.

PubMed

Lin, Cheng-Feng; Hua, Shiang-Hua; Huang, Ming-Tung; Lee, Hsing-Hsan; Liao, Jen-Chieh

2015-01-01

The contribution of core neuromuscular control to the dynamic stability of badminton players with and without knee pain during backhand lunges has not been investigated. Accordingly, this study compared the kinematics of the lower extremity, the trunk movement, the muscle activation and the balance performance of knee-injured and knee-uninjured badminton players when performing backhand stroke diagonal lunges. Seventeen participants with chronic knee pain (injured group) and 17 healthy participants (control group) randomly performed two diagonal backhand lunges in the forward and backward directions, respectively. This study showed that the injured group had lower frontal and horizontal motions of the knee joint, a smaller hip-shoulder separation angle and a reduced trunk tilt angle. In addition, the injured group exhibited a greater left paraspinal muscle activity, while the control group demonstrated a greater activation of the vastus lateralis, vastus medialis and medial gastrocnemius muscle groups. Finally, the injured group showed a smaller distance between centre of mass (COM) and centre of pressure, and a lower peak COM velocity when performing the backhand backward lunge tasks. In conclusion, the injured group used reduced knee and trunk motions to complete the backhand lunge tasks. Furthermore, the paraspinal muscles contributed to the lunge performance of the individuals with knee pain, whereas the knee extensors and ankle plantar flexor played a greater role for those without knee pain.

One-Loop One-Point Functions in Gauge-Gravity Dualities with Defects.

PubMed

Buhl-Mortensen, Isak; de Leeuw, Marius; Ipsen, Asger C; Kristjansen, Charlotte; Wilhelm, Matthias

2016-12-02

We initiate the calculation of loop corrections to correlation functions in 4D defect conformal field theories (dCFTs). More precisely, we consider N=4 SYM theory with a codimension-one defect separating two regions of space, x_{3}>0 and x_{3}<0, where the gauge group is SU(N) and SU(N-k), respectively. This setup is made possible by some of the real scalar fields acquiring a nonvanishing and x_{3}-dependent vacuum expectation value for x_{3}>0. The holographic dual is the D3-D5 probe brane system where the D5-brane geometry is AdS_{4}×S^{2} and a background gauge field has k units of flux through the S^{2}. We diagonalize the mass matrix of the dCFT making use of fuzzy-sphere coordinates and we handle the x_{3} dependence of the mass terms in the 4D Minkowski space propagators by reformulating these as standard massive AdS_{4} propagators. Furthermore, we show that only two Feynman diagrams contribute to the one-loop correction to the one-point function of any single-trace operator and we explicitly calculate this correction in the planar limit for the simplest chiral primary. The result of this calculation is compared to an earlier string-theory computation in a certain double scaling limit and perfect agreement is found. Finally, we discuss how to generalize our calculation to any single-trace operator, to finite N, and to other types of observables such as Wilson loops.

Quantum critical spin-2 chain with emergent SU(3) symmetry.

PubMed

Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

2015-04-10

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Experimental observation of the 1/3 magnetization plateau in the diamond-chain compound Cu3(CO3)2(OH)2.

PubMed

Kikuchi, H; Fujii, Y; Chiba, M; Mitsudo, S; Idehara, T; Tonegawa, T; Okamoto, K; Sakai, T; Kuwai, T; Ohta, H

2005-06-10

The magnetic susceptibility, high field magnetization, and specific heat measurements of Cu3(CO3)2(OH)2, which is a model substance for the frustrating diamond spin chain model, have been performed using single crystals. Two broad peaks are observed at around 20 and 5 K in both magnetic susceptibility and specific heat results. The magnetization curve has a clear plateau at one third of the saturation magnetization. The experimental results are examined in terms of theoretical expectations based on exact diagonalization and density matrix renormalization group methods. An origin of magnetic anisotropy is also discussed.

Population control of self-replicating systems

NASA Technical Reports Server (NTRS)

Mccord, R. L.

1982-01-01

The literature concerning fibonacci sequence and the mathematics of self replication are reviewed. One option allows each primary to generate n-replicas, one in each sequential time frame after its own generation with no restrictions on the number of ancestors per replica. The state vector of the replicas in an efficient manner is determined. Option-B has a fixed number of replicas per primary and no restrictions on the number of ancestors for a replica. Any element fij represents the number of elements of type-j in time frame k+1 generated from type-i in time frame k. Option-D is a diagonal matrix whose eigenvalues are precisely those of f.

Dimension-5 C P -odd operators: QCD mixing and renormalization

DOE PAGES

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; ...

2015-12-23

Here, we study the off-shell mixing and renormalization of flavor-diagonal dimension-five T- and P-odd operators involving quarks, gluons, and photons, including quark electric dipole and chromoelectric dipole operators. Furthermore, we present the renormalization matrix to one loop in themore » $$\\bar{MS}$$ scheme. We also provide a definition of the quark chromoelectric dipole operator in a regularization-independent momentum-subtraction scheme suitable for nonperturbative lattice calculations and present the matching coefficients with the $$\\bar{MS}$$ scheme to one loop in perturbation theory, using both the naïve dimensional regularization and ’t Hooft–Veltman prescriptions for γ 5.« less

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Resonance rotational level crossing in the fluorosulfate radical FSO3rad and experimental determination of the rotational A and the centrifugal distortion DK constants

NASA Astrophysics Data System (ADS)

Kolesniková, Lucie; Koucký, Jan; Kania, Patrik; Uhlíková, Tereza; Beckers, Helmut; Urban, Štěpán

2018-01-01

The resonance crossing of rotational levels with different fine-structure components and different k rotational quantum numbers was observed in the rotational spectra of the symmetric top fluorosulfate radical FSO3rad. Detailed measurements were performed to analyze these weak resonances as well as the A1-A2 splittings of the K = 3 and K = 6 transitions. The resonance level crossing enabled the experimental determination of "forbidden" parameters, the rotational A and the centrifugal distortion DK constants as well as the corresponding resonance off-diagonal matrix element.

Interband excitations in the 1D limit of two-band fractional Chern insulators

NASA Astrophysics Data System (ADS)

Jaworowski, Błażej; Kaczmarkiewicz, Piotr; Potasz, Paweł; Wójs, Arkadiusz

2018-05-01

We investigate the stability of the one-dimensional limit of ν = 1 / 3 Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system - the checkerboard lattice.

Efficient continuous-variable state tomography using Padua points

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

Further development of quantum technologies calls for efficient characterization methods for quantum systems. While recent work has focused on discrete systems of qubits, much remains to be done for continuous-variable systems such as a microwave mode in a cavity. We introduce a novel technique to reconstruct the full Husimi Q or Wigner function from measurements done at the Padua points in phase space, the optimal sampling points for interpolation in 2D. Our technique not only reduces the number of experimental measurements, but remarkably, also allows for the direct estimation of any density matrix element in the Fock basis, including off-diagonal elements. OLC acknowledges financial support from NSERC.

Extended Hellmann-Feynman theorem for degenerate eigenstates

NASA Astrophysics Data System (ADS)

Zhang, G. P.; George, Thomas F.

2004-04-01

In a previous paper, we reported a failure of the traditional Hellmann-Feynman theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.

CELES: CUDA-accelerated simulation of electromagnetic scattering by large ensembles of spheres

NASA Astrophysics Data System (ADS)

Egel, Amos; Pattelli, Lorenzo; Mazzamuto, Giacomo; Wiersma, Diederik S.; Lemmer, Uli

2017-09-01

CELES is a freely available MATLAB toolbox to simulate light scattering by many spherical particles. Aiming at high computational performance, CELES leverages block-diagonal preconditioning, a lookup-table approach to evaluate costly functions and massively parallel execution on NVIDIA graphics processing units using the CUDA computing platform. The combination of these techniques allows to efficiently address large electrodynamic problems (>104 scatterers) on inexpensive consumer hardware. In this paper, we validate near- and far-field distributions against the well-established multi-sphere T-matrix (MSTM) code and discuss the convergence behavior for ensembles of different sizes, including an exemplary system comprising 105 particles.

Framework for analyzing ecological trait-based models in multidimensional niche spaces

NASA Astrophysics Data System (ADS)

Biancalani, Tommaso; DeVille, Lee; Goldenfeld, Nigel

2015-05-01

We develop a theoretical framework for analyzing ecological models with a multidimensional niche space. Our approach relies on the fact that ecological niches are described by sequences of symbols, which allows us to include multiple phenotypic traits. Ecological drivers, such as competitive exclusion, are modeled by introducing the Hamming distance between two sequences. We show that a suitable transform diagonalizes the community interaction matrix of these models, making it possible to predict the conditions for niche differentiation and, close to the instability onset, the asymptotically long time population distributions of niches. We exemplify our method using the Lotka-Volterra equations with an exponential competition kernel.

Fourier transform emission spectra and deperturbation analysis of the A2Π - X2Σ+ and B2Σ+ - X2Σ+ electronic transitions of ZnH

NASA Astrophysics Data System (ADS)

Abbasi, Mahdi; Shayesteh, Alireza

2017-10-01

A discharge-furnace emission source was used to generate the A2Π → X2Σ+ and B2Σ+ → X2Σ+ spectra of ZnH radical. High resolution emission spectra were recorded with a Fourier transform spectrometer, and several bands have been assigned for the 64ZnH major isotopologue. The data span the v″ = 0-6 levels of the X2Σ+ ground state, the v‧ = 0-3 levels of the A2Π state, and the v‧ = 0-2 levels of the B2Σ+ state, extending to high rotational quantum numbers near and above the dissociation asymptote of the ground state. Large local perturbations were observed in the A2Π and B2Σ+ electronic states, and a deperturbation analysis was carried out using a single Hamiltonian matrix that includes 2Π and 2Σ+ matrix elements, as well as off-diagonal elements coupling vibrational levels of the two electronic states. Band constants and Dunham coefficients were obtained for the A2Π and B2Σ+ excited states by least-squares-fitting of all the experimental data. The equilibrium vibrational constants ωe and ωexe have been determined to be 1907.528(4) and 38.674(2) cm-1, respectively, for the A2Π state, and 1021.135(94) and 17.725(80) cm-1, for the B2Σ+ state, and the equilibrium Zn-H distances (re) are 1.511662(2) Å and 2.26805(7) Å for the A2Π and B2Σ+ states, respectively. The RKR potential curves were constructed for the A2Π and B2Σ+ states, and vibrational radial overlap integrals were computed. The off-diagonal matrix elements coupling the electronic wavefunctions of the A2Π and B2Σ+ states, i.e., a+ and b, were determined to be 228 ± 3 cm-1 and 0.73 ± 0.01, respectively, for the ZnH molecule.

Effects of upper-body sprint-interval training on strength and endurance capacities in female cross-country skiers

PubMed Central

Vandbakk, Kristine; Welde, Boye; Kruken, Andrea Hovstein; Baumgart, Julia; Ettema, Gertjan; Karlsen, Trine; Sandbakk, Øyvind

2017-01-01

This study compared the effects of adding upper-body sprint-intervals or continuous double poling endurance training to the normal training on maximal upper-body strength and endurance capacity in female cross-country skiers. In total, 17 female skiers (age: 18.1±0.8yr, body mass: 60±7 kg, maximal oxygen uptake (VO2max): 3.30±0.37 L.min-1) performed an 8-week training intervention. Here, either two weekly sessions of six to eight 30-s maximal upper-body double poling sprint-intervals (SIG, n = 8) or 45–75 min of continuous low-to-moderate intensity double poling on roller skis (CG, n = 9) were added to their training. Before and after the intervention, the participants were tested for physiological and kinematical responses during submaximal and maximal diagonal and double poling treadmill roller skiing. Additionally, we measured maximal upper-body strength (1RM) and average power at 40% 1RM in a poling-specific strength exercise. SIG improved absolute VO2max in diagonal skiing more than CG (8% vs 2%, p<0.05), and showed a tendency towards higher body-mass normalized VO2max (7% vs 2%, p = 0.07). Both groups had an overall improvement in double poling peak oxygen uptake (10% vs 6% for SIG and CG) (both p<0.01), but no group-difference was observed. SIG improved 1RM strength more than CG (18% vs 10%, p<0.05), while there was a tendency for difference in average power at 40% 1RM (20% vs 14%, p = 0.06). Oxygen cost and kinematics (cycle length and rate) in double poling and diagonal remained unchanged in both groups. In conclusion, our study demonstrates that adding upper-body sprint-interval training is more effective than continuous endurance training in improving upper-body maximal strength and VO2max. PMID:28241030

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics.

PubMed

Czakó, Gábor; Szalay, Viktor; Császár, Attila G

2006-01-07

The currently most efficient finite basis representation (FBR) method [Corey et al., in Numerical Grid Methods and Their Applications to Schrodinger Equation, NATO ASI Series C, edited by C. Cerjan (Kluwer Academic, New York, 1993), Vol. 412, p. 1; Bramley et al., J. Chem. Phys. 100, 6175 (1994)] designed specifically to deal with nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc., employs very special l-independent grids and results in a symmetric FBR. While highly efficient, this method is not general enough. For instance, it cannot deal with nondirect product bases of the above structure efficiently if the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are discrete variable representation (DVR) functions of the infinite type. The optimal-generalized FBR(DVR) method [V. Szalay, J. Chem. Phys. 105, 6940 (1996)] is designed to deal with general, i.e., direct and/or nondirect product, bases and grids. This robust method, however, is too general, and its direct application can result in inefficient computer codes [Czako et al., J. Chem. Phys. 122, 024101 (2005)]. It is shown here how the optimal-generalized FBR method can be simplified in the case of nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc. As a result the commonly used symmetric FBR is recovered and simplified nonsymmetric FBRs utilizing very special l-dependent grids are obtained. The nonsymmetric FBRs are more general than the symmetric FBR in that they can be employed efficiently even when the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are DVR functions of the infinite type. Arithmetic operation counts and a simple numerical example presented show unambiguously that setting up the Hamiltonian matrix requires significantly less computer time when using one of the proposed nonsymmetric FBRs than that in the symmetric FBR. Therefore, application of this nonsymmetric FBR is more efficient than that of the symmetric FBR when one wants to diagonalize the Hamiltonian matrix either by a direct or via a basis-set contraction method. Enormous decrease of computer time can be achieved, with respect to a direct application of the optimal-generalized FBR, by employing one of the simplified nonsymmetric FBRs as is demonstrated in noniterative calculations of the low-lying vibrational energy levels of the H3+ molecular ion. The arithmetic operation counts of the Hamiltonian matrix vector products and the properties of a recently developed diagonalization method [Andreozzi et al., J. Phys. A Math. Gen. 35, L61 (2002)] suggest that the nonsymmetric FBR applied along with this particular diagonalization method is suitable to large scale iterative calculations. Whether or not the nonsymmetric FBR is competitive with the symmetric FBR in large-scale iterative calculations still has to be investigated numerically.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Entanglement classification in the noninteracting Fermi gas

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Eghbalifam, F.; Nami, S.; Yahyavi, M.

In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group Sn. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur-Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even n qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of Sn. The restricted density matrix to the subspaces of the irreducible representations: Ssym, S3,1 and S2,2 are denoted by ρsym, ρ3,1 and ρ2,2, respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix ρ3,1 and ρ2,2, so these classes do not exist in the total Fermi gas density matrix.

Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

DTIC Science & Technology

2014-10-30

Houzeaux et al., 2009). The GM- RES solver is also employed to solve for the enthalpy and species mass fractions. The Gauss - Seidel iterative method is...the system is therefore split to solve the mo- mentum and continuity equations independently. This is achieved by applying an iterative strategy...the momentum equation twice and the continuity equation once. The momentum equation is solved using the GMRES or BICGSTAB method (diagonal and Gauss

Lightweight compact 2D/3D autostereoscopic LCD backlight for games, monitor, and notebook applications

NASA Astrophysics Data System (ADS)

Eichenlaub, Jesse B.

1998-04-01

At the 1997 conference DTI first reported on a low cost, thin, lightweight backlight for LCDs that generates a special illumination pattern to create autostereoscopic 3D images and can switch to conventional diffuse illumination for 2D images. The backlight is thin and efficient enough for use in portable computer and hand held games, as well as thin desktop displays. The system has been embodied in 5' (13 cm) diagonal backlights for gambling machines, and in the 12.1' (31 cm) diagonal DTI Virtual Window(TM) desktop product. During the past year, DTI has improved the technology considerably, reducing crosstalk, increasing efficiency, improving components for mass production, and developing prototypes that move the 3D viewing zones in response to the observer's head position. The paper will describe the 2D/3D backlights, improvements that have been made to their function, and their embodiments within the latest display products and prototypes.

Formulation of the relativistic quantum Hall effect and parity anomaly

NASA Astrophysics Data System (ADS)

Yonaga, Kouki; Hasebe, Kazuki; Shibata, Naokazu

2016-06-01

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and nonrelativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly." In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.

Improving the Numerical Stability of Fast Matrix Multiplication

DOE PAGES

Ballard, Grey; Benson, Austin R.; Druinsky, Alex; ...

2016-10-04

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm, they are not used even in cases where they provide a performance benefit. We argue in this study that the numerical sacrifice of fastmore » algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and we explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and we consider both contributions independently. We generalize and tighten previous error analyses of fast algorithms and compare their properties. We discuss algorithmic techniques for improving the error guarantees from two perspectives: manipulating the algorithms, and reducing input anomalies by various forms of diagonal scaling. In conclusion, we benchmark performance and demonstrate our improved numerical accuracy.« less

Underlying theory of a model for the Renner-Teller effect in tetra-atomic molecules: X(2)Πu electronic state of C2H2(+).

PubMed

Perić, M; Jerosimić, S; Mitić, M; Milovanović, M; Ranković, R

2015-05-07

In the present study, we prove the plausibility of a simple model for the Renner-Teller effect in tetra-atomic molecules with linear equilibrium geometry by ab initio calculations of the electronic energy surfaces and non-adiabatic matrix elements for the X(2)Πu state of C2H2 (+). This phenomenon is considered as a combination of the usual Renner-Teller effect, appearing in triatomic species, and a kind of the Jahn-Teller effect, similar to the original one arising in highly symmetric molecules. Only four parameters (plus the spin-orbit constant, if the spin effects are taken into account), which can be extracted from ab initio calculations carried out at five appropriate (planar) molecular geometries, are sufficient for building up the Hamiltonian matrix whose diagonalization results in the complete low-energy (bending) vibronic spectrum. The main result of the present study is the proof that the diabatization scheme, hidden beneath the apparent simplicity of the model, can safely be carried out, at small-amplitude bending vibrations, without cumbersome computation of non-adiabatic matrix elements at large number of molecular geometries.

Double Stokes-Mueller polarimetry in KTP (Potassium Titanyl Phosphate) crystal

NASA Astrophysics Data System (ADS)

Shaji, Chitra; S B, Sruthil Lal; Sharan, Alok

2017-04-01

Ultra-structural properties of material are being probed by Double Stokes-Mueller polarimetry (DSMP) technique. It makes use of higher dimensions of Stokes vector (9 X 1) and Mueller matrix (4 X9) to characterize the nonlinear optical properties of a material. Second harmonic generation (SHG) at 532nm using 1064nm as fundamental cw beam from Nd: YAG laser in type II phase matched KTP (Potassium Titanyl Phosphate) crystal is studied using DSMP. The experimental measurements for determining double Mueller matrix are carried out in the ``Polarization In Polarization Out'' (PIPO) arrangement. Nine input polarization states are incident on the sample and the linear Stokes vector of the emerging light from the sample is measured. The KTP crystal is oriented such that the SHG signal efficiency at the incident horizontal and vertical polarizations is high as compared to diagonal polarization states. The susceptibility tensor components and the phase difference between them at this orientation are determined from the double Mueller matrix elements. These determined values give information regarding the crystal axis orientations. To our knowledge, this is the first report of the use of DSMP technique to determine the crystal orientations of a biaxial crystal.

Energy levels scheme simulation of divalent cobalt doped bismuth germanate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andreici, Emiliana-Laura, E-mail: andreicilaura@yahoo.com; Petkova, Petya; Avram, Nicolae M.

The aim of this paper is to simulate the energy levels scheme for Bismuth Germanate (BGO) doped with divalent cobalt, in order to give a reliable explanation for spectral experimental data. In the semiempirical crystal field theory we first modeled the Crystal Field Parameters (CFPs) of BGO:Cr{sup 2+} system, in the frame of Exchange Charge Model (ECM), with actually site symmetry of the impurity ions after doping. The values of CFPs depend on the geometry of doped host matrix and by parameter G of ECM. First, we optimized the geometry of undoped BGO host matrix and afterwards, that of dopedmore » BGO with divalent cobalt. The charges effect of ligands and covalence bonding between cobalt cations and oxygen anions, in the cluster approach, also were taken into account. With the obtained values of the CFPs we simulate the energy levels scheme of cobalt ions, by diagonalizing the matrix of the doped crystal Hamiltonian. Obviously, energy levels and estimated Racah parameters B and C were compared with the experimental spectroscopic data and discussed. Comparison of obtained results with experimental data shows quite satisfactory, which justify the model and simulation schemes used for the title system.« less

A parallel algorithm for 2D visco-acoustic frequency-domain full-waveform inversion: application to a dense OBS data set

NASA Astrophysics Data System (ADS)

Sourbier, F.; Operto, S.; Virieux, J.

2006-12-01

We present a distributed-memory parallel algorithm for 2D visco-acoustic full-waveform inversion of wide-angle seismic data. Our code is written in fortran90 and use MPI for parallelism. The algorithm was applied to real wide-angle data set recorded by 100 OBSs with a 1-km spacing in the eastern-Nankai trough (Japan) to image the deep structure of the subduction zone. Full-waveform inversion is applied sequentially to discrete frequencies by proceeding from the low to the high frequencies. The inverse problem is solved with a classic gradient method. Full-waveform modeling is performed with a frequency-domain finite-difference method. In the frequency-domain, solving the wave equation requires resolution of a large unsymmetric system of linear equations. We use the massively parallel direct solver MUMPS (http://www.enseeiht.fr/irit/apo/MUMPS) for distributed-memory computer to solve this system. The MUMPS solver is based on a multifrontal method for the parallel factorization. The MUMPS algorithm is subdivided in 3 main steps: a symbolic analysis step that performs re-ordering of the matrix coefficients to minimize the fill-in of the matrix during the subsequent factorization and an estimation of the assembly tree of the matrix. Second, the factorization is performed with dynamic scheduling to accomodate numerical pivoting and provides the LU factors distributed over all the processors. Third, the resolution is performed for multiple sources. To compute the gradient of the cost function, 2 simulations per shot are required (one to compute the forward wavefield and one to back-propagate residuals). The multi-source resolutions can be performed in parallel with MUMPS. In the end, each processor stores in core a sub-domain of all the solutions. These distributed solutions can be exploited to compute in parallel the gradient of the cost function. Since the gradient of the cost function is a weighted stack of the shot and residual solutions of MUMPS, each processor computes the corresponding sub-domain of the gradient. In the end, the gradient is centralized on the master processor using a collective communation. The gradient is scaled by the diagonal elements of the Hessian matrix. This scaling is computed only once per frequency before the first iteration of the inversion. Estimation of the diagonal terms of the Hessian requires performing one simulation per non redondant shot and receiver position. The same strategy that the one used for the gradient is used to compute the diagonal Hessian in parallel. This algorithm was applied to a dense wide-angle data set recorded by 100 OBSs in the eastern Nankai trough, offshore Japan. Thirteen frequencies ranging from 3 and 15 Hz were inverted. Tweny iterations per frequency were computed leading to 260 tomographic velocity models of increasing resolution. The velocity model dimensions are 105 km x 25 km corresponding to a finite-difference grid of 4201 x 1001 grid with a 25-m grid interval. The number of shot was 1005 and the number of inverted OBS gathers was 93. The inversion requires 20 days on 6 32-bits bi-processor nodes with 4 Gbytes of RAM memory per node when only the LU factorization is performed in parallel. Preliminary estimations of the time required to perform the inversion with the fully-parallelized code is 6 and 4 days using 20 and 50 processors respectively.

Homogeneous Matrix Deposition on Dried Agar for MALDI Imaging Mass Spectrometry of Microbial Cultures

NASA Astrophysics Data System (ADS)

Hoffmann, Thomas; Dorrestein, Pieter C.

2015-11-01

Matrix deposition on agar-based microbial colonies for MALDI imaging mass spectrometry is often complicated by the complex media on which microbes are grown. This Application Note demonstrates how consecutive short spray pulses of a matrix solution can form an evenly closed matrix layer on dried agar. Compared with sieving dry matrix onto wet agar, this method supports analyte cocrystallization, which results in significantly more signals, higher signal-to-noise ratios, and improved ionization efficiency. The even matrix layer improves spot-to-spot precision of measured m/z values when using TOF mass spectrometers. With this technique, we established reproducible imaging mass spectrometry of myxobacterial cultures on nutrient-rich cultivation media, which was not possible with the sieving technique.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Jiasen; Yu Changshui; Song Heshan

We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.

Analytical and numerical construction of equivalent cables.

PubMed

Lindsay, K A; Rosenberg, J R; Tucker, G

2003-08-01

The mathematical complexity experienced when applying cable theory to arbitrarily branched dendrites has lead to the development of a simple representation of any branched dendrite called the equivalent cable. The equivalent cable is an unbranched model of a dendrite and a one-to-one mapping of potentials and currents on the branched model to those on the unbranched model, and vice versa. The piecewise uniform cable, with a symmetrised tri-diagonal system matrix, is shown to represent the canonical form for an equivalent cable. Through a novel application of the Laplace transform it is demonstrated that an arbitrary branched model of a dendrite can be transformed to the canonical form of an equivalent cable. The characteristic properties of the equivalent cable are extracted from the matrix for the transformed branched model. The one-to-one mapping follows automatically from the construction of the equivalent cable. The equivalent cable is used to provide a new procedure for characterising the location of synaptic contacts on spinal interneurons.

PyVCI: A flexible open-source code for calculating accurate molecular infrared spectra

NASA Astrophysics Data System (ADS)

Sibaev, Marat; Crittenden, Deborah L.

2016-06-01

The PyVCI program package is a general purpose open-source code for simulating accurate molecular spectra, based upon force field expansions of the potential energy surface in normal mode coordinates. It includes harmonic normal coordinate analysis and vibrational configuration interaction (VCI) algorithms, implemented primarily in Python for accessibility but with time-consuming routines written in C. Coriolis coupling terms may be optionally included in the vibrational Hamiltonian. Non-negligible VCI matrix elements are stored in sparse matrix format to alleviate the diagonalization problem. CPU and memory requirements may be further controlled by algorithmic choices and/or numerical screening procedures, and recommended values are established by benchmarking using a test set of 44 molecules for which accurate analytical potential energy surfaces are available. Force fields in normal mode coordinates are obtained from the PyPES library of high quality analytical potential energy surfaces (to 6th order) or by numerical differentiation of analytic second derivatives generated using the GAMESS quantum chemical program package (to 4th order).

Damping characterization in large structures

NASA Technical Reports Server (NTRS)

Eke, Fidelis O.; Eke, Estelle M.

1991-01-01

This research project has as its main goal the development of methods for selecting the damping characteristics of components of a large structure or multibody system, in such a way as to produce some desired system damping characteristics. The main need for such an analytical device is in the simulation of the dynamics of multibody systems consisting, at least partially, of flexible components. The reason for this need is that all existing simulation codes for multibody systems require component-by-component characterization of complex systems, whereas requirements (including damping) often appear at the overall system level. The main goal was met in large part by the development of a method that will in fact synthesize component damping matrices from a given system damping matrix. The restrictions to the method are that the desired system damping matrix must be diagonal (which is almost always the case) and that interbody connections must be by simple hinges. In addition to the technical outcome, this project contributed positively to the educational and research infrastructure of Tuskegee University - a Historically Black Institution.

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

DOE PAGES

Zhang, Hong; Zapol, Peter; Dixon, David A.; ...

2015-11-17

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPsmore » is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.« less

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong; Zapol, Peter; Dixon, David A.

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPsmore » is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.« less

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

NASA Astrophysics Data System (ADS)

Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei

2018-04-01

We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

NASA Technical Reports Server (NTRS)

Beam, Richard M.; Warming, Robert F.

1991-01-01

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Pressure profiles in detonation cells with rectangular and diagonal structures

NASA Astrophysics Data System (ADS)

Hanana, M.; Lefebvre, M. H.

Experimental results presented in this work enable us to classify the three-dimensional structure of the detonation into two fundamental types: a rectangular structure and a diagonal structure. The rectangular structure is well documented in the literature and consists of orthogonal waves travelling independently from each another. The soot record in this case shows the classical diamond detonation cell exhibiting `slapping waves'. The experiments indicate that the diagonal structure is a structure with the triple point intersections moving along the diagonal line of the tube cross section. The axes of the transverse waves are canted at 45 degrees to the wall, accounting for the lack of slapping waves. It is possible to reproduce these diagonal structures by appropriately controlling the experimental ignition procedure. The characteristics of the diagonal structure show some similarities with detonation structure in round tube. Pressure measurements recorded along the central axis of the cellular structure show a series of pressure peaks, depending on the type of structure and the position inside the detonation cell. Pressure profiles measured for the whole length of the two types of detonation cells show that the intensity of the shock front is higher and the length of the detonation cell is shorter for the diagonal structures.

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2932 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Improved L-BFGS diagonal preconditioners for a large-scale 4D-Var inversion system: application to CO2 flux constraints and analysis error calculation

NASA Astrophysics Data System (ADS)

Bousserez, Nicolas; Henze, Daven; Bowman, Kevin; Liu, Junjie; Jones, Dylan; Keller, Martin; Deng, Feng

2013-04-01

This work presents improved analysis error estimates for 4D-Var systems. From operational NWP models to top-down constraints on trace gas emissions, many of today's data assimilation and inversion systems in atmospheric science rely on variational approaches. This success is due to both the mathematical clarity of these formulations and the availability of computationally efficient minimization algorithms. However, unlike Kalman Filter-based algorithms, these methods do not provide an estimate of the analysis or forecast error covariance matrices, these error statistics being propagated only implicitly by the system. From both a practical (cycling assimilation) and scientific perspective, assessing uncertainties in the solution of the variational problem is critical. For large-scale linear systems, deterministic or randomization approaches can be considered based on the equivalence between the inverse Hessian of the cost function and the covariance matrix of analysis error. For perfectly quadratic systems, like incremental 4D-Var, Lanczos/Conjugate-Gradient algorithms have proven to be most efficient in generating low-rank approximations of the Hessian matrix during the minimization. For weakly non-linear systems though, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), a quasi-Newton descent algorithm, is usually considered the best method for the minimization. Suitable for large-scale optimization, this method allows one to generate an approximation to the inverse Hessian using the latest m vector/gradient pairs generated during the minimization, m depending upon the available core memory. At each iteration, an initial low-rank approximation to the inverse Hessian has to be provided, which is called preconditioning. The ability of the preconditioner to retain useful information from previous iterations largely determines the efficiency of the algorithm. Here we assess the performance of different preconditioners to estimate the inverse Hessian of a large-scale 4D-Var system. The impact of using the diagonal preconditioners proposed by Gilbert and Le Maréchal (1989) instead of the usual Oren-Spedicato scalar will be first presented. We will also introduce new hybrid methods that combine randomization estimates of the analysis error variance with L-BFGS diagonal updates to improve the inverse Hessian approximation. Results from these new algorithms will be evaluated against standard large ensemble Monte-Carlo simulations. The methods explored here are applied to the problem of inferring global atmospheric CO2 fluxes using remote sensing observations, and are intended to be integrated with the future NASA Carbon Monitoring System.

Texture zeros and hierarchical masses from flavour (mis)alignment

NASA Astrophysics Data System (ADS)

Hollik, W. G.; Saldana-Salazar, U. J.

2018-03-01

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrisation of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.

Tradeoffs between oscillator strength and lifetime in terahertz quantum cascade lasers

DOE PAGES

Chan, Chun Wang I.; Albo, Asaf; Hu, Qing; ...

2016-11-14

Contemporary research into diagonal active region terahertz quantum cascade lasers for high temperature operation has yielded little success. We present evidence that the failure of high diagonality alone as a design strategy is due to a fundamental trade-off between large optical oscillator strength and long upper-level lifetime. Here, we hypothesize that diagonality needs to be paired with increased doping in order to succeed, and present evidence that highly diagonal designs can benefit from much higher doping than normally found in terahertz quantum cascade lasers. In assuming the benefits of high diagonality paired with high doping, we also highlight important challengesmore » that need to be overcome, specifically the increased importance of carrier induced band-bending and impurity scattering.« less

Homogeneous matrix deposition on dried agar for MALDI imaging mass spectrometry of microbial cultures.

PubMed

Hoffmann, Thomas; Dorrestein, Pieter C

2015-11-01

Matrix deposition on agar-based microbial colonies for MALDI imaging mass spectrometry is often complicated by the complex media on which microbes are grown. This Application Note demonstrates how consecutive short spray pulses of a matrix solution can form an evenly closed matrix layer on dried agar. Compared with sieving dry matrix onto wet agar, this method supports analyte cocrystallization, which results in significantly more signals, higher signal-to-noise ratios, and improved ionization efficiency. The even matrix layer improves spot-to-spot precision of measured m/z values when using TOF mass spectrometers. With this technique, we established reproducible imaging mass spectrometry of myxobacterial cultures on nutrient-rich cultivation media, which was not possible with the sieving technique. Graphical Abstract ᅟ.

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2502 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 522 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 323' EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Mid-infrared matrix assisted laser desorption ionization with a water/glycerol matrix

NASA Astrophysics Data System (ADS)

Caldwell, Kathleen L.; Murray, Kermit K.

1998-05-01

Matrix-assisted laser desorption ionization (MALDI) mass spectra were obtained using a water and glycerol matrix with a tunable mid-infrared optical parametric oscillator. The matrix consists of a 1:1 mixture of water and glycerol deposited on a thin layer of nitrocellulose and cooled to -30°C. When exposed to vacuum, most of the water evaporates, leaving a matrix of glycerol with residual water. The peptide bradykinin and the protein bovine insulin were used to test this new matrix. Mass spectra were obtained for bradykinin between 2.76 and 3.1 μm with the maximum analyte signal at 2.8 μm. Mass resolution in excess of 2000 for bradykinin and 500 for insulin was obtained with delayed ion extraction and a linear time of flight mass spectrometer. The addition of nitrocellulose to the matrix resulted in exceptionally durable samples: more than 10,000 laser shots which produced analyte signal could be obtained from a single sample spot.

Diagonalizing Tensor Covariants, Light-Cone Commutators, and Sum Rules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lo, C. Y.

We derive fixed-mass sum rules for virtual Compton scattering the forward direction. We use the methods of both Dicus, Jackiw, and Teplitz (for the absorptive parts) and Heimann, Hey, and Mandula (for the real parts). We find a set of tensor covariansa such that the corresponding scalar amplitudes are proportional to simple t-channel parity-conserving helicity amplitudes. We give a relatively complete discussion of the convergence of the sum rules in a Regge model. (auth)

How the axial anomaly controls flavor mixing among mesons

NASA Astrophysics Data System (ADS)

Giacosa, Francesco; Koenigstein, Adrian; Pisarski, Robert D.

2018-05-01

It is well known that, because of the axial anomaly in QCD, mesons with JP=0- are close to S U (3 )V eigenstates; the η'(958 ) meson is largely a singlet, and the η meson an octet. In contrast, states with JP=1- are flavor diagonal; e.g., the ϕ (1020 ) is almost pure s ¯s . Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of Gfl=S U (3 )L×S U (3 )R. We construct effective Lagrangians from terms invariant under Gfl and introduce the concept of hetero- and homochiral multiplets. Because of the axial anomaly, only terms invariant under the Z (3 )A subgroup of the axial U (1 )A enter. For heterochiral multiplets, which begin with that including the η and η'(958 ), there are Z (3 )A invariant terms with low mass dimension which cause states to mix according to S U (3 )V flavor. For homochiral multiplets, which begin with that including the ϕ (1020 ), there are no Z (3 )A invariant terms with low mass dimension, and so states are diagonal in flavor. In this way, we predict the flavor mixing for the heterochiral multiplet with spin 1 as well as for hetero- and homochiral multiplets with spin 2 and spin 3.

Empirical performance of the multivariate normal universal portfolio

NASA Astrophysics Data System (ADS)

Tan, Choon Peng; Pang, Sook Theng

2013-09-01

Universal portfolios generated by the multivariate normal distribution are studied with emphasis on the case where variables are dependent, namely, the covariance matrix is not diagonal. The moving-order multivariate normal universal portfolio requires very long implementation time and large computer memory in its implementation. With the objective of reducing memory and implementation time, the finite-order universal portfolio is introduced. Some stock-price data sets are selected from the local stock exchange and the finite-order universal portfolio is run on the data sets, for small finite order. Empirically, it is shown that the portfolio can outperform the moving-order Dirichlet universal portfolio of Cover and Ordentlich[2] for certain parameters in the selected data sets.

Relativistic energy-dispersion relations of 2D rectangular lattices

NASA Astrophysics Data System (ADS)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia-Reyes, Gonzalo; Gonzalez, Guillermo A.

The interpretation of a family of electrovacuum stationary Taub-NUT-type fields in terms of finite charged perfect fluid disks is presented. The interpretation is made by means of an 'inverse problem' approach used to obtain disk sources of known solutions of the Einstein or Einstein-Maxwell equations. The diagonalization of the energy-momentum tensor of the disks is facilitated in this case by the fact that it can be written as an upper right triangular matrix. We find that the inclusion of electromagnetic fields changes significantly the different material properties of the disks and so we can obtain, for some values of themore » parameters, finite charged perfect fluid disks that are in agreement with all the energy conditions.« less

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.

PubMed

Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas

2015-07-14

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.

Decoherence dynamics of interacting qubits coupled to a bath of local optical phonons

NASA Astrophysics Data System (ADS)

Lone, Muzaffar Qadir; Yarlagadda, S.

2016-04-01

We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.

Decoupling correction system in RHIC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trbojevic, D.; Tepikian, S.; Peggs, S.

A global linear decoupling in the Relativistic Heavy Ion Collider (RHIC) is going to be performed with the three families of skew quadrupoles. The operating horizontal and vertical betatron tunes in the RHIC will be separated by one unit [nu][sub x]=28.19 and [nu][sub y]=29.18. The linear coupling is corrected by minimizing the tune splitting [Delta][nu]-the off diagonal matrix [bold m] (defined by Edwards and Teng). The skew quadrupole correction system is located close to each of the six interaction regions. A detail study of the system is presented by the use of the TEAPOT accelerator physics code. [copyright] 1994 Americanmore » Institute of Physics« less

Geometrical analysis of Cys-Cys bridges in proteins and their prediction from incomplete structural information

NASA Technical Reports Server (NTRS)

Goldblum, A.; Rein, R.

1987-01-01

Analysis of C-alpha atom positions from cysteines involved in disulphide bridges in protein crystals shows that their geometric characteristics are unique with respect to other Cys-Cys, non-bridging pairs. They may be used for predicting disulphide connections in incompletely determined protein structures, such as low resolution crystallography or theoretical folding experiments. The basic unit for analysis and prediction is the 3 x 3 distance matrix for Cx positions of residues (i - 1), Cys(i), (i +1) with (j - 1), Cys(j), (j + 1). In each of its columns, row and diagonal vector--outer distances are larger than the central distance. This analysis is compared with some analytical models.

Stochastic Formalism for Thermally Driven Distribution Frontier: A Nonempirical Approach to the Potential Escape Problem

NASA Astrophysics Data System (ADS)

Akashi, Ryosuke; Nagornov, Yuri S.

2018-06-01

We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the potential valleys. This method employs only the local gradient and diagonal part of the Hessian matrix of the potential. An application to a two-dimensional model potential is presented to demonstrate the successful finding of the paths to the saddle points. The present scheme could serve as a starting point toward first-principles simulation of rare events across the potential basins free from empirical collective variables.

SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1994-01-01

SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any SAMSAN algorithm; however, it is generally agreed by experienced users, and in the numerical error analysis literature, that computation with non-symmetric matrices of order greater than about 200 should be avoided or treated with extreme care. SAMSAN attempts to support the needs of application oriented analysis by providing: 1) a methodology with unlimited growth potential, 2) a methodology to insure that associated documentation is current and available "on demand", 3) a foundation of basic computational algorithms that most controls analysis procedures are based upon, 4) a set of check out and evaluation programs which demonstrate usage of the algorithms on a series of problems which are structured to expose the limits of each algorithm's applicability, and 5) capabilities which support both a priori and a posteriori error analysis for the computational algorithms provided. The SAMSAN algorithms are coded in FORTRAN 77 for batch or interactive execution and have been implemented on a DEC VAX computer under VMS 4.7. An effort was made to assure that the FORTRAN source code was portable and thus SAMSAN may be adaptable to other machine environments. The documentation is included on the distribution tape or can be purchased separately at the price below. SAMSAN version 2.0 was developed in 1982 and updated to version 3.0 in 1988.

Chaos in non-diagonal spatially homogeneous cosmological models in spacetime dimensions <=10

NASA Astrophysics Data System (ADS)

Demaret, Jacques; de Rop, Yves; Henneaux, Marc

1988-08-01

It is shown that the chaotic oscillatory behaviour, absent in diagonal homogeneous cosmological models in spacetime dimensions between 5 and 10, can be reestablished when off-diagonal terms are included. Also at Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile

Modular Exhaust Design and Manufacturing Techniques for Low Cost Mid Volume Rapid Buidl to Order Systems

DTIC Science & Technology

2014-08-06

the pressure field is uniform across them, but which allow mass flow to be diverted. Series elements have a constant mass flow across the ports...they can be used to calculate the pressure and mass flow after the element from the pressure and mass flow prior to the element, as shown in...the matrix product of each transfer matrix in turn. The final matrix gives no information about the pressures and mass flows within the element

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 270t EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE WEST GATE ROAD CULVERT, LOOKING 3052 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 2742 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Simplicity and Typical Rank Results for Three-Way Arrays

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2011-01-01

Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

Generalized Reich-Moore R-matrix approximation

NASA Astrophysics Data System (ADS)

Arbanas, Goran; Sobes, Vladimir; Holcomb, Andrew; Ducru, Pablo; Pigni, Marco; Wiarda, Dorothea

2017-09-01

A conventional Reich-Moore approximation (RMA) of R-matrix is generalized into a manifestly unitary form by introducing a set of resonant capture channels treated explicitly in a generalized, reduced R-matrix. A dramatic reduction of channel space witnessed in conventional RMA, from Nc × Nc full R-matrix to Np × Np reduced R-matrix, where Nc = Np + Nγ, Np and Nγ denoting the number of particle and γ-ray channels, respectively, is due to Np < Nγ. A corresponding reduction of channel space in generalized RMA (GRMA) is from Nc × Nc full R-matrix to N × N, where N = Np + N, and where N is the number of capture channels defined in GRMA. We show that N = Nλ where Nλ is the number of R-matrix levels. This reduction in channel space, although not as dramatic as in the conventional RMA, could be significant for medium and heavy nuclides where N < Nγ. The resonant capture channels defined by GRMA accommodate level-level interference (via capture channels) neglected in conventional RMA. The expression for total capture cross section in GRMA is formally equal to that of the full Nc × NcR-matrix. This suggests that GRMA could yield improved nuclear data evaluations in the resolved resonance range at a cost of introducing N(N - 1)/2 resonant capture width parameters relative to conventional RMA. Manifest unitarity of GRMA justifies a method advocated by Fröhner and implemented in the SAMMY nuclear data evaluation code for enforcing unitarity of conventional RMA. Capture widths of GRMA are exactly convertible into alternative R-matrix parameters via Brune tranform. Application of idealized statistical methods to GRMA shows that variance among conventional RMA capture widths in extant RMA evaluations could be used to estimate variance among off-diagonal elements neglected by conventional RMA. Significant departure of capture widths from an idealized distribution may indicate the presence of underlying doorway states.

Dissipation and distribution behavior of azoxystrobin, carbendazim, and difenoconazole in pomegranate fruits.

PubMed

Utture, Sagar C; Banerjee, Kaushik; Dasgupta, Soma; Patil, Sangram H; Jadhav, Manjusha R; Wagh, Sameer S; Kolekar, Sanjay S; Anuse, Mansing A; Adsule, Pandurang G

2011-07-27

The dissipation behavior and degradation kinetics of azoxystrobin, carbendazim, and difenoconazole in pomegranate are reported. Twenty fruits/hectare (5 kg) were collected at random, ensuring sample-to-sample relative standard deviation (RSD) within 20-25%. Each fruit was cut into eight equal portions, and two diagonal pieces per fruit were drawn and combined to constitute the laboratory sample, resulting in RSDs <6% (n = 6). Crushed sample (15 g) was extracted with 10 mL of ethyl acetate (+ 10 g Na(2)SO(4)), cleaned by dispersive solid phase extraction on primary secondary amine (25 mg) and C(18) (25 mg), and measured by liquid chromatography tandem mass spectrometry. The limit of quantification was ≤0.0025 μg g(-1) for all the three fungicides, with calibration linearity in the concentration range of 0.001-0.025 μg mL(-1) (r(2) ≥ 0.999). The recoveries of each chemical were 75-110% at 0.0025, 0.005, and 0.010 μg g(-1) with intralaboratory Horwitz ratio <0.32 at 0.0025 μg g(-1). Variable matrix effects were recorded in different fruit parts viz rind, albedo, membrane, and arils, which could be correlated to their biochemical constituents as evidenced from accurate mass measurements on a Q-ToF LC-MS. The residues of carbendazim and difenoconazole were confined within the outer rind of pomegranate; however, azoxystrobin penetrated into the inner fruit parts. The dissipation of azoxystrobin, carbendazim, and difenoconazole followed first + first order kinetics at both standard and double doses, with preharvest intervals being 9, 60, and 26 days at standard dose. At double dose, the preharvest intervals extended to 20.5, 100, and 60 days, respectively.

Reactive solute transport in an asymmetrical fracture-rock matrix system

NASA Astrophysics Data System (ADS)

Zhou, Renjie; Zhan, Hongbin

2018-02-01

The understanding of reactive solute transport in a single fracture-rock matrix system is the foundation of studying transport behavior in the complex fractured porous media. When transport properties are asymmetrically distributed in the adjacent rock matrixes, reactive solute transport has to be considered as a coupled three-domain problem, which is more complex than the symmetric case with identical transport properties in the adjacent rock matrixes. This study deals with the transport problem in a single fracture-rock matrix system with asymmetrical distribution of transport properties in the rock matrixes. Mathematical models are developed for such a problem under the first-type and the third-type boundary conditions to analyze the spatio-temporal concentration and mass distribution in the fracture and rock matrix with the help of Laplace transform technique and de Hoog numerical inverse Laplace algorithm. The newly acquired solutions are then tested extensively against previous analytical and numerical solutions and are proven to be robust and accurate. Furthermore, a water flushing phase is imposed on the left boundary of system after a certain time. The diffusive mass exchange along the fracture/rock matrixes interfaces and the relative masses stored in each of three domains (fracture, upper rock matrix, and lower rock matrix) after the water flushing provide great insights of transport with asymmetric distribution of transport properties. This study has the following findings: 1) Asymmetric distribution of transport properties imposes greater controls on solute transport in the rock matrixes. However, transport in the fracture is mildly influenced. 2) The mass stored in the fracture responses quickly to water flushing, while the mass stored in the rock matrix is much less sensitive to the water flushing. 3) The diffusive mass exchange during the water flushing phase has similar patterns under symmetric and asymmetric cases. 4) The characteristic distance which refers to the zero diffusion between the fracture and the rock matrix during the water flushing phase is closely associated with dispersive process in the fracture.

Influence of superoleophobic layer on the lubrication performance of partially textured bearing including cavitation

NASA Astrophysics Data System (ADS)

Tauviqirrahman, M.; Bayuseno, A. P.; Muchammad, Jamari, J.

2016-04-01

Surfaces with high superoleophobicity have attracted important attention because of their potential applications in scientific and industrial field. Especially classical metal bearing are faced with lubrication problem, because metal surface shows typically oleophilicity. The development of superolephobic metal surfaces which repel oil liquid droplet have significant applications in preventing the stiction. In addition, for classical bearing with texturing, the cavitation occurence is often considered as the main cause of the deterioration of the lubrication performance and thus shorten the lifetime of the bearing. In the present study, the exploration of the influence of adding the superoleophobic layer on the improvement of the performance of partially textured bearing in preventing the cavitation was performed. Navier slip model was used to model the behavior of the superoleophobic layer. A formulation of the modified Reynolds equation with mass-conserving boundary conditions was derived and the pressure distribution was of particular interest. The equations of lubrication were discretized using a finite volume method and solved using a tri-diagonal-matrix-algortihm. In this calculation, it was shown that after introducing the superoleophobic layer at the leading edge of the contact, the cavitation occurence can be prevented and thus the increased hydrodynamic pressure is found. However, the results showed that for deeper texture, the deterioration of the load support is noted. This findings may have useful implications to extend the life time of textured bearing.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noor, Fatimah A., E-mail: fatimah@fi.itb.ac.id; Iskandar, Ferry; Abdullah, Mikrajuddin

In this paper, we discuss the electron transmittance and tunneling current in high-k-based-MOS capacitors with trapping charge by including the off-diagonal effective-mass tensor elements and the effect of coupling between transverse and longitudinal energies represented by an electron velocity in the gate. The HfSiO{sub x}N/SiO{sub 2} dual ultrathin layer is used as the gate oxide in an n{sup +} poly- Si/oxide/Si capacitor to replace SiO{sub 2}. The main problem of using HfSiO{sub x}N is the charge trapping formed at the HfSiO{sub x}N/SiO{sub 2} interface that can influence the performance of the device. Therefore, it is important to develop a modelmore » taking into account the presence of electron traps at the HfSiO{sub x}N/SiO{sub 2} interface in the electron transmittance and tunneling current. The transmittance and tunneling current in n{sup +} poly- Si/HfSiO{sub x}N/trap/SiO2/Si(100) capacitors are calculated by using Airy wavefunctions and a transfer matrix method (TMM) as analytical and numerical approaches, respectively. The transmittance and tunneling current obtained from the Airy wavefunction are compared to those computed by the TMM. The effects of the electron velocity on the transmittance and tunneling current are also discussed.« less

Double-β decay within a consistent deformed approach

NASA Astrophysics Data System (ADS)

Delion, D. S.; Suhonen, J.

2015-05-01

In this paper we present a timely application of the proton-neutron deformed quasiparticle random-phase approximation (p n -dQRPA), designed to describe in a consistent way the 1+ Gamow-Teller states in odd-odd deformed nuclei. For this purpose we apply a projection before variation procedure by using a single-particle basis with projected angular momentum, provided by the diagonalization of a spherical mean field plus quadrupole-quadrupole interaction. The residual Hamiltonian contains pairing plus proton-neutron dipole terms in particle-hole and particle-particle channels, with constant strengths. As an example we describe the two-neutrino double-beta (2 ν β β ) decay of 150Nd to the ground state of 150Sm. The experimental (p ,n ) type of strength in 150Nd and the (n ,p ) type of strength in 150Sm are reasonably reproduced and the 2 ν β β decay matrix element depicts a strong dependence upon the particle-particle strength gp p. The experimental half-life is reproduced for gp p=0.05 . It turns out that the measured half-lives for 2 ν β β transitions between other deformed superfluid partners with mass numbers A =82 ,96,100,128,130,238 are reproduced with fairly good accuracy by using this value of gp p.

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling

PubMed Central

Meyer, Sarah; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale–international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting. PMID:28809939

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling.

PubMed

van Dijk, Margaretha M; Meyer, Sarah; Sandstad, Solveig; Wiskerke, Evelyne; Thuwis, Rhea; Vandekerckhove, Chesny; Myny, Charlotte; Ghosh, Nitesh; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale-international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting.

Steering Bell-diagonal states

PubMed Central

Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li

2016-01-01

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250

Two dimensional symmetric correlation functions of the S-circumflex operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Q.; Boulet, C.; Tipping, R. H.

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonalmore » elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.« less

VLBI-derived troposphere parameters during CONT08

NASA Astrophysics Data System (ADS)

Heinkelmann, R.; Böhm, J.; Bolotin, S.; Engelhardt, G.; Haas, R.; Lanotte, R.; MacMillan, D. S.; Negusini, M.; Skurikhina, E.; Titov, O.; Schuh, H.

2011-07-01

Time-series of zenith wet and total troposphere delays as well as north and east gradients are compared, and zenith total delays ( ZTD) are combined on the level of parameter estimates. Input data sets are provided by ten Analysis Centers (ACs) of the International VLBI Service for Geodesy and Astrometry (IVS) for the CONT08 campaign (12-26 August 2008). The inconsistent usage of meteorological data and models, such as mapping functions, causes systematics among the ACs, and differing parameterizations and constraints add noise to the troposphere parameter estimates. The empirical standard deviation of ZTD among the ACs with regard to an unweighted mean is 4.6 mm. The ratio of the analysis noise to the observation noise assessed by the operator/software impact (OSI) model is about 2.5. These and other effects have to be accounted for to improve the intra-technique combination of VLBI-derived troposphere parameters. While the largest systematics caused by inconsistent usage of meteorological data can be avoided and the application of different mapping functions can be considered by applying empirical corrections, the noise has to be modeled in the stochastic model of intra-technique combination. The application of different stochastic models shows no significant effects on the combined parameters but results in different mean formal errors: the mean formal errors of the combined ZTD are 2.3 mm (unweighted), 4.4 mm (diagonal), 8.6 mm [variance component (VC) estimation], and 8.6 mm (operator/software impact, OSI). On the one hand, the OSI model, i.e. the inclusion of off-diagonal elements in the cofactor-matrix, considers the reapplication of observations yielding a factor of about two for mean formal errors as compared to the diagonal approach. On the other hand, the combination based on VC estimation shows large differences among the VCs and exhibits a comparable scaling of formal errors. Thus, for the combination of troposphere parameters a combination of the two extensions of the stochastic model is recommended.

Recursive flexible multibody system dynamics using spatial operators

NASA Technical Reports Server (NTRS)

Jain, A.; Rodriguez, G.

1992-01-01

This paper uses spatial operators to develop new spatially recursive dynamics algorithms for flexible multibody systems. The operator description of the dynamics is identical to that for rigid multibody systems. Assumed-mode models are used for the deformation of each individual body. The algorithms are based on two spatial operator factorizations of the system mass matrix. The first (Newton-Euler) factorization of the mass matrix leads to recursive algorithms for the inverse dynamics, mass matrix evaluation, and composite-body forward dynamics for the systems. The second (innovations) factorization of the mass matrix, leads to an operator expression for the mass matrix inverse and to a recursive articulated-body forward dynamics algorithm. The primary focus is on serial chains, but extensions to general topologies are also described. A comparison of computational costs shows that the articulated-body, forward dynamics algorithm is much more efficient than the composite-body algorithm for most flexible multibody systems.

Automated acoustic matrix deposition for MALDI sample preparation.

PubMed

Aerni, Hans-Rudolf; Cornett, Dale S; Caprioli, Richard M

2006-02-01

Novel high-throughput sample preparation strategies for MALDI imaging mass spectrometry (IMS) and profiling are presented. An acoustic reagent multispotter was developed to provide improved reproducibility for depositing matrix onto a sample surface, for example, such as a tissue section. The unique design of the acoustic droplet ejector and its optimization for depositing matrix solution are discussed. Since it does not contain a capillary or nozzle for fluid ejection, issues with clogging of these orifices are avoided. Automated matrix deposition provides better control of conditions affecting protein extraction and matrix crystallization with the ability to deposit matrix accurately onto small surface features. For tissue sections, matrix spots of 180-200 microm in diameter were obtained and a procedure is described for generating coordinate files readable by a mass spectrometer to permit automated profile acquisition. Mass spectral quality and reproducibility was found to be better than that obtained with manual pipet spotting. The instrument can also deposit matrix spots in a dense array pattern so that, after analysis in a mass spectrometer, two-dimensional ion images may be constructed. Example ion images from a mouse brain are presented.