EIGENVALUE PROBLEM OF A LARGE SCALE INDEFINITE GYROSCOPIC DYNAMIC SYSTEM
Institute of Scientific and Technical Information of China (English)
SUI Yong-feng; ZHONG Wan-xie
2006-01-01
Gyroscopic dynamic system can be introduced to Hamiltonian system. Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system,an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system. The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used. The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented, and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem. Therefore, the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved, and two numerical examples were given to demonstrate that the eigensolutions converge exactly.
EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.
Tal-Ezer, Hillel
2016-05-19
Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.
Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design
Energy Technology Data Exchange (ETDEWEB)
Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC
2006-09-28
A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.
Luukko, P. J. J.; Räsänen, E.
2013-03-01
We present a code for solving the single-particle, time-independent Schrödinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP method: the arbitrary order operator factorization and the exact inclusion of a (possibly very strong) magnetic field. Our program is able to solve thousands of eigenstates of a two-dimensional quantum system in reasonable time with commonly available hardware. The main motivation behind our work is to allow the study of highly excited states and energy spectra of two-dimensional quantum dots and billiard systems with a single versatile code, e.g., in quantum chaos research. In our implementation we emphasize a modern and easily extensible design, simple and user-friendly interfaces, and an open-source development philosophy. Catalogue identifier: AENR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 11310 No. of bytes in distributed program, including test data, etc.: 97720 Distribution format: tar.gz Programming language: C++ and Python. Computer: Tested on x86 and x86-64 architectures. Operating system: Tested under Linux with the g++ compiler. Any POSIX-compliant OS with a C++ compiler and the required external routines should suffice. Has the code been vectorised or parallelized?: Yes, with OpenMP. RAM: 1 MB or more, depending on system size. Classification: 7.3. External routines: FFTW3 (http://www.fftw.org), CBLAS (http://netlib.org/blas), LAPACK (http://www.netlib.org/lapack), HDF5 (http://www.hdfgroup.org/HDF5), OpenMP (http://openmp.org), TCLAP (http://tclap.sourceforge.net), Python (http://python.org), Google Test (http://code.google.com/p/googletest/) Nature of problem: Numerical calculation
M. Genseberger (Menno)
2008-01-01
htmlabstractMost computational work in Jacobi-Davidson [9], an iterative method for large scale eigenvalue problems, is due to a so-called correction equation. In [5] a strategy for the approximate solution of the correction equation was proposed. This strategy is based on a domain decomposition
Sensitivity analysis for large-scale problems
Noor, Ahmed K.; Whitworth, Sandra L.
1987-01-01
The development of efficient techniques for calculating sensitivity derivatives is studied. The objective is to present a computational procedure for calculating sensitivity derivatives as part of performing structural reanalysis for large-scale problems. The scope is limited to framed type structures. Both linear static analysis and free-vibration eigenvalue problems are considered.
Quadratic eigenvalue problems.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Energy Technology Data Exchange (ETDEWEB)
Yamazaki, Ichitaro; Wu, Kesheng; Simon, Horst
2008-10-27
The original software package TRLan, [TRLan User Guide], page 24, implements the thick restart Lanczos method, [Wu and Simon 2001], page 24, for computing eigenvalues {lambda} and their corresponding eigenvectors v of a symmetric matrix A: Av = {lambda}v. Its effectiveness in computing the exterior eigenvalues of a large matrix has been demonstrated, [LBNL-42982], page 24. However, its performance strongly depends on the user-specified dimension of a projection subspace. If the dimension is too small, TRLan suffers from slow convergence. If it is too large, the computational and memory costs become expensive. Therefore, to balance the solution convergence and costs, users must select an appropriate subspace dimension for each eigenvalue problem at hand. To free users from this difficult task, nu-TRLan, [LNBL-1059E], page 23, adjusts the subspace dimension at every restart such that optimal performance in solving the eigenvalue problem is automatically obtained. This document provides a user guide to the nu-TRLan software package. The original TRLan software package was implemented in Fortran 90 to solve symmetric eigenvalue problems using static projection subspace dimensions. nu-TRLan was developed in C and extended to solve Hermitian eigenvalue problems. It can be invoked using either a static or an adaptive subspace dimension. In order to simplify its use for TRLan users, nu-TRLan has interfaces and features similar to those of TRLan: (1) Solver parameters are stored in a single data structure called trl-info, Chapter 4 [trl-info structure], page 7. (2) Most of the numerical computations are performed by BLAS, [BLAS], page 23, and LAPACK, [LAPACK], page 23, subroutines, which allow nu-TRLan to achieve optimized performance across a wide range of platforms. (3) To solve eigenvalue problems on distributed memory systems, the message passing interface (MPI), [MPI forum], page 23, is used. The rest of this document is organized as follows. In Chapter 2 [Installation
1987-06-01
and f. Let us consider the problem of finding the minimal constant C. We are thus interested in 2~ IVA u dx (1.24) C = sup . u2u (0 (F =0 (u dx"<u(O...fournir des bornes superieures ou inferieures, C.R. Acad. Sci., Paris 235, 995-997. .V Prodi, G. (1962]: Theoremi di tipo locale per il sistema de Navier
On the buckling eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Antunes, Pedro R S, E-mail: pant@cii.fc.ul.pt [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. do Campo Grande, 376, 1749-024 Lisboa (Portugal); Group of Mathematical Physics of the University of Lisbon, Complexo Interdisciplinar, Av. Professor Gama Pinto 2, P-1649-003 Lisboa (Portugal)
2011-05-27
We prove a density result which allows us to justify the application of the method of fundamental solutions to solve the buckling eigenvalue problem of a plate. We address an example of an analytic convex domain for which the first eigenfunction does change the sign and present a large-scale numerical study with polygons providing numerical evidence to some new conjectures.
Highly indefinite multigrid for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Borges, L.; Oliveira, S.
1996-12-31
Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as
Subspace Methods for Eigenvalue Problems
Hochstenbach, Michiel Erik
2003-01-01
This thesis treats a number of aspects of subspace methods for various eigenvalue problems. Vibrations and their corresponding eigenvalues (or frequencies) arise in science, engineering, and daily life. Matrix eigenvalue problems come from a large number of areas, such as chemistry, mechanics, dyn
Ensemble methods for large scale inverse problems
Heemink, A.W.; Umer Altaf, M.; Barbu, A.L.; Verlaan, M.
2013-01-01
Variational data assimilation, also sometimes simply called the ‘adjoint method’, is used very often for large scale model calibration problems. Using the available data, the uncertain parameters in the model are identified by minimizing a certain cost function that measures the difference between t
Random eigenvalue problems revisited
Indian Academy of Sciences (India)
S Adhikari
2006-08-01
The description of real-life engineering structural systems is associated with some amount of uncertainty in specifying material properties, geometric parameters, boundary conditions and applied loads. In the context of structural dynamics it is necessary to consider random eigenvalue problems in order to account for these uncertainties. Within the engineering literature, current methods to deal with such problems are dominated by approximate perturbation methods. Some exact methods to obtain joint distribution of the natural frequencies are reviewed and their applicability in the context of real-life engineering problems is discussed. A new approach based on an asymptotic approximation of multi-dimensional integrals is proposed. A closed-form expression for general order joint moments of arbitrary numbers of natural frequencies of linear stochastic systems is derived. The proposed method does not employ the ‘small randomness’ assumption usually used in perturbation based methods. Joint distributions of the natural frequencies are investigated using numerical examples and the results are compared with Monte Carlo simulation.
Energy Technology Data Exchange (ETDEWEB)
Lehoucq, Richard B.; Salinger, Andrew G.
1999-08-01
We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady state leads to a generalized eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration, which must be done iteratively for the algorithm to scale with problem size. A representative model problem of 3D incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation.
Stabilization Algorithms for Large-Scale Problems
DEFF Research Database (Denmark)
Jensen, Toke Koldborg
2006-01-01
The focus of the project is on stabilization of large-scale inverse problems where structured models and iterative algorithms are necessary for computing approximate solutions. For this purpose, we study various iterative Krylov methods and their abilities to produce regularized solutions. Some......-curve. This heuristic is implemented as a part of a larger algorithm which is developed in collaboration with G. Rodriguez and P. C. Hansen. Last, but not least, a large part of the project has, in different ways, revolved around the object-oriented Matlab toolbox MOORe Tools developed by PhD Michael Jacobsen. New...
THE EIGENVALUE PROBLEM FOR THE LAPLACIAN EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω, u = 0, x ∈ (δ)Ω, where Ω (∩) Rn is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T.Yau et al.
Iterative approach for the eigenvalue problems
Indian Academy of Sciences (India)
J Datta; P K Bera
2011-01-01
An approximation method based on the iterative technique is developed within the framework of linear delta expansion (LDE) technique for the eigenvalues and eigenfunctions of the one-dimensional and three-dimensional realistic physical problems. This technique allows us to obtain the coefficient in the perturbation series for the eigenfunctions and the eigenvalues directly by knowing the eigenfunctions and the eigenvalues of the unperturbed problems in quantum mechanics. Examples are presented to support this. Hence, the LDE technique can be used for non-perturbative as well as perturbative systems to find approximate solutions of eigenvalue problems.
A study of MLFMA for large-scale scattering problems
Hastriter, Michael Larkin
This research is centered in computational electromagnetics with a focus on solving large-scale problems accurately in a timely fashion using first principle physics. Error control of the translation operator in 3-D is shown. A parallel implementation of the multilevel fast multipole algorithm (MLFMA) was studied as far as parallel efficiency and scaling. The large-scale scattering program (LSSP), based on the ScaleME library, was used to solve ultra-large-scale problems including a 200lambda sphere with 20 million unknowns. As these large-scale problems were solved, techniques were developed to accurately estimate the memory requirements. Careful memory management is needed in order to solve these massive problems. The study of MLFMA in large-scale problems revealed significant errors that stemmed from inconsistencies in constants used by different parts of the algorithm. These were fixed to produce the most accurate data possible for large-scale surface scattering problems. Data was calculated on a missile-like target using both high frequency methods and MLFMA. This data was compared and analyzed to determine possible strategies to increase data acquisition speed and accuracy through multiple computation method hybridization.
Large-Scale Inverse Problems and Quantification of Uncertainty
Biegler, Lorenz; Ghattas, Omar
2010-01-01
Large-scale inverse problems and associated uncertainty quantification has become an important area of research, central to a wide range of science and engineering applications. Written by leading experts in the field, Large-scale Inverse Problems and Quantification of Uncertainty focuses on the computational methods used to analyze and simulate inverse problems. The text provides PhD students, researchers, advanced undergraduate students, and engineering practitioners with the perspectives of researchers in areas of inverse problems and data assimilation, ranging from statistics and large-sca
Topology Optimization of Large Scale Stokes Flow Problems
DEFF Research Database (Denmark)
Aage, Niels; Poulsen, Thomas Harpsøe; Gersborg-Hansen, Allan
2008-01-01
This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.......This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs....
Das, S.; Goswami, K.; Datta, B. N.
2016-05-01
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of a loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Finally the most robust set of feedback matrices is selected from the set of probabilistically characterized optimal closed-loop system to implement the new methodology for design of active controlled structures. Numerical examples are presented to illustrate the proposed methodology.
Multiparameter eigenvalue problems Sturm-Liouville theory
Atkinson, FV
2010-01-01
One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problems: Sturm-Liouville Theory reflects much of Dr. Atkinson's final work.After covering standard multiparameter problems, the book investigates the conditions for eigenvalues to be real and form a discrete set. It gives results on the determinants of fun
Multiparameter eigenvalue problems and expansion theorems
Volkmer, Hans
1988-01-01
This book provides a self-contained treatment of two of the main problems of multiparameter spectral theory: the existence of eigenvalues and the expansion in series of eigenfunctions. The results are first obtained in abstract Hilbert spaces and then applied to integral operators and differential operators. Special attention is paid to various definiteness conditions which can be imposed on multiparameter eigenvalue problems. The reader is not assumed to be familiar with multiparameter spectral theory but should have some knowledge of functional analysis, in particular of Brower's degree of maps.
Pattern selection as a nonlinear eigenvalue problem
Büchel, P
1996-01-01
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed through-flow. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the boundary conditions in addition to the driving rate and the through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation elucidates how the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation. PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.Ft
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
A note on quasilinear elliptic eigenvalue problems
Directory of Open Access Journals (Sweden)
Gianni Arioli
1999-11-01
Full Text Available We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.
The eigenvalue problem in phase space.
Cohen, Leon
2017-07-27
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Solving large scale traveling salesman problems by chaotic neurodynamics.
Hasegawa, Mikio; Ikeguch, Tohru; Aihara, Kazuyuki
2002-03-01
We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.
Inverse Eigenvalue Problem in Structural Dynamics Design
Institute of Scientific and Technical Information of China (English)
Huiqing Xie; Hua Dai
2006-01-01
A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum solution is proved. The directional derivative of the objective function is obtained and a necessary condition for a point to be a local minimum point is given. Then a numerical algorithm for solving the problem is presented and a plane-truss problem is discussed to show the applications of the theories and the algorithm.
SOLVING TRUST REGION PROBLEM IN LARGE SCALE OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Bing-sheng He
2000-01-01
This paper presents a new method for solving the basic problem in the “model trust region” approach to large scale minimization: Compute a vector x such that 1/2xTHx + cTx = min, subject to the constraint ‖x‖2≤a. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with x0 = 0 as the start point either directly offers a solution of the problem, or--as soon as the norm of the iterate greater than a, --it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.
Generalized Inverse Eigenvalue Problem for Centrohermitian Matrices
Institute of Scientific and Technical Information of China (English)
刘仲云; 谭艳祥; 田兆录
2004-01-01
In this paper we first consider the existence and the general form of solution to the following generalized inverse eigenvalue problem(GIEP) : given a set of n-dimension complex vectors { xj }jm = 1 and a set of complex numbers { λj} jm = 1, find two n × n centrohermitian matrices A, B such that { xj }jm = 1 and { λj }jm= 1 are the generalized eigenvectors and generalized eigenvalues of Ax = λBx, respectively. We then discuss the optimal approximation problem for the GIEP. More concretely, given two arbitrary matrices, A-, B- ∈Cn×n , we find two matrices A* and B* such that the matrix (A* ,B* ) is closest to (A- ,B-) in the Frobenius norm, where the matrix (A*, B* ) is the solution to the GIEP. We show that the expression of the solution of the optimal approximation is unique and derive the expression for it.
Sparse Regression as a Sparse Eigenvalue Problem
Moghaddam, Baback; Gruber, Amit; Weiss, Yair; Avidan, Shai
2008-01-01
We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization
Kernel Projection Algorithm for Large-Scale SVM Problems
Institute of Scientific and Technical Information of China (English)
王家琦; 陶卿; 王珏
2002-01-01
Support Vector Machine (SVM) has become a very effective method in sta-tistical machine learning and it has proved that training SVM is to solve Nearest Point pairProblem (NPP) between two disjoint closed convex sets. Later Keerthi pointed out that it isdifficult to apply classical excellent geometric algorithms directly to SVM and so designed anew geometric algorithm for SVM. In this article, a new algorithm for geometrically solvingSVM, Kernel Projection Algorithm, is presented based on the theorem on fixed-points of pro-jection mapping. This new algorithm makes it easy to apply classical geometric algorithmsto solving SVM and is more understandable than Keerthi's. Experiments show that the newalgorithm can also handle large-scale SVM problems. Geometric algorithms for SVM, such asKeerthi's algorithm, require that two closed convex sets be disjoint and otherwise the algo-rithms are meaningless. In this article, this requirement will be guaranteed in theory by usingthe theoretic result on universal kernel functions.
Periodic cells for large-scale problem initialization
Ciantia, Matteo O.; Arroyo, Marcos; Zhang, Ningning; Emam, Sacha
2017-06-01
In geotechnical applications the success of the discrete element method (DEM) in simulating fundamental aspects of soil behaviour has increased the interest in applications for direct simulation of engineering scale boundary value problems (BVP's). The main problem is that the method remains relatively expensive in terms of computational cost. A non-negligible part of that cost is related to specimen creation and initialization. As the response of soil is strongly dependant on its initial state (stress and porosity), attaining a specified initial state is a crucial part of a DEM model. Different procedures for controlled sample generation are available. However, applying the existing REV-oriented initialization procedures to such models is inefficient in terms of computational cost and challenging in terms of sample homogeneity. In this work a simple but efficient procedure to initialize large-scale DEM models is presented. Periodic cells are first generated with a sufficient number of particles matching a desired particle size distribution (PSD). The cells are then equilibrated at low-level isotropic stress at target porosity. Once the cell is in equilibrium, it is replicated in space in order to fill the model domain. After the domain is thus filled a few mechanical cycles are needed to re-equilibrate the large domain. The result is a large, homogeneous sample, equilibrated under prescribed stress at the desired porosity. The method is applicable to both isotropic and anisotropic initial stress states, with stress magnitude varying in space.
Iterative solution of the reduced eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Sauer, G. (Technischer Ueberwachungs-Verein Bayern e.V., Muenchen (Germany, F.R.))
1991-04-01
The Guyan method of reducing the stiffness and mass matrices of large linear structures introduces errors in the reduced mass matrix. These errors cannot be completely avoided even if the analysis coordinates are chosen optimally. However, they can be elimiated by iterating on the eigenvectors found from the Guyan reduced matrices. The necessary iteration steps follow directly from the eigenvalue problem. The resulting iteration procedures are presented and applied to two test problems showing that the iterations enable the exact eigensolutions to be extracted. All errors from the Guyan reduced matrices are removed or substantially decreased. (orig.).
Frequency response as a surrogate eigenvalue problem in topology optimization
DEFF Research Database (Denmark)
Andreassen, Erik; Ferrari, Federico; Sigmund, Ole
2017-01-01
This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...
Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision.
Kukelova, Zuzana; Bujnak, Martin; Pajdla, Tomas
2012-07-01
We present a method for solving systems of polynomial equations appearing in computer vision. This method is based on polynomial eigenvalue solvers and is more straightforward and easier to implement than the state-of-the-art Gröbner basis method since eigenvalue problems are well studied, easy to understand, and efficient and robust algorithms for solving these problems are available. We provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems (PEPs) and present a resultant-based method for transforming a system of polynomial equations to a polynomial eigenvalue problem. We propose techniques that can be used to reduce the size of the computed polynomial eigenvalue problems. To show the applicability of the proposed polynomial eigenvalue method, we present the polynomial eigenvalue solutions to several important minimal relative pose problems.
DERIVATIVES OF EIGENPAIRS OF SYMMETRIC QUADRATIC EIGENVALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Derivatives of eigenvalues and eigenvectors with respect to parameters in symmetric quadratic eigenvalue problem are studied. The first and second order derivatives of eigenpairs are given. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space representation is avoided, hence the cost of computation is greatly reduced. The efficiency of the presented method is demonstrated by considering a spring-mass-damper system.
Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem
Schwarz, A
2000-01-01
We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\\lambda$ where $\\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem about the structure of perturbation series for Tr $x^r$ where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).
A randomized Mirror-Prox method for solving structured large-scale matrix saddle-point problems
Baes, Michel; Nemirovski, Arkadi
2011-01-01
In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's Smoothing Techniques or standard Mirror-Prox methods, require the exact computation of a matrix exponential at every iteration, limiting the size of the problems they can solve. Our method allows us to use stochastic approximations of matrix exponentials. We prove that our randomized scheme decreases significantly the complexity of its deterministic counterpart for large-scale matrix saddle-point problems. Numerical experiments illustrate and confirm our theoretical results.
Newton Methods for Large Scale Problems in Machine Learning
Hansen, Samantha Leigh
2014-01-01
The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…
Newton Methods for Large Scale Problems in Machine Learning
Hansen, Samantha Leigh
2014-01-01
The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…
Preconditioned Krylov subspace methods for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Wu, Kesheng; Saad, Y.; Stathopoulos, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
Lanczos algorithm is a commonly used method for finding a few extreme eigenvalues of symmetric matrices. It is effective if the wanted eigenvalues have large relative separations. If separations are small, several alternatives are often used, including the shift-invert Lanczos method, the preconditioned Lanczos method, and Davidson method. The shift-invert Lanczos method requires direct factorization of the matrix, which is often impractical if the matrix is large. In these cases preconditioned schemes are preferred. Many applications require solution of hundreds or thousands of eigenvalues of large sparse matrices, which pose serious challenges for both iterative eigenvalue solver and preconditioner. In this paper we will explore several preconditioned eigenvalue solvers and identify the ones suited for finding large number of eigenvalues. Methods discussed in this paper make up the core of a preconditioned eigenvalue toolkit under construction.
A Two-Level Method for Nonsymmetric Eigenvalue Problems
Institute of Scientific and Technical Information of China (English)
Karel Kolman
2005-01-01
A two-level discretization method for eigenvalue problems is studied. Compared to the standard Galerkin finite element discretization technique performed on a fine grid this method discretizes the eigenvalue problem on a coarse grid and obtains an improved eigenvector (eigenvalue) approximation by solving only a linear problem on the fine grid (or two linear problems for the case of eigenvalue approximation of nonsymmetric problems). The improved solution has the asymptotic accuracy of the Galerkin discretization solution. The link between the method and the iterated Galerkin method is established. Error estimates for the general nonsymmetric case are derived.
Inverse Eigenvalue Problems for Two Special Acyclic Matrices
Directory of Open Access Journals (Sweden)
Debashish Sharma
2016-03-01
Full Text Available In this paper, we study two inverse eigenvalue problems (IEPs of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix and one eigenvalue of each of its leading principal submatrices. The second problem involves reconstruction of matrices whose graph is a broom, the eigen data being the maximum and minimum eigenvalues of each of the leading principal submatrices of the required matrix. In order to solve the problems, we use the recurrence relations among leading principal minors and the property of simplicity of the extremal eigenvalues of acyclic matrices.
Enabling High Performance Large Scale Dense Problems through KBLAS
Abdelfattah, Ahmad
2014-05-04
KBLAS (KAUST BLAS) is a small library that provides highly optimized BLAS routines on systems accelerated with GPUs. KBLAS is entirely written in CUDA C, and targets NVIDIA GPUs with compute capability 2.0 (Fermi) or higher. The current focus is on level-2 BLAS routines, namely the general matrix vector multiplication (GEMV) kernel, and the symmetric/hermitian matrix vector multiplication (SYMV/HEMV) kernel. KBLAS provides these two kernels in all four precisions (s, d, c, and z), with support to multi-GPU systems. Through advanced optimization techniques that target latency hiding and pushing memory bandwidth to the limit, KBLAS outperforms state-of-the-art kernels by 20-90% improvement. Competitors include CUBLAS-5.5, MAGMABLAS-1.4.0, and CULAR17. The SYMV/HEMV kernel from KBLAS has been adopted by NVIDIA, and should appear in CUBLAS-6.0. KBLAS has been used in large scale simulations of multi-object adaptive optics.
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second......This thesis investigates new optimization methods for structural topology optimization problems. The aim of topology optimization is finding the optimal design of a structure. The physical problem is modelled as a nonlinear optimization problem. This powerful tool was initially developed...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...
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.
High-precision methods in eigenvalue problems and their applications
Akulenko, Leonid D
2004-01-01
This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and consider numerous eigenvalue problems that appear in oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics, structural mechanics, electrodynamics, and microelectronics.
Convergence of adaptive finite element methods for eigenvalue problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2008-01-01
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
The interior transmission problem and bounds on transmission eigenvalues
Hitrik, Michael; Ola, Petri; Päivärinta, Lassi
2010-01-01
We study the interior transmission eigenvalue problem for sign-definite multiplicative perturbations of the Laplacian in a bounded domain. We show that all but finitely many complex transmission eigenvalues are confined to a parabolic neighborhood of the positive real axis.
Local and Parallel Finite Element Algorithms for Eigenvalue Problems
Institute of Scientific and Technical Information of China (English)
Jinchao Xu; Aihui Zhou
2002-01-01
Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed.Some relationships between the finite element method and the finite difference method are addressed,too.
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions
Institute of Scientific and Technical Information of China (English)
DAI Xiaoying; YANG Zhang; ZHOU Aihui
2008-01-01
Based on a linear finite element space, two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed. Some relationships between the finite element method and the finite difference method are addressed, too.
On a quasilinear elliptic eigenvalue problem with constraint
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.
A generalized eigenvalue problem solution for an uncoupled multicomponent system
Energy Technology Data Exchange (ETDEWEB)
Diago-Cisneros, L; Fernandez-Anaya, G; Bonfanti-Escalera, G [Departamento de Fisica y Matematicas, Universidad Iberoamericana, CP 01219, DF Mexico (Mexico)], E-mail: ldiago@fisica.uh.cu
2008-09-15
Meaningful and well-founded physical quantities are convincingly determined by eigenvalue problem solutions emerging from a second-order N-coupled system of differential equations, known as the Sturm-Liouville matrix boundary problem. Via the generalized Schur decomposition procedure and imposing to the multicomponent system to be decoupled, which is a widely accepted remarkable physical situation, we have unambiguously demonstrated a simultaneously triangularizable scenario for (2Nx2N) matrices content in a generalized eigenvalue equation.
Hybrid constraint programming and metaheuristic methods for large scale optimization problems
2011-01-01
This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatori...
Existence of a principal eigenvalue for the Tricomi problem
Directory of Open Access Journals (Sweden)
Daniela Lupo
2000-10-01
Full Text Available The existence of a principal eigenvalue is established for the Tricomi problem in normal domains; that is, the existence of a positive eigenvalue of minimum modulus with an associated positive eigenfunction. The argument here uses prior results of the authors on the generalized solvability in weighted Sobolev spaces and associated maximum/minimum principles cite{[LP2]} coupled with known results of Krein-Rutman type.
NUMERICAL SOLUTIONS OF AN EIGENVALUE PROBLEM IN UNBOUNDED DOMAINS
Institute of Scientific and Technical Information of China (English)
Han Houde; Zhou Zhenya; Zheng Chunxiong
2005-01-01
A coupling method of finite element and infinite large element is proposed for the numerical solution of an eigenvalue problem in unbounded domains in this paper. With some conditions satisfied, the considered problem is proved to have discrete spectra. Several numerical experiments are presented. The results demonstrate the feasibility of the proposed method.
Institute of Scientific and Technical Information of China (English)
Qin Ni
2001-01-01
An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and possesses Q-quadratic convergence rate. The global convergence of this new method is proved,the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.
MODIFIED BOTTLENECK-BASED PROCEDURE FOR LARGE-SCALE FLOW-SHOP SCHEDULING PROBLEMS WITH BOTTLENECK
Institute of Scientific and Technical Information of China (English)
ZUO Yan; GU Hanyu; XI Yugeng
2006-01-01
A new bottleneck-based heuristic for large-scale flow-shop scheduling problems with a bottleneck is proposed, which is simpler but more tailored than the shifting bottleneck (SB)procedure. In this algorithm, a schedule for the bottleneck machine is first constructed optimally and then the non-bottleneck machines are scheduled around the bottleneck schedule by some effective dispatching rules. Computational results show that the modified bottleneck-based procedure can achieve a tradeoff between solution quality and computational time comparing with SB procedure for medium-size problems. Furthermore it can obtain a good solution in quite short time for large-scale scheduling problems.
An Inverse Eigenvalue Problem for Jacobi Matrices
Directory of Open Access Journals (Sweden)
Zhengsheng Wang
2011-01-01
eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.
Nonlinear eigenvalue problems with semipositone structure
Directory of Open Access Journals (Sweden)
Alfonso Castro
2000-10-01
Full Text Available In this paper we summarize the developments of semipositone problems to date, including very recent results on semipositone systems. We also discuss applications and open problems.
An eigenvalue problem for the associated Askey-Wilson polynomials
Bruder, Andrea; Suslov, Sergei K
2012-01-01
To derive an eigenvalue problem for the associated Askey-Wilson polynomials, we consider an auxiliary function in two variables which is related to the associated Askey-Wilson polynomials introduced by Ismail and Rahman. The Askey-Wilson operator, applied in each variable separately, maps this function to the ordinary Askey-Wilson polynomials with different sets of parameters. A third Askey-Wilson operator is found with the help of a computer algebra program which links the two, and an eigenvalue problem is stated.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The performance of analytical derivative and sparse matrix techniques applied to a traditional densesequential quadratic programming(SQP) is studied, and the strategy utilizing those techniques is also presented. Computational results on two typicalchemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy ispromising and suitable for large-scale process optimization problems.
A multilevel finite element method for Fredholm integral eigenvalue problems
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
Tavakoli, Ruhollah
2010-01-01
The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly called as continuous knapsack problems. Since there are efficient methods to solve large-scale bound constrained nonlinear programs, it is desirable to adapt these methods to solve knapsack problems, while preserving their efficiency and convergence theories. The goal of this paper is to introduce a general framework to extend a box-constrained optimization solver to solve knapsack problems. This framework includes two main ingredients which are O(n) methods; in terms of the computational cost and required memory; for the projection onto the knapsack constrains and the null-space manipulation of the related linear constraint. The main focus of this work is on the extension of Hager-Zhang active set algorithm (SIAM J. Optim. 2006, pp. 526--557). The main reasons for this ch...
He, Qiang; Hu, Xiangtao; Ren, Hong; Zhang, Hongqi
2015-11-01
A novel artificial fish swarm algorithm (NAFSA) is proposed for solving large-scale reliability-redundancy allocation problem (RAP). In NAFSA, the social behaviors of fish swarm are classified in three ways: foraging behavior, reproductive behavior, and random behavior. The foraging behavior designs two position-updating strategies. And, the selection and crossover operators are applied to define the reproductive ability of an artificial fish. For the random behavior, which is essentially a mutation strategy, the basic cloud generator is used as the mutation operator. Finally, numerical results of four benchmark problems and a large-scale RAP are reported and compared. NAFSA shows good performance in terms of computational accuracy and computational efficiency for large scale RAP.
On the eigenvalue spectrum for time-delayed Floquet problems
Just, Wolfram
2000-08-01
A linear homogeneous scalar differential-difference equation with harmonic time dependence is investigated. The associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation. The dependence of the largest eigenvalue on the system parameters, being relevant for stability of periodic states in delay systems, is discussed in detail. The competition between the two timescales, the delay and the external period cause intricate structures. The result suggests features to improve control of chaos by time-delayed feedback schemes with time-dependent control amplitudes.
A filtering method for the interval eigenvalue problem
DEFF Research Database (Denmark)
Hladik, Milan; Daney, David; Tsigaridas, Elias
2011-01-01
We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer approximation (superset) of the real eigenvalue set of an interval matrix, we propose a filtering method that iteratively improves the approximation. Even though our method...... is based on a sufficient regularity condition, it is very efficient in practice and our experimental results suggest that it improves, in general, significantly the initial outer approximation. The proposed method works for general, as well as for symmetric interval matrices....
Biharmonic eigen-value problems and Lp estimates
Directory of Open Access Journals (Sweden)
Chaitan P. Gupta
1990-01-01
Full Text Available Biharmonic eigen-values arise in the study of static equilibrium of an elastic body which has been suitably secured at the boundary. This paper is concerned mainly with the existence of and Lp-estimates for the solutions of certain biharmonic boundary value problems which are related to the first eigen-values of the associated biharmonic operators. The methods used in this paper consist of the a-priori estimates due to Agmon-Douglas-Nirenberg and P. L. Lions along with the Fredholm theory for compact operators.
Boundary and eigenvalue problems in mathematical physics
Sagan, Hans
1989-01-01
This well-known text uses a limited number of basic concepts and techniques - Hamilton's principle, the theory of the first variation and Bernoulli's separation method - to develop complete solutions to linear boundary value problems associated with second order partial differential equations such as the problems of the vibrating string, the vibrating membrane, and heat conduction. It is directed to advanced undergraduate and beginning graduate students in mathematics, applied mathematics, physics, and engineering who have completed a course in advanced calculus. In the first three chapters,
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2016-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet is demonstrated.
A note on solving large-scale zero-one programming problems
Adema, Jos J.
1988-01-01
A heuristic for solving large-scale zero-one programming problems is provided. The heuristic is based on the modifications made by H. Crowder et al. (1983) to the standard branch-and-bound strategy. First, the initialization is modified. The modification is only useful if the objective function valu
Large scale inverse problems computational methods and applications in the earth sciences
Scheichl, Robert; Freitag, Melina A; Kindermann, Stefan
2013-01-01
This book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.
A note on solving large-scale zero-one programming problems
Adema, Jos J.
1988-01-01
A heuristic for solving large-scale zero-one programming problems is provided. The heuristic is based on the modifications made by H. Crowder et al. (1983) to the standard branch-and-bound strategy. First, the initialization is modified. The modification is only useful if the objective function valu
A note on solving large-scale zero-one programming problems
Adema, Jos J.
1988-01-01
A heuristic for solving large-scale zero-one programming problems is provided. The heuristic is based on the modifications made by H. Crowder et al. (1983) to the standard branch-and-bound strategy. First, the initialization is modified. The modification is only useful if the objective function
Benders' Decomposition Based Heuristics for Large-Scale Dynamic Quadratic Assignment Problems
Directory of Open Access Journals (Sweden)
Sirirat Muenvanichakul
2009-01-01
Full Text Available Problem statement: Dynamic Quadratic Assignment Problem (DQAP is NP hard problem. Benders decomposition based heuristics method is applied to the equivalent mixed-integer linear programming problem of the original DQAP. Approach: Approximate Benders Decomposition (ABD generates the ensemble of a subset of feasible layout for Approximate Dynamic Programming (ADP to determine the sub-optimal optimal solution. A Trust-Region Constraint (TRC for the master problem in ABD and a Successive Adaptation Procedure (SAP were implemented to accelerate the convergence rate of the method. Results: The sub-optimal solutions of large-scales DQAPs from the method and its variants were compared well with other metaheuristic methods. Conclusion: Overall performance of the method is comparable to other metaheuristic methods for large-scale DQAPs.
A Reduced Basis Framework: Application to large scale non-linear multi-physics problems
Directory of Open Access Journals (Sweden)
Daversin C.
2013-12-01
Full Text Available In this paper we present applications of the reduced basis method (RBM to large-scale non-linear multi-physics problems. We first describe the mathematical framework in place and in particular the Empirical Interpolation Method (EIM to recover an affine decomposition and then we propose an implementation using the open-source library Feel++ which provides both the reduced basis and finite element layers. Large scale numerical examples are shown and are connected to real industrial applications arising from the High Field Resistive Magnets development at the Laboratoire National des Champs Magnétiques Intenses.
Combining Nearest Neighbor Search with Tabu Search for Large-Scale Vehicle Routing Problem
Du, Lingling; He, Ruhan
The vehicle routing problem is a classical problem in operations research, where the objective is to design least cost routes for a fleet of identical capacitated vehicles to service geographically scattered customers. In this paper, we present a new and effective hybrid metaheuristic algorithm for large-scale vehicle routing problem. The algorithm combines the strengths of the well-known Nearest Neighbor Search and Tabu Search into a two-stage procedure. More precisely, Nearest Neighbor Search is used to construct initial routes in the first stage and the Tabu Search is utilized to optimize the intra-route and the inter-route in the second stage. The presented algorithm is specifically designed for large-scale problems. The computational experiments were carried out on a standard benchmark and a real dataset with 6772 tobacco customers. The results demonstrate that the suggested method is highly competitive.
Ergul, Ozgur
2014-01-01
The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetic Problems provides a detailed and instructional overview of implementing MLFMA. The book: Presents a comprehensive treatment of the MLFMA algorithm, including basic linear algebra concepts, recent developments on the parallel computation, and a number of application examplesCovers solutions of electromagnetic problems involving dielectric objects and perfectly-conducting objectsDiscusses applications including scattering from airborne targets, scattering from red
A NESTED PARTITIONS FRAMEWORK FOR SOLVING LARGE-SCALE MULTICOMMODITY FACILITY LOCATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
Leyuan SHI; Robert R.MEYER; Mehmet BOZBAY; Andrew J.MILLER
2004-01-01
Large-scale multicommodity facility location problems are generally intractable with respect to standard mixed-integer programming (MIP) tools such as the direct application of general-purpose Branch & Cut (BC) commercial solvers i.e. CPLEX. In this paper, the authors investigate a nested partitions (NP) framework that combines meta-heuristics with MIP tools (including branch-and-cut).We also consider a variety of alternative formulations and decomposition methods for this problem class. Our results show that our NP framework is capable of efficiently producing very high quality solutions to multicommodity facility location problems. For large-scale problems in this class, this approach is significantly faster and generates better feasible solutions than either CPLEX (applied directly to the given MIP) or the iterative Lagrangian-based methods that have generally been regarded as the most effective structure-based techniques for optimization of these problems. We also briefly discuss some other large-scale MIP problem classes for which this approach is expected to be very effective.
Luukko, P J J
2013-01-01
We present a code for solving the single-particle, time-independent Schr\\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP method: the arbitrary order operator factorization and the exact inclusion of a (possibly very strong) magnetic field. Our program is able to solve thousands of eigenstates of a two-dimensional quantum system in reasonable time with commonly available hardware. The main motivation behind our work is to allow the study of highly excited states and energy spectra of two-dimensional quantum dots and billiard systems with a single versatile code, e.g., in quantum chaos research. In our implementation we emphasize a modern and easily extensible design, simple and user-friendly interfaces, and an open-source development philosophy.
2013-01-01
We present a code for solving the single-particle, time-independent Schr\\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP method: the arbitrary order operator factorization and the exact inclusion of a (possibly very strong) magnetic field. Our program is able to solve thousands of eigenstates of a two-dimensional quantum system in reasonable time with commonly available hardware. ...
Explicit solution for an infinite dimensional generalized inverse eigenvalue problem
Directory of Open Access Journals (Sweden)
Kazem Ghanbari
2001-01-01
Full Text Available We study a generalized inverse eigenvalue problem (GIEP, Ax=λBx, in which A is a semi-infinite Jacobi matrix with positive off-diagonal entries ci>0, and B= diag (b0,b1,…, where bi≠0 for i=0,1,…. We give an explicit solution by establishing an appropriate spectral function with respect to a given set of spectral data.
Kulshreshtha, Kshitij; Nataraj, Neela
2005-08-01
The paper deals with a parallel implementation of a mixed finite element method of approximation of eigenvalues and eigenvectors of fourth order eigenvalue problems with variable/constant coefficients. The implementation has been done in Silicon Graphics Origin 3800, a four processor Intel Xeon Symmetric Multiprocessor and a beowulf cluster of four Intel Pentium III PCs. The generalised eigenvalue problem obtained after discretization using the mixed finite element method is solved using the package LANSO. The numerical results obtained are compared with existing results (if available). The time, speedup comparisons in different environments for some examples of practical and research interest and importance are also given.
Solving a large-scale precedence constrained scheduling problem with elastic jobs using tabu search
DEFF Research Database (Denmark)
Pedersen, C.R.; Rasmussen, R.V.; Andersen, Kim Allan
2007-01-01
This paper presents a solution method for minimizing makespan of a practical large-scale scheduling problem with elastic jobs. The jobs are processed on three servers and restricted by precedence constraints, time windows and capacity limitations. We derive a new method for approximating the server...... exploitation of the elastic jobs and solve the problem using a tabu search procedure. Finding an initial feasible solution is in general -complete, but the tabu search procedure includes a specialized heuristic for solving this problem. The solution method has proven to be very efficient and leads...
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2017-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated.
Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method
Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter
2017-01-01
An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851
Minimization of Linear Functionals Defined on| Solutions of Large-Scale Discrete Ill-Posed Problems
DEFF Research Database (Denmark)
Elden, Lars; Hansen, Per Christian; Rojas, Marielba
2003-01-01
The minimization of linear functionals de ned on the solutions of discrete ill-posed problems arises, e.g., in the computation of con dence intervals for these solutions. In 1990, Elden proposed an algorithm for this minimization problem based on a parametric-programming reformulation involving...... the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat...
Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction
Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng
2017-01-01
Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.
Plain strain problem of poroelasticity using eigenvalue approach
Indian Academy of Sciences (India)
Rajneesh Kumar; Aseem Miglani; N R Garg
2000-09-01
A plain strain problem of an isotropic elastic liquid-saturated porous medium in poroelasticity has been studied. The eigenvalue approach using the Laplace and Fourier transforms has been employed and these transforms have been inverted by using a numerical technique. An application of infinite space with concentrated force at the origin has been presented to illustrate the utility of the approach. The displacement and stress components in the physical domain are obtained numerically. The results are shown graphically and can be used for a broad class of problems related to liquid-saturated porous media.
An Integer Programming-based Local Search for Large-scale Maximal Covering Problems
Directory of Open Access Journals (Sweden)
Junha Hwang
2011-02-01
Full Text Available Maximal covering problem (MCP is classified as a linear integer optimization problem which can be effectively solved by integer programming technique. However, as the problem size grows, integerprogramming requires excessive time to get an optimal solution. This paper suggests a method for applying integer programming-based local search (IPbLS to solve large-scale maximal covering problems. IPbLS, which is a hybrid technique combining integer programming and local search, is a kind of local search using integer programming for neighbor generation. IPbLS itself is very effective for MCP. In addition, we improve the performance of IPbLS for MCP through problem reduction based on the current solution. Experimental results show that the proposed method considerably outperforms any other local search techniques and integer programming.
An Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems
Directory of Open Access Journals (Sweden)
Yongxin Yuan
2009-01-01
analytical mass and stiffness matrices, so that ( has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are specified.
HIGH ACCURACY ANALYSIS OF ELLIPTIC EIGENVALUE PROBLEM FOR THE WILSON NONCONFORMING FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
吴冬生
2001-01-01
In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigen-value problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue are obtained.
Scaled first-order methods for a class of large-scale constrained least square problems
Coli, Vanna Lisa; Ruggiero, Valeria; Zanni, Luca
2016-10-01
Typical applications in signal and image processing often require the numerical solution of large-scale linear least squares problems with simple constraints, related to an m × n nonnegative matrix A, m « n. When the size of A is such that the matrix is not available in memory and only the operators of the matrix-vector products involving A and AT can be computed, forward-backward methods combined with suitable accelerating techniques are very effective; in particular, the gradient projection methods can be improved by suitable step-length rules or by an extrapolation/inertial step. In this work, we propose a further acceleration technique for both schemes, based on the use of variable metrics tailored for the considered problems. The numerical effectiveness of the proposed approach is evaluated on randomly generated test problems and real data arising from a problem of fibre orientation estimation in diffusion MRI.
A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
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Fatemeh Mohammad
2014-05-01
Full Text Available In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem $Ax = \\lambda Bx$[Q.~Ye and P.~Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011 1697-1715]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
Levenberg-Marquardt method for the eigenvalue complementarity problem.
Chen, Yuan-yuan; Gao, Yan
2014-01-01
The eigenvalue complementarity problem (EiCP) is a kind of very useful model, which is widely used in the study of many problems in mechanics, engineering, and economics. The EiCP was shown to be equivalent to a special nonlinear complementarity problem or a mathematical programming problem with complementarity constraints. The existing methods for solving the EiCP are all nonsmooth methods, including nonsmooth or semismooth Newton type methods. In this paper, we reformulate the EiCP as a system of continuously differentiable equations and give the Levenberg-Marquardt method to solve them. Under mild assumptions, the method is proved globally convergent. Finally, some numerical results and the extensions of the method are also given. The numerical experiments highlight the efficiency of the method.
Solving a real-life large-scale energy management problem
Godskesen, Steffen; Kjeldsen, Niels; Larsen, Rune
2010-01-01
This paper introduces a three-phase heuristic approach for a large-scale energy management and maintenance scheduling problem. The problem is concerned with scheduling maintenance and refueling for nuclear power plants up to five years into the future, while handling a number of scenarios for future demand and prices. The goal is to minimize the expected total production costs. The first phase of the heuristic solves a simplified constraint programming model of the problem, the second performs a local search, and the third handles overproduction in a greedy fashion. This work was initiated in the context of the ROADEF/EURO Challenge 2010, a competition organized jointly by the French Operational Research and Decision Support Society, the European Operational Research Society, and the European utility company Electricite de France. In the concluding phase of the competition our team ranked second in the junior category and sixth overall. After correcting an implementation bug in the program that was submitted ...
A raw material storage yard allocation problem for a large-scale steelworks
Energy Technology Data Exchange (ETDEWEB)
Kim, B.I.; Koo, J.; Park, B.S. [POSTECH, Pohang (Republic of Korea). Department of Industrial and Management Engineering
2009-04-15
This paper addresses a raw material storage yard allocation problem at a large-scale steelworks. At the steelworks, raw materials such as coal and iron ore are imported by ships from overseas, discharged from the ships by unloading equipment, and transported into and stored in the yards. The stored materials then are transported and used in the production equipment such as steel mills. The yard allocation decision, i.e., where to store the materials, determines the travel distance of the materials as well as the storage efficiency of the yards. Here, the yard allocation problem is solved using a mixed integer programming model. The solution compares favorably with the current practice of the steelworks.
Consensus properties and their large-scale applications for the gene duplication problem.
Moon, Jucheol; Lin, Harris T; Eulenstein, Oliver
2016-06-01
Solving the gene duplication problem is a classical approach for species tree inference from gene trees that are confounded by gene duplications. This problem takes a collection of gene trees and seeks a species tree that implies the minimum number of gene duplications. Wilkinson et al. posed the conjecture that the gene duplication problem satisfies the desirable Pareto property for clusters. That is, for every instance of the problem, all clusters that are commonly present in the input gene trees of this instance, called strict consensus, will also be found in every solution to this instance. We prove that this conjecture does not generally hold. Despite this negative result we show that the gene duplication problem satisfies a weaker version of the Pareto property where the strict consensus is found in at least one solution (rather than all solutions). This weaker property contributes to our design of an efficient scalable algorithm for the gene duplication problem. We demonstrate the performance of our algorithm in analyzing large-scale empirical datasets. Finally, we utilize the algorithm to evaluate the accuracy of standard heuristics for the gene duplication problem using simulated datasets.
Approximation on computing partial sum of nonlinear differential eigenvalue problems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In computing the electronic structure and energy band in a system of multi-particles, quite a large number of problems are referred to the acquisition of obtaining the partial sum of densities and energies using the “first principle”. In the conventional method, the so-called self-consistency approach is limited to a small scale because of high computing complexity. In this paper, the problem of computing the partial sum for a class of nonlinear differential eigenvalue equations is changed into the constrained functional minimization. By space decomposition and perturbation method, a secondary approximating formula for the minimal is provided. It is shown that this formula is more precise and its quantity of computation can be reduced significantly
Application of spectral Lanczos decomposition method to large scale problems arising geophysics
Energy Technology Data Exchange (ETDEWEB)
Tamarchenko, T. [Western Atlas Logging Services, Houston, TX (United States)
1996-12-31
This paper presents an application of Spectral Lanczos Decomposition Method (SLDM) to numerical modeling of electromagnetic diffusion and elastic waves propagation in inhomogeneous media. SLDM approximates an action of a matrix function as a linear combination of basis vectors in Krylov subspace. I applied the method to model electromagnetic fields in three-dimensions and elastic waves in two dimensions. The finite-difference approximation of the spatial part of differential operator reduces the initial boundary-value problem to a system of ordinary differential equations with respect to time. The solution to this system requires calculating exponential and sine/cosine functions of the stiffness matrices. Large scale numerical examples are in a good agreement with the theoretical error bounds and stability estimates given by Druskin, Knizhnerman, 1987.
On large-scale nonlinear programming techniques for solving optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
A multi-step method for partial eigenvalue assignment problem of high order control systems
Liu, Hao; Xu, Jiajia
2017-09-01
In this paper, we consider the partial eigenvalue assignment problem of high order control systems. Based on the orthogonality relations, we propose a new method for solving this problem by which the undesired eigenvalues are moved to desired values and keep the remaining eigenvalues unchanged. Using the inverse of Cauchy matrix, we give the solvable condition and the explicit solutions to this problem. Numerical examples show that our method is effective.
Dual mean field search for large scale linear and quadratic knapsack problems
Banda, Juan; Velasco, Jonás; Berrones, Arturo
2017-07-01
An implementation of mean field annealing to deal with large scale linear and non linear binary optimization problems is given. Mean field annealing is based on the analogy between combinatorial optimization and interacting physical systems at thermal equilibrium. Specifically, a mean field approximation of the Boltzmann distribution given by a Lagrangian that encompass the objective function and the constraints is calculated. The original discrete task is in this way transformed into a continuous variational problem. In our version of mean field annealing, no temperature parameter is used, but a good starting point in the dual space is given by a ;thermodynamic limit; argument. The method is tested in linear and quadratic knapsack problems with sizes that are considerably larger than those used in previous studies of mean field annealing. Dual mean field annealing is capable to find high quality solutions in running times that are orders of magnitude shorter than state of the art algorithms. Moreover, as may be expected for a mean field theory, the solutions tend to be more accurate as the number of variables grow.
Indefinite Eigenvalue Problems for p-Laplacian Operators with Potential Terms on Networks
Directory of Open Access Journals (Sweden)
Jea-Hyun Park
2014-01-01
Full Text Available We address some forward and inverse problems involving indefinite eigenvalues for discrete p-Laplacian operators with potential terms. These indefinite eigenvalues are the discrete analogues of p-Laplacians on Riemannian manifolds with potential terms. We first define and discuss some fundamental properties of the indefinite eigenvalue problems for discrete p-Laplacian operators with potential terms with respect to some given weight functions. We then discuss resonance problems, anti-minimum principles, and inverse conductivity problems for the discrete p-Laplacian operators with potential terms involving the smallest indefinite eigenvalues.
Several concepts to investigate strongly nonnormal eigenvalue problems
Dorsselaer, J.L.M. van
2001-01-01
Eigenvalue analysis plays an important role in understanding physical phenomena. However, if one deals with strongly nonnormal matrices or operators, the eigenvalues alone may not tell the full story. A popular tool which can be useful to get more insight in the reliability or sensitivity of eigenva
Numerical study of three-parameter matrix eigenvalue problem by Rayleigh quotient method
Bora, Niranjan; Baruah, Arun Kumar
2016-06-01
In this paper, an attempt is done to find approximate eigenvalues and the corresponding eigenvectors of three-parameter matrix eigenvalue problem by extending Rayleigh Quotient Iteration Method (RQIM), which is generally used to solve generalized eigenvalue problems of the form Ax = λBx. Convergence criteria of RQIM will be derived in terms of matrix 2-norm. We will test the computational efficiency of the Method analytically with the help of numerical examples. All calculations are done in MATLAB software.
MULTICRITERIА PROBLEM OF FINDING THE OPTIMAL PATHS FOR LARGE-SCALE TRANSPORT SYSTEM
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Pavlov D. A.
2015-11-01
Full Text Available This article explores the multicriteria problems arise in the organization of routes in large-scale transport management system. As a mathematical tool for constructing a model, we were using the prefractal graphs. Prefractal graphs naturally reflect structure of the device of communications of transport system, reflecting its important features – locality and differentiation. Locality is provided with creation of internal routes (city, raionwide, etc.. Differentiation is understood as division of routes on intra regional, interregional and international. The objective is reduced to a covering of prefractal graphs by the simple paths which are crossed on edges and nodes. On the set of feasible solutions, vector criterion function with certain criteria is based. In concepts of transport system, the given criteria have concrete substantial interpretation, the transport routes allowing to design considering features of system. In this article, we construct polynomial algorithms for finding optimal according to certain criteria decision. By the criteria which aren't optimizing the allocated routes their estimates of the lower and upper bounds are given. On all given algorithms the estimates of computing complexity confirming advantage of use of methods of prefractal and fractal graphs before classical methods of the theory of graphs are constructed and proved
A Framing Link Based Tabu Search Algorithm for Large-Scale Multidepot Vehicle Routing Problems
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Xuhao Zhang
2014-01-01
Full Text Available A framing link (FL based tabu search algorithm is proposed in this paper for a large-scale multidepot vehicle routing problem (LSMDVRP. Framing links are generated during continuous great optimization of current solutions and then taken as skeletons so as to improve optimal seeking ability, speed up the process of optimization, and obtain better results. Based on the comparison between pre- and postmutation routes in the current solution, different parts are extracted. In the current optimization period, links involved in the optimal solution are regarded as candidates to the FL base. Multiple optimization periods exist in the whole algorithm, and there are several potential FLs in each period. If the update condition is satisfied, the FL base is updated, new FLs are added into the current route, and the next period starts. Through adjusting the borderline of multidepot sharing area with dynamic parameters, the authors define candidate selection principles for three kinds of customer connections, respectively. Link split and the roulette approach are employed to choose FLs. 18 LSMDVRP instances in three groups are studied and new optimal solution values for nine of them are obtained, with higher computation speed and reliability.
Gross, Lutz; Altinay, Cihan; Fenwick, Joel; Smith, Troy
2014-05-01
inversion and appropriate solution schemes in escript. We will also give a brief introduction into escript's open framework for defining and solving geophysical inversion problems. Finally we will show some benchmark results to demonstrate the computational scalability of the inversion method across a large number of cores and compute nodes in a parallel computing environment. References: - L. Gross et al. (2013): Escript Solving Partial Differential Equations in Python Version 3.4, The University of Queensland, https://launchpad.net/escript-finley - L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306 - T. Poulet, L. Gross, D. Georgiev, J. Cleverley (2012): escript-RT: Reactive transport simulation in Python using escript, Computers & Geosciences, Volume 45, 168-176. http://dx.doi.org/10.1016/j.cageo.2011.11.005.
Quantum inequalities and "quantum interest" as eigenvalue problems
Fewster, C J; Fewster, Christopher J.; Teo, Edward
2000-01-01
Quantum inequalities (QI's) provide lower bounds on the averaged energy density of a quantum field. We show how the QI's for massless scalar fields in even dimensional Minkowski space may be reformulated in terms of the positivity of a certain self-adjoint operator - a generalised Schroedinger operator with the energy density as the potential - and hence as an eigenvalue problem. We use this idea to verify that the energy density produced by a moving mirror in two dimensions is compatible with the QI's for a large class of mirror trajectories. In addition, we apply this viewpoint to the `quantum interest conjecture' of Ford and Roman, which asserts that the positive part of an energy density always overcompensates for any negative components. For various simple models in two and four dimensions we obtain the best possible bounds on the `quantum interest rate' and on the maximum delay between a negative pulse and a compensating positive pulse. Perhaps surprisingly, we find that - in four dimensions - it is imp...
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
PRECONDITIONING BLOCK LANCZOS ALGORITHM FOR SOLVING SYMMETRIC EIGENVALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
Hua Dai; Peter Lancaster
2000-01-01
A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated.
Antar, B. N.
1976-01-01
A numerical technique is presented for locating the eigenvalues of two point linear differential eigenvalue problems. The technique is designed to search for complex eigenvalues belonging to complex operators. With this method, any domain of the complex eigenvalue plane could be scanned and the eigenvalues within it, if any, located. For an application of the method, the eigenvalues of the Orr-Sommerfeld equation of the plane Poiseuille flow are determined within a specified portion of the c-plane. The eigenvalues for alpha = 1 and R = 10,000 are tabulated and compared for accuracy with existing solutions.
On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations
Directory of Open Access Journals (Sweden)
Heinrich Voss
2016-06-01
Full Text Available Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi–Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example.
Integral Transforms and a Class of Singular S-Hermitian Eigenvalue Problems
Dijksma, A.; Snoo, H.S.V. de
1973-01-01
For a class of singular S-hermitian eigenvalue problems we show that the corresponding integral transforms are surjective. This class was discussed by us earlier and is more restricted than the one, which has been considered by others.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A modified bottleneck-based (MB) heuristic for large-scale job-shop scheduling problems with a welldefined bottleneck is suggested,which is simpler but more tailored than the shifting bottleneck (SB) procedure.In this algorithm,the bottleneck is first scheduled optimally while the non-bottleneck machines are subordinated around the solutions of the bottleneck schedule by some effective dispatching rules.Computational results indicate that the MB heuristic can achieve a better tradeoff between solution quality and computational time compared to SB procedure for medium-size problems.Furthermore,it can obtain a good solution in a short time for large-scale job-shop scheduling problems.
Directory of Open Access Journals (Sweden)
Pengzhan Huang
2011-01-01
Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.
Directory of Open Access Journals (Sweden)
Yidu Yang
2012-01-01
Full Text Available This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.
An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy
Energy Technology Data Exchange (ETDEWEB)
Wu Yongtang [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Wang Hongye [Department of Mathematics, Zhengzhou University, Henan (China); Du Dianlou [Department of Mathematics, Zhengzhou University, Henan (China)]. E-mail: ddl@zzu.edu.cn
2002-05-03
A 3x3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2x2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation. (author)
A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
Directory of Open Access Journals (Sweden)
Yidu Yang
2012-01-01
Full Text Available This paper discusses highly efficient discretization schemes for mixed variational formulation of eigenvalue problems. A new finite element two-scale discretization scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue problems. With this scheme, the solution of an eigenvalue problem on a fine grid Kh is reduced to the solution of an eigenvalue problem on a much coarser grid KH and the solution of a linear algebraic system on the fine grid Kh. Theoretical analysis shows that the scheme has high efficiency. For instance, when using the Mini element to solve Stokes eigenvalue problem, the resulting solution can maintain an asymptotically optimal accuracy by taking H=O(h4, and when using the Pk+1-Pk element to solve eigenvalue problems of electric field, the calculation results can maintain an asymptotically optimal accuracy by taking H=O(h3. Finally, numerical experiments are presented to support the theoretical analysis.
TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.
Directory of Open Access Journals (Sweden)
Yingni Zhai
2014-10-01
Full Text Available Purpose: A decomposition heuristics based on multi-bottleneck machines for large-scale job shop scheduling problems (JSP is proposed.Design/methodology/approach: In the algorithm, a number of sub-problems are constructed by iteratively decomposing the large-scale JSP according to the process route of each job. And then the solution of the large-scale JSP can be obtained by iteratively solving the sub-problems. In order to improve the sub-problems' solving efficiency and the solution quality, a detection method for multi-bottleneck machines based on critical path is proposed. Therewith the unscheduled operations can be decomposed into bottleneck operations and non-bottleneck operations. According to the principle of “Bottleneck leads the performance of the whole manufacturing system” in TOC (Theory Of Constraints, the bottleneck operations are scheduled by genetic algorithm for high solution quality, and the non-bottleneck operations are scheduled by dispatching rules for the improvement of the solving efficiency.Findings: In the process of the sub-problems' construction, partial operations in the previous scheduled sub-problem are divided into the successive sub-problem for re-optimization. This strategy can improve the solution quality of the algorithm. In the process of solving the sub-problems, the strategy that evaluating the chromosome's fitness by predicting the global scheduling objective value can improve the solution quality.Research limitations/implications: In this research, there are some assumptions which reduce the complexity of the large-scale scheduling problem. They are as follows: The processing route of each job is predetermined, and the processing time of each operation is fixed. There is no machine breakdown, and no preemption of the operations is allowed. The assumptions should be considered if the algorithm is used in the actual job shop.Originality/value: The research provides an efficient scheduling method for the
Energy Technology Data Exchange (ETDEWEB)
Schiffmann, Florian; VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch [Nanoscale Simulations, Department of Materials, ETH Zürich, Wolfgang-Pauli-Str. 27, CH-8093 Zürich (Switzerland)
2015-06-28
We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filtering small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.
Large-scale Inference Problems in Astronomy: Building a 3D Galactic Dust Map
Finkbeiner, Douglas
2016-03-01
The term ''Big Data'' has become trite, as modern technology has made data sets of terabytes or even petabytes easy to store. Such data sets provide a sandbox in which to develop new statistical inference techniques that can extract interesting results from increasingly rich (and large) databases. I will give an example from my work on mapping the interstellar dust of the Milky Way. 2D emission-based maps have been used for decades to estimate the reddening and emission from interstellar dust, with applications from CMB foregrounds to surveys of large-scale structure. For studies within the Milky Way, however, the third dimension is required. I will present our work on a 3D dust map based on Pan-STARRS1 and 2MASS over 3/4 of the sky (http://arxiv.org/abs/1507.01005), assess its usefulness relative to other dust maps, and discuss future work. Supported by the NSF.
Quadratic partial eigenvalue assignment problem with time delay for active vibration control
Pratt, J. M.; Singh, K. V.; Datta, B. N.
2009-08-01
Partial pole assignment in active vibration control refers to reassigning a small set of unwanted eigenvalues of the quadratic eigenvalue problem (QEP) associated with the second order system of a vibrating structure, by using feedback control force, to suitably chosen location without altering the remaining large number of eigenvalues and eigenvectors. There are several challenges of solving this quadratic partial eigenvalue assignment problem (QPEVAP) in a computational setting which the traditional pole-placement problems for first-order control systems do not have to deal with. In order to these challenges, there has been some work in recent years to solve QPEVAP in a computationally viable way. However, these works do not take into account of the practical phenomenon of the time-delay effect in the system. In this paper, a new "direct and partial modal" approach of the quadratic partial eigenvalue assignment problem with time-delay is proposed. The approach works directly in the quadratic system without requiring transformation to a standard state-space system and requires the knowledge of only a small number of eigenvalues and eigenvectors that can be computed or measured in practice. Two illustrative examples are presented in the context of active vibration control with constant time-delay to illustrate the success of our proposed approach. Future work includes generalization of this approach to a more practical complex time-delay system and extension of this work to the multi-input problem.
Inverse Eigenvalue Problems for a Structure with Linear Parameters
Institute of Scientific and Technical Information of China (English)
WU Liang-sheng; YANG Jia-hua; WEI Yuan-qian; MEN Hao; YANG Qing-kun; LIU Zhen-yu
2005-01-01
The inverse design method of a dynamic system with linear parameters has been studied. For some specified eigenvalues and eigenvectors, the design parameter vector which is often composed of whole or part of coefficients of spring and mass of the system can be obtained and the rigidity and mass matrices of an initially designed structure can be reconstructed through solving linear algebra equations. By using implicit function theorem, the conditions of existence and uniqueness of the solution are also deduced. The theory and method can be used for inverse vibration design of complex structure system.
HOMOTOPY SOLUTION OF THE INVERSE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS
Institute of Scientific and Technical Information of China (English)
李书; 王波; 胡继忠
2004-01-01
The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method.
Murphy, W D; Bernabe, M L
1978-08-01
The Prony method is extended to handle the nonsymmetric algebraic eigenvalue problem and improved to search automatically for the number of dominant eigenvalues. A simple iterative algorithm is given to compute the associated eigenvectors. Resolution studies using the QR method are made in order to determine the accuracy of the matrix approximation. Numerical results are given for both simple well defined resonators and more complex advanced designs containing multiple propagation geometries and misaligned mirrors.
A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Dou Jingbo
2007-01-01
Full Text Available Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the -sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.
A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Zixia Yuan
2007-12-01
Full Text Available Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the p-sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.
Institute of Scientific and Technical Information of China (English)
Qiumei Huang; Yidu Yang
2008-01-01
In this paper,we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms.Using this extrapolation formula,we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues.Some numerical experiments are carried out to demonstrate the effectiveness of OUr new method and to confirm our theoretical results.
Large scale stochastic inventory routing problems with split delivery and service level constraints
Y. Yu (Yugang); C. Chu (Chengbin); H.X. Chen (Haoxun); F. Chu (Feng)
2010-01-01
textabstractA stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. Th
Large scale stochastic inventory routing problems with split delivery and service level constraints
Y. Yu (Yugang); C. Chu (Chengbin); H.X. Chen (Haoxun); F. Chu (Feng)
2012-01-01
textabstractA stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. Th
Y. Yu (Yugang); C. Chu (Chengbin); H.X. Chen (Haoxun); F. Chu (Feng)
2010-01-01
textabstractA stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, for a depot to determine delivery volumes to its customers in each period, and vehicle routes to distribute the delivery volumes. This
AN EFFECTIVE CONTINUOUS ALGORITHM FOR APPROXIMATE SOLUTIONS OF LARGE SCALE MAX-CUT PROBLEMS
Institute of Scientific and Technical Information of China (English)
Cheng-xian Xu; Xiao-liang He; Feng-min Xu
2006-01-01
An effective continuous algorithm is proposed to find approximate solutions of NP-hard max-cut problems. The algorithm relaxes the max-cut problem into a continuous nonlinear programming problem by replacing n discrete constraints in the original problem with one single continuous constraint. A feasible direction method is designed to solve the resulting nonlinear programming problem. The method employs only the gradient evaluations of the objective function, and no any matrix calculations and no line searches are required.This greatly reduces the calculation cost of the method, and is suitable for the solution of large size max-cut problems. The convergence properties of the proposed method to KKT points of the nonlinear programming are analyzed. If the solution obtained by the proposed method is a global solution of the nonlinear programming problem, the solution will provide an upper bound on the max-cut value. Then an approximate solution to the max-cut problem is generated from the solution of the nonlinear programming and provides a lower bound on the max-cut value. Numerical experiments and comparisons on some max-cut test problems (small and large size) show that the proposed algorithm is efficient to get the exact solutions for all small test problems and well satisfied solutions for most of the large size test problems with less calculation costs.
Solving Large-Scale Computational Problems Using Insights from Statistical Physics
Energy Technology Data Exchange (ETDEWEB)
Selman, Bart [Cornell University
2012-02-29
Many challenging problems in computer science and related fields can be formulated as constraint satisfaction problems. Such problems consist of a set of discrete variables and a set of constraints between those variables, and represent a general class of so-called NP-complete problems. The goal is to find a value assignment to the variables that satisfies all constraints, generally requiring a search through and exponentially large space of variable-value assignments. Models for disordered systems, as studied in statistical physics, can provide important new insights into the nature of constraint satisfaction problems. Recently, work in this area has resulted in the discovery of a new method for solving such problems, called the survey propagation (SP) method. With SP, we can solve problems with millions of variables and constraints, an improvement of two orders of magnitude over previous methods.
Real dqds for the nonsymmetric tridiagonal eigenvalue problem
Ferreira, Carla
2012-01-01
We present a new transform, triple dqds, to help to compute the eigenvalues of a real tridiagonal matrix C using real arithmetic. The algorithm uses the real dqds transform to shift by a real number and triple dqds to shift by a complex conjugate pair. We present what seems to be a new criteria for splitting the current pair L,U. The algorithm rejects any transform which suffers from excessive element growth and then tries a new transform. Our numerical tests show that the algorithm is about 100 times faster than the Ehrlich-Aberth method of D. A. Bini, L. Gemignani and F. Tisseur. Our code is comparable in performance to a complex dqds code and is sometimes 3 times faster.
A numerical method for eigenvalue problems in modeling liquid crystals
Energy Technology Data Exchange (ETDEWEB)
Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A. [Kent State Univ., OH (United States); Calvetti, D. [Stevens Inst. of Technology, Hoboken, NJ (United States)
1996-12-31
Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.
Eigenvalue problems of Atkinson, Feller and Krein, and their mutual relationship
Directory of Open Access Journals (Sweden)
Hans Volkmer
2005-04-01
Full Text Available It is shown that every regular Krein-Feller eigenvalue problem can be transformed to a semidefinite Sturm-Liouville problem introduced by Atkinson. This makes it possible to transfer results between the corresponding theories. In particular, Prufer angle methods become available for Krein-Feller problems.
DEFF Research Database (Denmark)
Quaglia, Alberto; Sarup, Bent; Sin, Gürkan;
2013-01-01
The formulation of Enterprise-Wide Optimization (EWO) problems as mixed integer nonlinear programming requires collecting, consolidating and systematizing large amount of data, coming from different sources and specific to different disciplines. In this manuscript, a generic and flexible data...... structure for efficient formulation of enterprise-wide optimization problems is presented. Through the integration of the described data structure in our synthesis and design framework, the problem formulation workflow is automated in a software tool, reducing time and resources needed to formulate large...... problems, while ensuring at the same time data consistency and quality at the application stage....
INVERSE EIGENVALUE PROBLEM OF HERMITIAN GENERALIZED ANTI-HAMILTONIAN MATRICES%HGAH矩阵的逆特征值问题
Institute of Scientific and Technical Information of China (English)
张忠志; Liu Changrong
2004-01-01
In this paper, the inverse eigenvalue problem of Hermitian generalized anti-Hamiltonian matrices and relevant optimal approximate problem are considered. The necessary and sufficient conditions of the solvability for inverse eigenvalue problem and an expression of the general solution of the problem are derived. The solution of the relevant optimal approximate problem is given.
Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems
Frohne, Jörg
2015-08-06
© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.
An efficient regularization method for a large scale ill-posed geothermal problem
Berntsson, Fredrik; Lin, Chen; Xu, Tao; Wokiyi, Dennis
2017-08-01
The inverse geothermal problem consists of estimating the temperature distribution below the earth's surface using measurements on the surface. The problem is important since temperature governs a variety of geologic processes, including the generation of magmas and the deformation style of rocks. Since the thermal properties of rocks depend strongly on temperature the problem is non-linear. The problem is formulated as an ill-posed operator equation, where the righthand side is the heat-flux at the surface level. Since the problem is ill-posed regularization is needed. In this study we demonstrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well-posed problem related to the above mentioned operator. The algorithm is designed in such a way that it can deal with both 2 D and 3 D calculations. Numerical results, for 2 D domains, show that the algorithm works well and the inverse problem can be solved accurately with a realistic noise level in the surface data.
Brahma, Sanjoy; Datta, Biswa
2009-07-01
The partial quadratic eigenvalue assignment problem (PQEVAP) concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil, while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged. The problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems. The solution of this problem requires computations of a pair of feedback matrices. For practical effectiveness, these feedback matrices must be computed in such a way that their norms and the condition number of the closed-loop eigenvector matrix are as small as possible. These considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem (MNPQEVAP) and the robust partial quadratic eigenvalue assignment problem (RPQEVAP), respectively. In this paper we propose new optimization based algorithms for solving these problems. The problems are solved directly in a second-order setting without resorting to a standard first-order formulation so as to avoid the inversion of a possibly ill-conditioned matrix and the loss of exploitable structures of the original model. The algorithms require the knowledge of only the open-loop eigenvalues to be replaced and their corresponding eigenvectors. The remaining open-loop eigenvalues and their corresponding eigenvectors are kept unchanged. The invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result. Furthermore, the gradient formulas needed to solve the problems by using the quasi-Newton optimization technique employed are computed in terms of the known quantities only. Above all, the proposed methods do not require the reduction of the model order or the order of the controller, even when the underlying finite element model has a very large degree of freedom. These attractive features, coupled with minimal computational requirements, such as solutions of small
A POSTERIORI ERROR ANALYSIS OF NONCONFORMING METHODS FOR THE EIGENVALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
Youai LI
2009-01-01
This paper extends the unifying theory for a posteriori error analysis of the nonconforming finite element methods to the second order elliptic eigenvalue problem. In particular, the author proposes the a posteriori error estimator for nonconforming methods of the eigenvalue problems and prove its reliability and efficiency based on two assumptions concerning both the weak continuity and the weak orthogonality of the nonconforming finite element spaces, respectively. In addition, the author examines these two assumptions for those nonconforming methods checked in literature for the Laplace, Stokes, and the linear elasticity problems.
The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory
Energy Technology Data Exchange (ETDEWEB)
Woznicki, Z.I. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.
The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory
Energy Technology Data Exchange (ETDEWEB)
Woznicki, Z.I. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1995-12-31
The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs.
Emerging solution of large-scale unit commitment problem by Stochastic Priority List
Energy Technology Data Exchange (ETDEWEB)
Senjyu, Tomonobu; Miyagi, Tsukasa; Saber, Ahmed Yousuf; Urasaki, Naomitsu [Faculty of Engineering, University of the Ryukyus, 1 Senbaru Nishihara-cho Nakagami, Okinawa 903-0213 (Japan); Funabashi, Toshihisa [Meidensha Corporation Riverside Building 36-2, Nihonbashi Hokozakicho, Chuo-ku, Tokyo 103-8515 (Japan)
2006-03-15
This paper presents a new approach for unit commitment problem using Stochastic Priority List method. In this method, rapidly some initial unit commitment schedules are generated by Priority List method and priority based stochastic window system. Excess units are added with system dependent probability distribution to avoid overlooking a desired solution during repeated search. Constraints are not considered in this stage. Then schedules are modified gradually using the problem specific heuristics to fulfill constraints. To reduce calculations, heuristics are applied only to the solutions, which can be expected to improve. Besides, sign vector is introduced to reduce economic load dispatch (ELD) overhead recalculations. This process is repeated for optimal solution. The proposed method is tested using the reported problem data set. Simulation results for the systems up to 100-unit are compared to previous reported results. Numerical results show an improvement in solution cost and time compared to the results obtained from Genetic Algorithm and others. (author)
Solving Large-Scale QAP Problems in Parallel with the Search
DEFF Research Database (Denmark)
Clausen, Jens; Brüngger, A.; Marzetta, A.
1998-01-01
Program libraries are one tool to make the cooperation between specialists from various fields successful: the separation of application-specific knowledge from application-independent tasks ensures portability, maintenance, extensibility, and flexibility. The current paper demonstrates the success...... in combining problem-specific knowledge for the quadratic assignment problem (QAP) with the raw computing power offered by contemporary parallel hardware by using the library of parallel search algorithms ZRAM. Solutions of previously unsolved large standard test-instances of the QAP are presented....
A modified priority list-based MILP method for solving large-scale unit commitment problems
Energy Technology Data Exchange (ETDEWEB)
Ke, Xinda; Lu, Ning; Wu, Di; Kintner-Meyer, Michael CW
2015-07-26
This paper studies the typical pattern of unit commitment (UC) results in terms of generator’s cost and capacity. A method is then proposed to combine a modified priority list technique with mixed integer linear programming (MILP) for UC problem. The proposed method consists of two steps. At the first step, a portion of generators are predetermined to be online or offline within a look-ahead period (e.g., a week), based on the demand curve and generator priority order. For the generators whose on/off status is predetermined, at the second step, the corresponding binary variables are removed from the UC MILP problem over the operational planning horizon (e.g., 24 hours). With a number of binary variables removed, the resulted problem can be solved much faster using the off-the-shelf MILP solvers, based on the branch-and-bound algorithm. In the modified priority list method, scale factors are designed to adjust the tradeoff between solution speed and level of optimality. It is found that the proposed method can significantly speed up the UC problem with minor compromise in optimality by selecting appropriate scale factors.
Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control
Kamyar, Reza
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to
Institute of Scientific and Technical Information of China (English)
吴颖; 罗亚军; 杨晓雪
2003-01-01
We present a novel formalism for energy eigenvalue problems when the corresponding Hamiltonians can be expressed as a function of an angular momentum. The problems are turned into finding operator polynomials by solving a c-number differential equation. Simple and efficient computer-aided analytical and numerical methods may be developed based on the formalism.
A Jacobi-Davidson type method for a right definite two-parameter eigenvalue problem
Hochstenbach, M.; Plestenjak, B.
2001-01-01
We present a new numerical iterative method for computing selected eigenpairs of a right definite two-parameter eigenvalue problem. The method works even without good initial approximations and is able to tackle large problems that are too expensive for existing methods. The new method is similar
An Approach to Some Non-Classical Eigenvalue Problems of Structural Dynamics
Directory of Open Access Journals (Sweden)
Sandi Horea
2015-12-01
Full Text Available Two main shortcomings of common formulations, encountered in the literature concerning the linear problems of structural dynamics are revealed: the implicit, not discussed, postulation, of the use of Kelvin – Voigt constitutive laws (which is often infirmed by experience and the calculation difficulties involved by the attempts to use other constitutive laws. In order to overcome these two categories of shortcomings, the use of the bilateral Laplace – Carson transformation is adopted. Instead of the dependence on time, t, of a certain function f (t, the dependence of its image f# (p on the complex parameter p = χ + iω (ω: circular frequency will occur. This leads to the formulation of associated non-classical eigenvalue problems. The basic relations satisfied by the eigenvalues λr#(p and the eigenvectors vr#(p of dynamic systems are examined (among other, the property of orthogonality of eigenvectors is replaced by the property of pseudo-orthogonality. The case of points p = p’, where multiple eigenvalues occur and where, as a rule, chains of principal vectors are to be considered, is discussed. An illustrative case, concerning a non-classical eigenvalue problem, is presented. Plots of variation along the ω axis, for the real and imaginary components of eigenvalues and eigenvectors, are presented. A brief final discussion closes the paper.
TWO-GRID DISCRETIZATION SCHEMES OF THE NONCONFORMING FEM FOR EIGENVALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
Yidu Yang
2009-01-01
This paper extends the two-grid discretization scheme of the conforming finite elements proposed by Xu and Zhou (Math. Comput., 70 (2001), pp.17-25) to the nonconforming finite elements for eigenvalue problems. In particular, two two-grid discretization schemes based on Rayleigh quotient technique are proposed. By using these new schemes, the solution of an eigenvalue problem on a fine mesh is reduced to that on a much coarser mesh together with the solution of a linear algebraic system on the fine mesh. The resulting solution still maintains an asymptotically optimal accuracy. Comparing with the two-grid discretization scheme of the conforming finite elements, the main advantages of our new schemes are twofold when the mesh size is small enough. First, the lower bounds of the exact eigenvalues in our two-grid discretization schemes can be obtained. Second, the first eigenvalue given by the new schemes has much better accuracy than that obtained by solving the eigenvalue problems on the fine mesh directly.
Bui-Thanh, T.; Girolami, M.
2014-11-01
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint
An Implementation and Evaluation of the AMLS Method for SparseEigenvalue Problems
Energy Technology Data Exchange (ETDEWEB)
Gao, Weiguo; Li, Xiaoye S.; Yang, Chao; Bai, Zhaojun
2006-02-14
We describe an efficient implementation and present aperformance study of an algebraic multilevel sub-structuring (AMLS)method for sparse eigenvalue problems. We assess the time and memoryrequirements associated with the key steps of the algorithm, and compareitwith the shift-and-invert Lanczos algorithm in computational cost. Oureigenvalue problems come from two very different application areas: theaccelerator cavity design and the normal mode vibrational analysis of thepolyethylene particles. We show that the AMLS method, when implementedcarefully, is very competitive with the traditional method in broadapplication areas, especially when large numbers of eigenvalues aresought.
A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES
Institute of Scientific and Technical Information of China (English)
SHI Xin-gang; FAN Zhi-song; LIU Hai-long
2009-01-01
Generally speaking, the background shear current U(z)must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Let G = (V, E) be a complete undirected graph with vertex set V, edge set E, and edge weights I(e)satisfying the triangle inequality. The vertex set V is partitioned into clusters V1, V2 Vk. The clustered traveling salesman problem (CTSP) seeks to compute the shortest Hamiltonian tour that visits all the vertices, in which the vertices of each cluster are visited consecutively. A two-level genetic algorithm (TLGA) was developed for the problem, which favors neither intra-cluster paths nor inter-cluster paths, thus realized integrated evolutionary optimization for both levels of the CTSP. Results show that the algorithm is more effective than known algorithms. A large-scale traveling salesman problem (TSP) can be converted into a CTSP by clustering so that it can then be solved by the algorithm. Test results demonstrate that the clustering TLGA for large TSPs is more effective and efficient than the classical genetic algorithm.
Solving Man-Induced Large-Scale Conservation Problems: The Spanish Imperial Eagle and Power Lines
López-López, Pascual; Ferrer, Miguel; Madero, Agustín; Casado, Eva; McGrady, Michael
2011-01-01
Background Man-induced mortality of birds caused by electrocution with poorly-designed pylons and power lines has been reported to be an important mortality factor that could become a major cause of population decline of one of the world rarest raptors, the Spanish imperial eagle (Aquila adalberti). Consequently it has resulted in an increasing awareness of this problem amongst land managers and the public at large, as well as increased research into the distribution of electrocution events and likely mitigation measures. Methodology/Principal Findings We provide information of how mitigation measures implemented on a regional level under the conservation program of the Spanish imperial eagle have resulted in a positive shift of demographic trends in Spain. A 35 years temporal data set (1974–2009) on mortality of Spanish imperial eagle was recorded, including population censuses, and data on electrocution and non-electrocution of birds. Additional information was obtained from 32 radio-tracked young eagles and specific field surveys. Data were divided into two periods, before and after the approval of a regional regulation of power line design in 1990 which established mandatory rules aimed at minimizing or eliminating the negative impacts of power lines facilities on avian populations. Our results show how population size and the average annual percentage of population change have increased between the two periods, whereas the number of electrocuted birds has been reduced in spite of the continuous growing of the wiring network. Conclusions Our results demonstrate that solving bird electrocution is an affordable problem if political interest is shown and financial investment is made. The combination of an adequate spatial planning with a sustainable development of human infrastructures will contribute positively to the conservation of the Spanish imperial eagle and may underpin population growth and range expansion, with positive side effects on other endangered
Perturbation of a Multiple Eigenvalue in the Benard Problem for Two Fluid Layers.
1984-12-01
EIGENVAWUE IN THlE BENARtD PROBLEM FOR TWO FLUID LAYERS Ca O~ Yuriko Renardy and Michael Renardy MUathematics Research Center University of Wisconsin...OF WISCONSIN - MADISON MATHEMATICS RESEARCH CENTER PERTUBBATION OF A MULTIPLE EIGENVALUE IN THE BENARD PROBLEM FOR TWO FLUID LAYERS Yuriko Renardy and...PROBLEM FOR TWO FLUID LAYERS Yuriko Renardy and Michael Renardy 1. INTRODUCTION In the B6nard problem for one fluid, "exchange of stabilities" holds
Minimization and error estimates for a class of the nonlinear Schrodinger eigenvalue problems
Institute of Scientific and Technical Information of China (English)
MurongJIANG; JiachangSUN
2000-01-01
It is shown that the nonlinear eigenvaiue problem can be transformed into a constrained functional problem. The corresponding minimal function is a weak solution of this nonlinear problem. In this paper, one type of the energy functional for a class of the nonlinear SchrSdinger eigenvalue problems is proposed, the existence of the minimizing solution is proved and the error estimate is given out.
Quoc, Tran Dinh; Diehl, Moritz
2011-01-01
A new algorithm for solving large-scale separable convex optimization problems is proposed. The basic idea is to combine three techniques including Lagrangian dual decomposition, excessive gap and smoothing techniques. The main advantage of this algorithm is to dynamically update the smoothness parameters which leads to a numerically stable performance ability. The convergence of the algorithm is proved under weak conditions imposed on the original problem. The worst-case complexity is estimated which is $O(1/k)$, where $k$ is the iteration counter. Then, the algorithm is coupled with a dual scheme to construct a switching variant of the dual decomposition. Discussion on the implementation issues is presented and theoretical comparison is analyzed. Numerical results are implemented to confirm the theoretical development.
Cakoni, Fioralba; Haddar, Houssem
2013-10-01
In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission
A Nonlinera Krylov Accelerator for the Boltzmann k-Eigenvalue Problem
Calef, Matthew T; Warsa, James S; Berndt, Markus; Carlson, Neil N
2011-01-01
We compare variants of Anderson Mixing with the Jacobian-Free Newton-Krylov and Broyden methods applied to the k-eigenvalue formulation of the linear Boltzmann transport equation. We present evidence that one variant of Anderson Mixing finds solutions in the fewest number of iterations. We examine and strengthen theoretical results of Anderson Mixing applied to linear problems.
Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem
Raman, Aaswath
2010-02-26
We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.
Bonito, Andrea
2011-01-01
We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.
The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces
Ćurgus, Branko; Dijksma, Aad; Read, Tom
2001-01-01
The boundary eigenvalue problems for the adjoint of a symmetric relation S in a Hilbert space with finite, not necessarily equal, defect numbers, which are related to the selfadjoint Hilbert space extensions of S are characterized in terms of boundary coefficients and the reproducing kernel Hilbert
Some remarks on the optimization of eigenvalue problems involving the p-Laplacian
Directory of Open Access Journals (Sweden)
Wacław Pielichowski
2008-01-01
Full Text Available Given a bounded domain \\(\\Omega \\subset \\mathbb{R}^n\\, numbers \\(p \\gt 1\\, \\(\\alpha \\geq 0\\ and \\(A \\in [0,|\\Omega |]\\, consider the optimization problem: find a subset \\(D \\subset \\Omega \\, of measure \\(A\\, for which the first eigenvalue of the operator \\(u\\mapsto -\\text{div} (|\
Eigenvalues of a baroclinic stability problem with Ekman damping
Antar, B. N.; Fowlis, W. W.
1980-01-01
An analytical solution is presented for the baroclinic stability problem of a Boussinesq fluid in a beta-plane channel with Ekman suction boundary conditions. All of the modes, stable and unstable, belonging to this problem are identified. It is found that an unstable mode exists for only a certain range of values of the Burger number. The value of the Burger number at the upper limit of this range increases as the Ekman number decreases. Beyond this upper limit only a damped mode exists. It is also found that this transition in parameter space from the unstable to the stable mode occurs in a discontinuous manner.
Eigenvalues of the time—dependent fluid flow problem I
Directory of Open Access Journals (Sweden)
El-Sayed M. Zayed
1990-01-01
Full Text Available The direct and inverse boundary value problems for the linear unsteady viscous fluid flow through a closed conduit of a circular annular cross-section Ω with arbitrary time-dependent pressure gradient under the third boundary conditions have been investigated.
Determination of Electromagnetic Source Direction as an Eigenvalue Problem
Martínez-Oliveros, Juan C; Bale, Stuart D; Krucker, Säm
2012-01-01
Low-frequency solar and interplanetary radio bursts are generated at frequencies below the ionospheric plasma cutoff and must therefore be measured in space, with deployable antenna systems. The problem of measuring both the general direction and polarization of an electromagnetic source is commonly solved by iterative fitting methods such as linear regression that deal simultaneously with both directional and polarization parameters. We have developed a scheme that separates the problem of deriving the source direction from that of determining the polarization, avoiding iteration in a multi-dimensional manifold. The crux of the method is to first determine the source direction independently of concerns as to its polarization. Once the source direction is known, its direct characterization in terms of Stokes vectors in a single iteration if desired, is relatively simple. This study applies the source-direction determination to radio signatures of flares received by STEREO. We studied two previously analyzed r...
Positive solutions and eigenvalues of nonlocal boundary-value problems
Directory of Open Access Journals (Sweden)
Jifeng Chu
2005-07-01
Full Text Available We study the ordinary differential equation $x''+lambda a(tf(x=0$ with the boundary conditions $x(0=0$ and $x'(1=int_{eta}^{1}x'(sdg(s$. We characterize values of $lambda$ for which boundary-value problem has a positive solution. Also we find appropriate intervals for $lambda$ so that there are two positive solutions.
Eigenvalues of boundary value problems for higher order differential equations
Wong, Patricia J. Y.; Agarwal, Ravi P.
1996-01-01
We shall consider the boundary value problem y ( n ) + λ Q ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 2 ) ) = λ P ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 1 ) ) , n ≥ 2 , t ∈ ( 0 , 1 ) , y ( i ) ( 0 ) = 0 , 0 ≤ i ≤ n − 3 , α y ( n − 2 ) ( 0 ) − β y ( n − 1 ) ( 0 ) = 0 , γ y ( n − 2 ) ( 1 ) + δ y ( n...
Eigenvalues of boundary value problems for higher order differential equations
Patricia J. Y. Wong; Agarwal, Ravi P.
1996-01-01
We shall consider the boundary value problem y ( n ) + λ Q ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 2 ) ) = λ P ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 1 ) ) , n ≥ 2 , t ∈ ( 0 , 1 ) , y ( i ) ( 0 ) = 0 , 0 ≤ i ≤ n − 3 , α y ( n − 2 ) ( 0 ) − β y ( n − 1 ) ( 0 ) = 0 , γ y ( n − 2 ) ( 1 ) + δ y ( n...
Nodal Solutions for a Nonlinear Fourth-Order Eigenvalue Problem
Institute of Scientific and Technical Information of China (English)
Ru Yun MA; Bevan THOMPSON
2008-01-01
We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y =λa(x)f(y),00 for all u ≠0. We give conditions on the ratio f (s)/s,at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques.
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Jiuping Xu
2012-01-01
Full Text Available The aim of this study is to deal with a minimum cost network flow problem (MCNFP in a large-scale construction project using a nonlinear multiobjective bilevel model with birandom variables. The main target of the upper level is to minimize both direct and transportation time costs. The target of the lower level is to minimize transportation costs. After an analysis of the birandom variables, an expectation multiobjective bilevel programming model with chance constraints is formulated to incorporate decision makers’ preferences. To solve the identified special conditions, an equivalent crisp model is proposed with an additional multiobjective bilevel particle swarm optimization (MOBLPSO developed to solve the model. The Shuibuya Hydropower Project is used as a real-world example to verify the proposed approach. Results and analysis are presented to highlight the performances of the MOBLPSO, which is very effective and efficient compared to a genetic algorithm and a simulated annealing algorithm.
Periodic-parabolic eigenvalue problems with a large parameter and degeneration
Daners, Daniel; Thornett, Christopher
2016-07-01
We consider a periodic-parabolic eigenvalue problem with a non-negative potential λm vanishing on a non-cylindrical domain Dm satisfying conditions similar to those for the parabolic maximum principle. We show that the limit as λ → ∞ leads to a periodic-parabolic problem on Dm having a periodic-parabolic principal eigenvalue and eigenfunction which are unique in some sense. We substantially improve a result from [Du and Peng, Trans. Amer. Math. Soc. 364 (2012), p. 6039-6070]. At the same time we offer a different approach based on a periodic-parabolic initial boundary value problem. The results are motivated by an analysis of the asymptotic behaviour of positive solutions to semilinear logistic periodic-parabolic problems with temporal and spacial degeneracies.
A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.
Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas
2015-12-01
Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.
{\\it Ab initio} nuclear structure - the large sparse matrix eigenvalue problem
Vary, James P; Ng, Esmond; Yang, Chao; Sosonkina, Masha
2009-01-01
The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several {\\it ab initio} methods have now emerged that provide nearly exact solutions for some nuclear properties. The {\\it ab initio} no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds $10^{10}$ and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving t...
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Macdonald, Colin B.; Brandman, Jeremy; Ruuth, Steven J.
2011-09-01
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach.
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Macdonald, Colin B; Ruuth, Steven J
2011-01-01
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach.
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Macdonald, Colin B.
2011-06-01
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.
Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem
Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul; Lee, Deokjung
2015-12-01
In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.
Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Jeong, Yongjin; Park, Jinsu [Ulsan National Institute of Science and Technology, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798 (Korea, Republic of); Lee, Hyun Chul [Korea Atomic Energy Research Institute, 111 Daedeok-daero 989 beon-gil, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Lee, Deokjung, E-mail: deokjung@unist.ac.kr [Ulsan National Institute of Science and Technology, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798 (Korea, Republic of)
2015-12-01
In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.
Ltaief, Hatem
2012-01-01
This paper proposes an efficient implementation of the generalized symmetric eigenvalue problem on multicore architecture. Based on a four-stage approach and tile algorithms, the original problem is first transformed into a standard symmetric eigenvalue problem by computing the Cholesky factorization of the right hand side symmetric definite positive matrix (first stage), and applying the inverse of the freshly computed triangular Cholesky factors to the original dense symmetric matrix of the problem (second stage). Calculating the eigenpairs of the resulting problem is then equivalent to the eigenpairs of the original problem. The computation proceeds by reducing the updated dense symmetric matrix to symmetric band form (third stage). The band structure is further reduced by applying a bulge chasing procedure, which annihilates the extra off-diagonal entries using orthogonal transformations (fourth stage). More details on the third and fourth stage can be found in Haidar et al. [Accepted at SC\\'11, November 2011]. The eigenvalues are then calculated from the tridiagonal form using the standard LAPACK QR algorithm (i.e., DTSEQR routine), while the complex and challenging eigenvector computations will be addressed in a companion paper. The tasks from the various stages can concurrently run in an out-of-order fashion. The data dependencies are cautiously tracked by the dynamic runtime system environment QUARK, which ensures the dependencies are not violated for numerical correctness purposes. The obtained tile four-stage generalized symmetric eigenvalue solver significantly outperforms the state-of-the-art numerical libraries (up to 21-fold speed up against multithreaded LAPACK with optimized multithreaded MKL BLAS and up to 4-fold speed up against the corresponding routine from the commercial numerical software Intel MKL) on four sockets twelve cores AMD system with a 24000×24000 matrix size. © 2012 The authors and IOS Press. All rights reserved.
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Tarek H. M. Abou-El-Enien
2015-04-01
Full Text Available This paper extended TOPSIS (Technique for Order Preference by Similarity Ideal Solution method for solving Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters in the righthand side of the constraints (TL-LSLMOP-SPrhs of block angular structure. In order to obtain a compromise ( satisfactory solution to the (TL-LSLMOP-SPrhs of block angular structure using the proposed TOPSIS method, a modified formulas for the distance function from the positive ideal solution (PIS and the distance function from the negative ideal solution (NIS are proposed and modeled to include all the objective functions of the two levels. In every level, as the measure of ―Closeness‖ dp-metric is used, a k-dimensional objective space is reduced to two –dimentional objective space by a first-order compromise procedure. The membership functions of fuzzy set theory is used to represent the satisfaction level for both criteria. A single-objective programming problem is obtained by using the max-min operator for the second –order compromise operaion. A decomposition algorithm for generating a compromise ( satisfactory solution through TOPSIS approach is provided where the first level decision maker (FLDM is asked to specify the relative importance of the objectives. Finally, an illustrative numerical example is given to clarify the main results developed in the paper.
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Hua Wang
2008-01-01
Full Text Available With the movement of magnetic resonance imaging (MRI technology towards higher field (and therefore frequency systems, the interaction of the fields generated by the system with patients, healthcare workers, and internally within the system is attracting more attention. Due to the complexity of the interactions, computational modeling plays an essential role in the analysis, design, and development of modern MRI systems. As a result of the large computational scale associated with most of the MRI models, numerical schemes that rely on a single computer processing unit often require a significant amount of memory and long computational times, which makes modeling of these problems quite inefficient. This paper presents dedicated message passing interface (MPI, OPENMP parallel computing solvers for finite-difference time-domain (FDTD, and quasistatic finite-difference (QSFD schemes. The FDTD and QSFD methods have been widely used to model/ analyze the induction of electric fields/ currents in voxel phantoms and MRI system components at high and low frequencies, respectively. The power of the optimized parallel computing architectures is illustrated by distinct, large-scale field calculation problems and shows significant computational advantages over conventional single processing platforms.
Cui, Tiangang; Marzouk, Youssef; Willcox, Karen
2016-06-01
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.
Mode decomposition of nonlinear eigenvalue problems and application in flow stability
Institute of Scientific and Technical Information of China (English)
高军; 罗纪生
2014-01-01
Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to an N th-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.
Júdice, Joaquim; Raydan, Marcos; Rosa, Silvério; Santos, Sandra
2008-04-01
This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849-1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find a complementarity eigenvalue by computing a stationary point of an appropriate merit function on a special convex set. A variant of the spectral projected gradient algorithm with a specially designed line search is introduced to solve the EiCP. Computational experience shows that the application of this algorithm to the logarithmic function formulation is a quite efficient way to find a solution to the symmetric EiCP.
Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region
Marachevsky, V N; Marachevsky, Valeri; Vassilevich, Dmitri
1995-01-01
We suggest a method of construction of general diffeomorphism invariant boundary conditions for metric fluctuations. The case of d+1 dimensional Euclidean disk is studied in detail. The eigenvalue problem for the Laplace operator on metric perturbations is reduced to that on d-dimensional vector, tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace operator is derived. We also study restrictions on boundary conditions which are imposed by hermiticity of the Laplace operator.
Lyapunov inequalities for the periodic boundary value problem at higher eigenvalues
Canada, Antonio
2009-01-01
This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the study of some special minimization problems, where the Lagrange multiplier Theorem plays a fundamental role. This allows to obtain the optimal constants. Our applications include the Hill's equation where we give some new conditions on its stability properties and also the study of periodic and nonlinear problems at resonance where we show some new conditions which allow to prove the existence and uniqueness of solutions.
A case against a divide and conquer approach to the nonsymmetric eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Jessup, E.R.
1991-12-01
Divide and conquer techniques based on rank-one updating have proven fast, accurate, and efficient in parallel for the real symmetric tridiagonal and unitary eigenvalue problems and for the bidiagonal singular value problem. Although the divide and conquer mechanism can also be adapted to the real nonsymmetric eigenproblem in a straightforward way, most of the desirable characteristics of the other algorithms are lost. In this paper, we examine the problems of accuracy and efficiency that can stand in the way of a nonsymmetric divide and conquer eigensolver based on low-rank updating. 31 refs., 2 figs.
Alzahrani, Faris S.; Abbas, Ibrahim A.
2016-08-01
The present paper is devoted to the study of a two-dimensional thermal shock problem with weak, normal and strong conductivity using the eigenvalue approach. The governing equations are taken in the context of the new consideration of heat conduction with fractional order generalized thermoelasticity with the Lord-Shulman model (LS model). The bounding surface of the half-space is taken to be traction free and subjected to a time-dependent thermal shock. The Laplace and the exponential Fourier transform techniques are used to obtain the analytical solutions in the transformed domain by the eigenvalue approach. Numerical computations have been done for copper-like material for weak, normal and strong conductivity and the results are presented graphically to estimate the effects of the fractional order parameter.
Haidar, Azzam
2012-01-01
Classical solvers for the dense symmetric eigenvalue problem suffer from the first step, which involves a reduction to tridiagonal form that is dominated by the cost of accessing memory during the panel factorization. The solution is to reduce the matrix to a banded form, which then requires the eigenvalues of the banded matrix to be computed. The standard divide and conquer algorithm can be modified for this purpose. The paper combines this insight with tile algorithms that can be scheduled via a dynamic runtime system to multicore architectures. A detailed analysis of performance and accuracy is included. Performance improvements of 14-fold and 4-fold speedups are reported relative to LAPACK and Intel\\'s Math Kernel Library.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Chen, Yong
2010-01-01
For an indecomposable $3\\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means of an alternate parameterization of the transition rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids calculating matrix logarithm or matrix square root. In addition, an implicit description of the imbedding problem for the $3\\times 3$ stochastic matrix in Johansen [J. Lond. Math. Soc., 8, 345-351. (1974)] is pointed out.
Suplatov, Dmitry; Popova, Nina; Zhumatiy, Sergey; Voevodin, Vladimir; Švedas, Vytas
2016-04-01
Rapid expansion of online resources providing access to genomic, structural, and functional information associated with biological macromolecules opens an opportunity to gain a deeper understanding of the mechanisms of biological processes due to systematic analysis of large datasets. This, however, requires novel strategies to optimally utilize computer processing power. Some methods in bioinformatics and molecular modeling require extensive computational resources. Other algorithms have fast implementations which take at most several hours to analyze a common input on a modern desktop station, however, due to multiple invocations for a large number of subtasks the full task requires a significant computing power. Therefore, an efficient computational solution to large-scale biological problems requires both a wise parallel implementation of resource-hungry methods as well as a smart workflow to manage multiple invocations of relatively fast algorithms. In this work, a new computer software mpiWrapper has been developed to accommodate non-parallel implementations of scientific algorithms within the parallel supercomputing environment. The Message Passing Interface has been implemented to exchange information between nodes. Two specialized threads - one for task management and communication, and another for subtask execution - are invoked on each processing unit to avoid deadlock while using blocking calls to MPI. The mpiWrapper can be used to launch all conventional Linux applications without the need to modify their original source codes and supports resubmission of subtasks on node failure. We show that this approach can be used to process huge amounts of biological data efficiently by running non-parallel programs in parallel mode on a supercomputer. The C++ source code and documentation are available from http://biokinet.belozersky.msu.ru/mpiWrapper .
da Silva, Aleksandra do Socorro; de Brito, Silvana Rossy; Vijaykumar, Nandamudi Lankalapalli; da Rocha, Cláudio Alex Jorge; Monteiro, Maurílio de Abreu; Costa, João Crisóstomo Weyl Albuquerque; Francês, Carlos Renato Lisboa
2016-01-01
The published literature reveals several arguments concerning the strategic importance of information and communication technology (ICT) interventions for developing countries where the digital divide is a challenge. Large-scale ICT interventions can be an option for countries whose regions, both urban and rural, present a high number of digitally excluded people. Our goal was to monitor and identify problems in interventions aimed at certification for a large number of participants in different geographical regions. Our case study is the training at the Telecentros.BR, a program created in Brazil to install telecenters and certify individuals to use ICT resources. We propose an approach that applies social network analysis and mining techniques to data collected from Telecentros.BR dataset and from the socioeconomics and telecommunications infrastructure indicators of the participants' municipalities. We found that (i) the analysis of interactions in different time periods reflects the objectives of each phase of training, highlighting the increased density in the phase in which participants develop and disseminate their projects; (ii) analysis according to the roles of participants (i.e., tutors or community members) reveals that the interactions were influenced by the center (or region) to which the participant belongs (that is, a community contained mainly members of the same region and always with the presence of tutors, contradicting expectations of the training project, which aimed for intense collaboration of the participants, regardless of the geographic region); (iii) the social network of participants influences the success of the training: that is, given evidence that the degree of the community member is in the highest range, the probability of this individual concluding the training is 0.689; (iv) the North region presented the lowest probability of participant certification, whereas the Northeast, which served municipalities with similar
Lin, Lin
2016-01-01
We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second order linear operators. Eigenvalue problems of such types play important roles in scientific and engineering applications, particularly in theoretical chemistry, solid state physics and material science. Based on the framework developed in [{\\it L. Lin, B. Stamm, http://dx.doi.org/10.1051/m2an/2015069}] for second order PDEs, we develop residual type upper and lower bound error estimates for measuring the a posteriori error for eigenvalue problems. The main merit of our method is that the method is parameter-free, in the sense that all but one solution-dependent constants appearing in the upper and lower bound estimates are explicitly computable by solving local and independent eigenvalue problems, and the only non-computable constant can be reasonably approximated by a com...
Zhidkov, E P; Solovieva, T M
2001-01-01
The spectral problems with the eigenvalue-depending operator usually appear when the relative variants of the Schroedinger equation are considered in the impulse space. The eigenvalues and eigenfunctions calculation error caused by the numerical solving of such equations is the sum of the error entering the approximation of a continuous equation by the discrete equations systems with the help of the Bubnov-Galerkine method and the iterative method one. It is shown that the iterative method error is one-two order smaller than the problem of the discretisation one. Hence, the eigenvalues and eigenfunctions calculation accuracy of the spectral problem with the eigenvalue-depending operator is not worse than the linear spectral problem solution accuracy.
A Posterior Error Analysis for the Nonconforming Discretization of Stokes Eigenvalue Problem
Institute of Scientific and Technical Information of China (English)
Shang Hui JIA; Fu Sheng LUO; He Hu XIE
2014-01-01
In this paper, we present a posteriori error estimator for the nonconforming finite element approximation, including using Crouzeix-Raviart element and extended Crouzeix-Raviart element, of the Stokes eigenvalue problem. With the technique of Helmholtz decomposition, we first give out a posteriori error estimator and prove it as the global upper bound and local lower bound of the approximation error. Then, by deleting a jump term in the indicator, another simpler but equivalent indicator is obtained. Some numerical experiments are provided to verify our analysis.
Li, Huai-Fan
2013-01-01
We take advantage of the Sturm-Liouville eigenvalue problem to analytically study the holographic insulator/superconductor phase transition in the probe limit. The interesting point is that this analytical method can not only estimate the most stable mode of the phase transition, but also the second stable mode. We find that this analytical method perfectly matches with other numerical methods, such as the shooting method. Besides, we argue that only Dirichlet boundary condition of the trial function is enough under certain circumstances, which will lead to a more precise estimation. This relaxation for the boundary condition of the trial function is first observed in this paper as far as know.
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Xuqing Zhang
2013-01-01
Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.
Recurrence relation for the 6j-symbol of suq(2) as a symmetric eigenvalue problem
Khavkine, Igor
2015-08-01
A well-known recurrence relation for the 6j-symbol of the quantum group suq(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking advantage of existing specialized numerical packages. For convenience, all formulas relevant for such an implementation are collected in Appendix A. This realization is a byproduct of an alternative proof of the recurrence relation, which generalizes a classical (q = 1) result of Schulten and Gordon and uses the diagrammatic spin network formalism of Temperley-Lieb recoupling theory to simplify intermediate calculations.
A Structured Approach to Solve the Inverse Eigenvalue Problem for a Beam with Added Mass
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Farhad Mir Hosseini
2014-01-01
Full Text Available The problem of determining the eigenvalues of a vibrational system having multiple lumped attachments has been investigated extensively. However, most of the research conducted in this field focuses on determining the natural frequencies of the combined system assuming that the characteristics of the combined vibrational system are known (forward problem. A problem of great interest from the point of view of engineering design is the ability to impose certain frequencies on the vibrational system or to avoid certain frequencies by modifying the characteristics of the vibrational system (inverse problem. In this paper, a method to impose two natural frequencies on a dynamical system consisting of an Euler-Bernoulli beam and carrying a single mass attachment is evaluated.
Energy Technology Data Exchange (ETDEWEB)
Stathopoulos, A.; Fischer, C.F. [Vanderbilt Univ., Nashville, TN (United States); Saad, Y.
1994-12-31
The solution of the large, sparse, symmetric eigenvalue problem, Ax = {lambda}x, is central to many scientific applications. Among many iterative methods that attempt to solve this problem, the Lanczos and the Generalized Davidson (GD) are the most widely used methods. The Lanczos method builds an orthogonal basis for the Krylov subspace, from which the required eigenvectors are approximated through a Rayleigh-Ritz procedure. Each Lanczos iteration is economical to compute but the number of iterations may grow significantly for difficult problems. The GD method can be considered a preconditioned version of Lanczos. In each step the Rayleigh-Ritz procedure is solved and explicit orthogonalization of the preconditioned residual ((M {minus} {lambda}I){sup {minus}1}(A {minus} {lambda}I)x) is performed. Therefore, the GD method attempts to improve convergence and robustness at the expense of a more complicated step.
Pak, Chan-gi; Lung, Shu
2009-01-01
Modern airplane design is a multidisciplinary task which combines several disciplines such as structures, aerodynamics, flight controls, and sometimes heat transfer. Historically, analytical and experimental investigations concerning the interaction of the elastic airframe with aerodynamic and in retia loads have been conducted during the design phase to determine the existence of aeroelastic instabilities, so called flutter .With the advent and increased usage of flight control systems, there is also a likelihood of instabilities caused by the interaction of the flight control system and the aeroelastic response of the airplane, known as aeroservoelastic instabilities. An in -house code MPASES (Ref. 1), modified from PASES (Ref. 2), is a general purpose digital computer program for the analysis of the closed-loop stability problem. This program used subroutines given in the International Mathematical and Statistical Library (IMSL) (Ref. 3) to compute all of the real and/or complex conjugate pairs of eigenvalues of the Hessenberg matrix. For high fidelity configuration, these aeroelastic system matrices are large and compute all eigenvalues will be time consuming. A subspace iteration method (Ref. 4) for complex eigenvalues problems with nonsymmetric matrices has been formulated and incorporated into the modified program for aeroservoelastic stability (MPASES code). Subspace iteration method only solve for the lowest p eigenvalues and corresponding eigenvectors for aeroelastic and aeroservoelastic analysis. In general, the selection of p is ranging from 10 for wing flutter analysis to 50 for an entire aircraft flutter analysis. The application of this newly incorporated code is an experiment known as the Aerostructures Test Wing (ATW) which was designed by the National Aeronautic and Space Administration (NASA) Dryden Flight Research Center, Edwards, California to research aeroelastic instabilities. Specifically, this experiment was used to study an instability
Directory of Open Access Journals (Sweden)
Jie Liu
2014-01-01
discusses the nonconforming rotated Q1 finite element computable upper bound a posteriori error estimate of the boundary value problem established by M. Ainsworth and obtains efficient computable upper bound a posteriori error indicators for the eigenvalue problem associated with the boundary value problem. We extend the a posteriori error estimate to the Steklov eigenvalue problem and also derive efficient computable upper bound a posteriori error indicators. Finally, through numerical experiments, we verify the validity of the a posteriori error estimate of the boundary value problem; meanwhile, the numerical results show that the a posteriori error indicators of the eigenvalue problem and the Steklov eigenvalue problem are effective.
Numerical approximation on computing partial sum of nonlinear Schroedinger eigenvalue problems
Institute of Scientific and Technical Information of China (English)
JiachangSUN; DingshengWANG; 等
2001-01-01
In computing electronic structure and energy band in the system of multiparticles,quite a large number of problems are to obtain the partial sum of the densities and energies by using “First principle”。In the ordinary method,the so-called self-consistency approach,the procedure is limited to a small scale because of its high computing complexity.In this paper,the problem of computing the partial sum for a class of nonlinear Schroedinger eigenvalue equations is changed into the constrained functional minimization.By space decompostion and Rayleigh-Schroedinger method,one approximating formula for the minimal is provided.The numerical experiments show that this formula is more precise and its quantity of computation is smaller.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
Optical reflection from planetary surfaces as an operator-eigenvalue problem
Wildey, R.L.
1986-01-01
The understanding of quantum mechanical phenomena has come to rely heavily on theory framed in terms of operators and their eigenvalue equations. This paper investigates the utility of that technique as related to the reciprocity principle in diffuse reflection. The reciprocity operator is shown to be unitary and Hermitian; hence, its eigenvectors form a complete orthonormal basis. The relevant eigenvalue is found to be infinitely degenerate. A superposition of the eigenfunctions found from solution by separation of variables is inadequate to form a general solution that can be fitted to a one-dimensional boundary condition, because the difficulty of resolving the reciprocity operator into a superposition of independent one-dimensional operators has yet to be overcome. A particular lunar application in the form of a failed prediction of limb-darkening of the full Moon from brightness versus phase illustrates this problem. A general solution is derived which fully exploits the determinative powers of the reciprocity operator as an unresolved two-dimensional operator. However, a solution based on a sum of one-dimensional operators, if possible, would be much more powerful. A close association is found between the reciprocity operator and the particle-exchange operator of quantum mechanics, which may indicate the direction for further successful exploitation of the approach based on the operational calculus. ?? 1986 D. Reidel Publishing Company.
Jarlebring, Elias; Michiels, Wim
2012-01-01
The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a technique to compute a partial Schur factorization of a nonlinear eigenvalue problem (NEP). The technique is inspired by the algorithm in [8], now called the infinite Arnoldi method. The infinite Arnoldi method is a method designed for NEPs, and can be interpreted as Arnoldi's method applied to a linear infinite-dimensional operator, whose reciprocal eigenvalues are the solutions to the NEP. As a first result we show that the invariant pairs of the operator are equivalent to invariant pairs of the NEP. We characterize the structure of the invariant pairs of the operator and show how one can carry out a modification of the infinite Arnoldi method by respecting the structure. This also allows us to naturally add the feature known as locking. We nest this algorithm with an outer iter...
Non-local bias and the problem of large-scale power in the Standard Cold Dark Matter model
Popolo, A D; Kiuchi, H; Gambera, M
1999-01-01
We study the effect of non-radial motions, originating from the gravitational interaction of the quadrupole moment of a protogalaxy with the tidal field of the matter of the neighboring protostructures, on the angular correlation function of galaxies. We calculate the angular correlation function using a Standard Cold Dark Matter (hereafter SCDM) model (Omega=1, h=0.5, n=1) and we compare it with the angular correlation function of the APM galaxy survey (Maddox et al. 1990; Maddox et al. 1996). We find that taking account of non-radial motions in the calculation of the angular correlation function gives a better agreement of the theoretical prediction of the SCDM model to the observed estimates of large-scale power in the galaxy distribution.
Amirkhanov, I V; Zhidkova, I E; Vasilev, S A
2000-01-01
Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.
Graph theory approach to the eigenvalue problem of large space structures
Reddy, A. S. S. R.; Bainum, P. M.
1981-01-01
Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.
A High-Performance Numerical Library for Solving Eigenvalue Problems: FEAST Solver v2.0 User's Guide
Polizzi, Eric
2012-01-01
The FEAST solver package is a free high-performance numerical library for solving the standard or generalized eigenvalue problem, and obtaining all the eigenvalues and eigenvectors within a given search interval. It is based on an innovative fast and stable numerical algorithm presented in Phys. Rev B Vol.79, p115112 (2009) - named the FEAST algorithm - which deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques. The FEAST algorithm takes its inspiration from the density-matrix representation and contour integration technique in quantum mechanics. It is free from orthogonalization procedures, and its main computational tasks consist of solving very few inner independent linear systems with multiple right-hand sides and one reduced eigenvalue problem orders of magnitude smaller than the original one. The FEAST algorithm combines simplicity and efficiency and offers many important capabilities for achieving hig...
Energy Technology Data Exchange (ETDEWEB)
Myers, D.R.; Lee, W.C.; Yabroff, I.W.
1980-06-16
The effectiveness of a large-scale electric power system can be measured by four factors: system performance, system availability, system cost, and system worth (from the user perspective). In response to the need for synergistic effectiveness measures. A broad, multi-contractor research project is being conducted to integrate those four categories. This report describes system cost at two levels: a conceptual framework for measuring the total cost of producing electricity under diverse system effectiveness measures, and a set of general cost inputs that relate the framework to specific utility types. In this report, Chapter II describes the general-level conceptual framework for assessing the cost of system effectivenss attributes. Chapter III shows how the actual costs of a power system can be disaggregated and then integrated into the broad-level conceptual framework. Chapter IV utilizes the conceptual framework and the concepts underlying its development to produce some concrete examples of measures of cost of system effectiveness. Appendix A is a more in-depth look at the cost of fuel, and illustrates the level of analytical detail necessary for putting the framework into practice.
Transmission eigenvalues for elliptic operators
Hitrik, Michael; Ola, Petri; Päivärinta, Lassi
2010-01-01
A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trace class case, the generic existence of transmission eigenvalues is established.
Kurashige, Yuki; Yanai, Takeshi
2009-06-01
This article presents an efficient and parallelized implementation of the density matrix renormalization group (DMRG) algorithm for quantum chemistry calculations. The DMRG method as a large-scale multireference electronic structure model is by nature particularly efficient for one-dimensionally correlated systems, while the present development is oriented toward applications for polynuclear transition metal compounds, in which the macroscopic one-dimensional structure of electron correlation is absent. A straightforward extension of the DMRG algorithm is proposed with further improvements and aggressive optimizations to allow its application with large multireference active space, which is often demanded for metal compound calculations. Special efficiency is achieved by making better use of sparsity and symmetry in the operator and wave function representations. By accomplishing computationally intensive DMRG calculations, the authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution. Potential energy curve calculations for the Cr2 molecule near the known equilibrium precisely predicted the full configuration interaction energies with a correlation space of 24 electrons in 30 orbitals [denoted by (24e,30o)]. The energies are demonstrated to be accurate to 0.6mEh (the error from the extrapolated best value) when as many as 10 000 renormalized basis states are employed for the left and right DMRG block representations. The relative energy curves for [Cu2O2]2+ along the isomerization coordinate were obtained from DMRG and other correlated calculations, for which a fairly large orbital space (32e,62o) is modeled as a full correlation space. The DMRG prediction nearly overlaps
Institute of Scientific and Technical Information of China (English)
ZHANG Zhong-zhi; HAN Xu-li
2005-01-01
By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.
DEFF Research Database (Denmark)
Lusby, Richard Martin; Muller, Laurent Flindt; Petersen, Bjørn
2013-01-01
This paper describes a Benders decomposition-based framework for solving the large scale energy management problem that was posed for the ROADEF 2010 challenge. The problem was taken from the power industry and entailed scheduling the outage dates for a set of nuclear power plants, which need...... to be regularly taken down for refueling and maintenance, in such away that the expected cost of meeting the power demand in a number of potential scenarios is minimized. We show that the problem structure naturally lends itself to Benders decomposition; however, not all constraints can be included in the mixed...... integer programming model. We present a two phase approach that first uses Benders decomposition to solve the linear programming relaxation of a relaxed version of the problem. In the second phase, integer solutions are enumerated and a procedure is applied to make them satisfy constraints not included...
实对称五对角矩阵逆特征值问题%INVERSE EIGENVALUE PROBLEM FOR REAL SYMMETRIC FIVE-DIAGONAL MATRIX
Institute of Scientific and Technical Information of China (English)
王正盛
2002-01-01
In this paper, a kind of inverse eigenvalue problem which is the recon-struction of real symmetric five-diagonal matrix by three eigenvalues and corre-sponding eigenvectors is proposed. The solvability of the problem is disucssedand some sufficient and necessary conditions for existence of solution of thisproblem are given. Furthermore numerical algorithm and some numerical experi-ments are given.
Mashood, K. K.; Singh, Vijay A.
2013-01-01
Research suggests that problem-solving skills are transferable across domains. This claim, however, needs further empirical substantiation. We suggest correlation studies as a methodology for making preliminary inferences about transfer. The correlation of the physics performance of students with their performance in chemistry and mathematics in…
Mashood, K. K.; Singh, Vijay A.
2013-01-01
Research suggests that problem-solving skills are transferable across domains. This claim, however, needs further empirical substantiation. We suggest correlation studies as a methodology for making preliminary inferences about transfer. The correlation of the physics performance of students with their performance in chemistry and mathematics in…
Directory of Open Access Journals (Sweden)
Serguei I. Iakovlev
2013-01-01
Full Text Available It is shown that any \\(\\mu \\in \\mathbb{C}\\ is an infinite multiplicity eigenvalue of the Steklov smoothing operator \\(S_h\\ acting on the space \\(L^1_{loc}(\\mathbb{R}\\. For \\(\\mu \
Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions
Directory of Open Access Journals (Sweden)
Guotao Wang
2014-01-01
Full Text Available By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.
MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1997-10-01
A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)
Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Yuguo Lin
2007-10-01
Full Text Available Krasnoselskii's fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone right focal eigenvalue problems (Ã¢ÂˆÂ’1nÃ¢ÂˆÂ’pu(n(t=ÃŽÂ»f(t,u(t,u'(t,Ã¢Â€Â¦,u(pÃ¢ÂˆÂ’1(t, u(i(0=0, 0Ã¢Â‰Â¤iÃ¢Â‰Â¤pÃ¢ÂˆÂ’1, u(i(1=0, pÃ¢Â‰Â¤iÃ¢Â‰Â¤nÃ¢ÂˆÂ’1, where nÃ¢Â‰Â¥2, 1Ã¢Â‰Â¤pÃ¢Â‰Â¤nÃ¢ÂˆÂ’1 is fixed, f:[0,1]ÃƒÂ—[0,Ã¢ÂˆÂžpÃ¢Â†Â’(Ã¢ÂˆÂ’Ã¢ÂˆÂž,Ã¢ÂˆÂž is continuous with f(t,u1,u2,Ã¢Â€Â¦,upÃ¢Â‰Â¥Ã¢ÂˆÂ’M for some positive constant M.
1980-09-29
FOUNDATIONS OF EIGENVALUE DISTRIBUTION THEORY FOR GENERAL A NON--ETC(U) SEP 80 M MARCUS, M GOLDBERG, M NEWMAN AFOSR-79-0127 UNCLASSIFIED AFOSR-TR-80...September 1980 Title of Research: Foundations of Eigenvalue Distribution Theory for General & Nonnegative Matrices, Stability Criteria for Hyperbolic
Bousserez, Nicolas
2016-01-01
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian inversion is proposed and efficiently constructed using a scalable randomized SVD algorithm. Useful optimality results are established for the associated posterior error covariance matrix and posterior mean approximations, which are further investigated in a numerical experiment consisting of a large-scale atmospheric tracer transport source-inversion problem. This method proves to be a robust and efficient approach to dimension reduction, as well as a natural framework to analyze the information content of the inversion. Possible extensions of this approach to the non-linear framework in the context of operational numerical weather forecast data assimilation systems based on the incremental 4D-Var technique are also discussed, and a detailed implementation of a new Randomized Incr...
Xu, Jiuping; Feng, Cuiying
2014-01-01
This paper presents an extension of the multimode resource-constrained project scheduling problem for a large scale construction project where multiple parallel projects and a fuzzy random environment are considered. By taking into account the most typical goals in project management, a cost/weighted makespan/quality trade-off optimization model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform the fuzzy random parameters into fuzzy variables that are subsequently defuzzified using an expected value operator with an optimistic-pessimistic index. Then a combinatorial-priority-based hybrid particle swarm optimization algorithm is developed to solve the proposed model, where the combinatorial particle swarm optimization and priority-based particle swarm optimization are designed to assign modes to activities and to schedule activities, respectively. Finally, the results and analysis of a practical example at a large scale hydropower construction project are presented to demonstrate the practicality and efficiency of the proposed model and optimization method.
A Variational Approach to the Isoperimetric Inequality for the Robin Eigenvalue Problem
Bucur, Dorin; Giacomini, Alessandro
2010-12-01
The isoperimetric inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions was recently proved by Daners in the context of Lipschitz sets. This paper introduces a new approach to the isoperimetric inequality, based on the theory of special functions of bounded variation (SBV). We extend the notion of the first eigenvalue λ1 for general domains with finite volume (possibly unbounded and with irregular boundary), and we prove that the balls are the unique minimizers of λ1 among domains with prescribed volume.
Existence and comparison of smallest eigenvalues for a fractional boundary-value problem
Directory of Open Access Journals (Sweden)
Paul W. Eloe
2014-02-01
Full Text Available The theory of $u_0$-positive operators with respect to a cone in a Banach space is applied to the fractional linear differential equations $$ D_{0+}^{\\alpha} u+\\lambda_1p(tu=0\\quad\\text{and}\\quad D_{0+}^{\\alpha} u+\\lambda_2q(tu=0, $$ $0< t< 1$, with each satisfying the boundary conditions $u(0=u(1=0$. The existence of smallest positive eigenvalues is established, and a comparison theorem for smallest positive eigenvalues is obtained.
Indian Academy of Sciences (India)
Rahul Sharma; Subbajit Nandy; S P Bhattacharyya
2006-06-01
An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin's strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed.
Eigenvalue study of a chaotic resonator
Energy Technology Data Exchange (ETDEWEB)
Banova, Todorka [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany); Technische Universitaet Darmstadt, Graduate School of Computational Engineering, Dolivostrasse 15, D-64293 Darmstadt (Germany); Ackermann, Wolfgang; Weiland, Thomas [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)
2013-07-01
The field of quantum chaos comprises the study of the manifestations of classical chaos in the properties of the corresponding quantum systems. Within this work, we compute the eigenfrequencies that are needed for the level spacing analysis of a microwave resonator with chaotic characteristics. The major challenges posed by our work are: first, the ability of the approaches to tackle the large scale eigenvalue problem and second, the capability to extract many, i.e. order of thousands, eigenfrequencies for the considered cavity. The first proposed approach for an accurate eigenfrequency extraction takes into consideration the evaluated electric field computations in time domain of a superconducting cavity and by means of signal-processing techniques extracts the eigenfrequencies. The second approach is based on the finite element method with curvilinear elements, which transforms the continuous eigenvalue problem to a discrete generalized eigenvalue problem. Afterwards, the Lanczos algorithm is used for the solution of the generalized eigenvalue problem. In the poster, a summary of the applied algorithms, as well as, critical implementation details together with the simulation results are provided.
Photonic crystal fibres: mapping Maxwell's equations onto a Schrödinger equation eigenvalue problem
DEFF Research Database (Denmark)
Mortensen, Niels Asger
2006-01-01
We consider photonic crystal fibres (PCFs) made from arbitrary base materials and introduce a short-wavelength approximation which allows for a mapping of the Maxwell's equations onto a dimensionless eigenvalue equations which has the form of the Schröding equation in quantum mechanics. The mappi...
Sleijpen, G.L.G.; Vorst, H.A. van der
1995-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix.The matrix may be complex and non-normal.The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors,
The Jacobi-Davidson method for eigenvalue problems as an accelerated inexact Newton scheme
Sleijpen, G.L.G.; Vorst, H.A. van der
1995-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix. The matrix may be complex and non-normal. The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors,
A POSTERIORI ERROR ESTIMATES IN ADINI FINITE ELEMENT FOR EIGENVALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
Yi-du Yang
2000-01-01
In this paper, we discuss a posteriori error estimates of the eigenvalue λh given by Adini nonconforming finite element. We give an assymptotically exact error estimator of the λh. We prove that the order of convergence of the λh is just 2and the λh converge from below for sufficiently small h.
Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter
Hassi, Seppo; Moller, M; de Snoo, H
2004-01-01
Let -Domega((.), z)D + q be a differential operator in L-2(0, infinity) whose leading coefficient contains the eigenvalue parameter z. For the case that omega((.), z) has the particular form omega(t, z) = p(t) + c(t)(2)/(z - r (t)), z is an element of C \\ R, and the coefficient functions satisfy cer
The Jacobi-Davidson method for eigenvalue problems as an accelerated inexact Newton scheme
Sleijpen, G.L.G.; Vorst, H.A. van der
2001-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix. The matrix may be complex and non-normal. The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors,
Sleijpen, G.L.G.; Vorst, H.A. van der
2006-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix.The matrix may be complex and non-normal.The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors, an
A generalized Jacobi-Davidson iteration method for linear eigenvalue problems
Sleijpen, G.L.G.; Vorst, H.A. van der
1998-01-01
In this paper we propose a new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi's approach, combined with Davidson's method, leads to a new meth
DEFF Research Database (Denmark)
Bache, Anja Margrethe
2010-01-01
WORLD FAMOUS ARCHITECTS CHALLENGE TODAY THE EXPOSURE OF CONCRETE IN THEIR ARCHITECTURE. IT IS MY HOPE TO BE ABLE TO COMPLEMENT THESE. I TRY TO DEVELOP NEW AESTHETIC POTENTIALS FOR THE CONCRETE AND CERAMICS, IN LARGE SCALES THAT HAS NOT BEEN SEEN BEFORE IN THE CERAMIC AREA. IT IS EXPECTED TO RESULT...
Eigenvalue problems for a quasilinear elliptic equation on ℝN
Directory of Open Access Journals (Sweden)
Marilena N. Poulou
2005-01-01
Full Text Available We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x|u|p−2u, x∈ℝN, lim|x|→+∞u(x=0, where Δpu=div(|∇u|p−2∇u is the p-Laplacian operator and the weight function g(x, being bounded, changes sign and is negative and away from zero at infinity.
On the Asymptotic of an Eigenvalue Problem with 2 Interior Singularities
Indian Academy of Sciences (India)
A Neamaty; S Haghaieghy
2009-11-01
In this paper we consider the linear differential equation of the form $$-y''(x)+q(x)y(x)= y(x),\\quad -∞ < a < x < b < ∞$$ where satisfies Dirichlet boundary conditions and is a real-valued function which has even number of singularities at $c_1,\\ldots,c_{2n}\\in(a, b)$. We will study the asymptotic eigenvalue near the singularity points.
Kochunas, Brendan; Fitzgerald, Andrew; Larsen, Edward
2017-09-01
A central problem in nuclear reactor analysis is calculating solutions of steady-state k-eigenvalue problems with thermal hydraulic feedback. In this paper we propose and utilize a model problem that permits the theoretical analysis of iterative schemes for solving such problems. To begin, we discuss a model problem (with nonlinear cross section feedback) and its justification. We proceed with a Fourier analysis for source iteration schemes applied to the model problem. Then we analyze commonly-used iteration schemes involving non-linear diffusion acceleration and feedback. For each scheme we show (1) that they are conditionally stable, (2) the conditions that lead to instability, and (3) that traditional relaxation approaches can improve stability. Lastly, we propose a new iteration scheme that theory predicts is an improvement upon the existing methods.
Li, Tiexiang; Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Jenn-Nan
2017-03-01
We propose an efficient eigensolver for computing densely distributed spectra of the two-dimensional transmission eigenvalue problem (TEP), which is derived from Maxwell’s equations with Tellegen media and the transverse magnetic mode. The governing equations, when discretized by the standard piecewise linear finite element method, give rise to a large-scale quadratic eigenvalue problem (QEP). Our numerical simulation shows that half of the positive eigenvalues of the QEP are densely distributed in some interval near the origin. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Extensive numerical simulations show that our proposed method processes the convergence efficiently, even when it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by nonlinear functions, which can be applied to estimate the denseness of the eigenvalues for the TEP.
Energy Technology Data Exchange (ETDEWEB)
Bottcher, C.; Strayer, M.R. [Oak Ridge National Lab., TN (United States); Werby, M.F. [Naval Research Lab. Detachment, Stennis Space Center, MS (United States)
1993-10-01
The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWE`s. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can by obtained in matrix form be expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways to long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology will be explained in detail and examples will be presented.
Directory of Open Access Journals (Sweden)
Guillermo Cabrera G.
2012-01-01
Full Text Available We present a hybridization of two different approaches applied to the well-known Capacitated Facility Location Problem (CFLP. The Artificial Bee algorithm (BA is used to select a promising subset of locations (warehouses which are solely included in the Mixed Integer Programming (MIP model. Next, the algorithm solves the subproblem by considering the entire set of customers. The hybrid implementation allows us to bypass certain inherited weaknesses of each algorithm, which means that we are able to find an optimal solution in an acceptable computational time. In this paper we demonstrate that BA can be significantly improved by use of the MIP algorithm. At the same time, our hybrid implementation allows the MIP algorithm to reach the optimal solution in a considerably shorter time than is needed to solve the model using the entire dataset directly within the model. Our hybrid approach outperforms the results obtained by each technique separately. It is able to find the optimal solution in a shorter time than each technique on its own, and the results are highly competitive with the state-of-the-art in large-scale optimization. Furthermore, according to our results, combining the BA with a mathematical programming approach appears to be an interesting research area in combinatorial optimization.
Institute of Scientific and Technical Information of China (English)
Chong-hua Yu; O. Axelsson
2000-01-01
In this paper, an algorithm for computing some of the largest (smallest) generalized eigenvalues with corresponding eigenvectors of a sparse symmetric positive definite matrix pencil is presented. The algorithm uses an iteration function and inverse power iteration process to get the largest one first, then executes m-1Lanczos-like steps to get initial approximations of the next m - 1 ones, without computing any Ritz pair, for which a procedure combining Rayleigh quotient iteration with shifted inverse power iteration is used to obtain more accurate eigenvalues and eigenvectors. This algorithm keeps the advantages of preserving sparsity of the original matrices as in Lanczos method and RQI and converges with a higher rate than the method described in[12] and provides a simple technique to compute initial approximate pairs which are guaranteed to converge to the wanted m largest eigenpairs using RQI. In addition, it avoids some of the disadvantages of Lanczos and RQI, for solving extreme eigenproblems. When symmetric positive definfite linear systems must be solved in the process, an algebraic multilevel iteration method (AMLI) is applied. The algorithm is fully parallelizable.
DEFF Research Database (Denmark)
Heller, Alfred
2001-01-01
The main objective of the research was to evaluate large-scale solar heating connected to district heating (CSDHP), to build up a simulation tool and to demonstrate the application of the simulation tool for design studies and on a local energy planning case. The evaluation was mainly carried out...... model is designed and validated on the Marstal case. Applying the Danish Reference Year, a design tool is presented. The simulation tool is used for proposals for application of alternative designs, including high-performance solar collector types (trough solar collectors, vaccum pipe collectors......). Simulation programs are proposed as control supporting tool for daily operation and performance prediction of central solar heating plants. Finaly the CSHP technolgy is put into persepctive with respect to alternatives and a short discussion on the barries and breakthrough of the technology are given....
BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS ), (* PARTIAL DIFFERENTIAL EQUATIONS , BOUNDARY VALUE PROBLEMS), (*NUMERICAL ANALYSIS, BOUNDARY VALUE PROBLEMS), FUNCTIONS(MATHEMATICS), DIFFERENCE EQUATIONS
Olivier, C. P.; Herbst, B. M.; Molchan, M. A.
2012-06-01
Deconinck and Kutz (2006 J. Comput. Phys. 219 296-321) developed an efficient algorithm for solving the Zakharov-Shabat eigenvalue problem with periodic potentials numerically. It is natural to use the same algorithm for solving the problem for non-periodic potential (decaying potentials defined over the whole real line) using large periods. In this paper, we propose the use of a specific value of the Floquet exponent. Our numerical results indicate that it can produce accurate results long before the period becomes large enough for the analytical convergence results of Gardner (1997 J. Reine Angew. Math. 491 149-81) to be valid. We also illustrate the rather complicated path to convergence of some nonlinear Schrödinger potentials.
Large scale tracking algorithms
Energy Technology Data Exchange (ETDEWEB)
Hansen, Ross L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Love, Joshua Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Melgaard, David Kennett [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Pitts, Todd Alan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Zollweg, Joshua David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Anderson, Dylan Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Nandy, Prabal [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Whitlow, Gary L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bender, Daniel A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Byrne, Raymond Harry [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-01-01
Low signal-to-noise data processing algorithms for improved detection, tracking, discrimination and situational threat assessment are a key research challenge. As sensor technologies progress, the number of pixels will increase signi cantly. This will result in increased resolution, which could improve object discrimination, but unfortunately, will also result in a significant increase in the number of potential targets to track. Many tracking techniques, like multi-hypothesis trackers, suffer from a combinatorial explosion as the number of potential targets increase. As the resolution increases, the phenomenology applied towards detection algorithms also changes. For low resolution sensors, "blob" tracking is the norm. For higher resolution data, additional information may be employed in the detection and classfication steps. The most challenging scenarios are those where the targets cannot be fully resolved, yet must be tracked and distinguished for neighboring closely spaced objects. Tracking vehicles in an urban environment is an example of such a challenging scenario. This report evaluates several potential tracking algorithms for large-scale tracking in an urban environment.
Large scale tracking algorithms.
Energy Technology Data Exchange (ETDEWEB)
Hansen, Ross L.; Love, Joshua Alan; Melgaard, David Kennett; Karelitz, David B.; Pitts, Todd Alan; Zollweg, Joshua David; Anderson, Dylan Z.; Nandy, Prabal; Whitlow, Gary L.; Bender, Daniel A.; Byrne, Raymond Harry
2015-01-01
Low signal-to-noise data processing algorithms for improved detection, tracking, discrimination and situational threat assessment are a key research challenge. As sensor technologies progress, the number of pixels will increase signi cantly. This will result in increased resolution, which could improve object discrimination, but unfortunately, will also result in a significant increase in the number of potential targets to track. Many tracking techniques, like multi-hypothesis trackers, suffer from a combinatorial explosion as the number of potential targets increase. As the resolution increases, the phenomenology applied towards detection algorithms also changes. For low resolution sensors, "blob" tracking is the norm. For higher resolution data, additional information may be employed in the detection and classfication steps. The most challenging scenarios are those where the targets cannot be fully resolved, yet must be tracked and distinguished for neighboring closely spaced objects. Tracking vehicles in an urban environment is an example of such a challenging scenario. This report evaluates several potential tracking algorithms for large-scale tracking in an urban environment.
The general solution of the eigenvalue problem for a high-gain FEL
Saldin, E L; Yurkov, M V
2001-01-01
The exact solution of the eigenvalue equation for a high-gain FEL derived in Xie (Nucl. Instr. and Meth. A 445 (2000) 59) is generalized in order to include the space charge effects. This solution is valid not only for natural undulator focusing, but also for alternating-gradient focusing under some condition that is presented. At such, the obtained solution includes all the important effects in the system of axially homogeneous electron beam and undulator: diffraction, betatron motion, energy spread, space charge and frequency detuning. It is valid for ground TEM sub 0 sub 0 mode as well as for high-order modes and can be used for calculation of high-gain FEL amplifiers operating in the wavelength regions from far infrared down to X-ray. In addition, a computationally efficient approximate solution for TEM sub 0 sub 0 mode is derived providing high accuracy (better than 1% in the whole range of parameters). It can be used for quick optimization of FEL amplifiers.
An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry
Shiozaki, Toru
2015-01-01
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N > 10000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige-Van Loan algorithm [D. Kressner, BIT 43, 775 (2003)], which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of two than state-of-the-art implementations of complex Hermitian diagonalization; diagonalizing a 12800 x 12800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel MKL's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD license.
Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates
Kitahara, M
1985-01-01
The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro
Large Scale Correlation Clustering Optimization
Bagon, Shai
2011-01-01
Clustering is a fundamental task in unsupervised learning. The focus of this paper is the Correlation Clustering functional which combines positive and negative affinities between the data points. The contribution of this paper is two fold: (i) Provide a theoretic analysis of the functional. (ii) New optimization algorithms which can cope with large scale problems (>100K variables) that are infeasible using existing methods. Our theoretic analysis provides a probabilistic generative interpretation for the functional, and justifies its intrinsic "model-selection" capability. Furthermore, we draw an analogy between optimizing this functional and the well known Potts energy minimization. This analogy allows us to suggest several new optimization algorithms, which exploit the intrinsic "model-selection" capability of the functional to automatically recover the underlying number of clusters. We compare our algorithms to existing methods on both synthetic and real data. In addition we suggest two new applications t...
The Eigenvalue Method for Extremal Problems on Infinite Vertex-Transitive Graphs
DeCorte, P.E.B.
2015-01-01
This thesis is about maximum independent set and chromatic number problems on certain kinds of infinite graphs. A typical example comes from the Witsenhausen problem: For $n \\geq 2$, let $S^{n-1} := \\{ x \\in \\R^n : \\|x\\|_2 =1 \\}$ be the unit sphere in $\\R^n$, and let $G=(V,E)$ be the graph with $V =
Some properties of eigenvalues and generalized eigenvectors of one boundary-value problem
Olgar, Hayati; Mukhtarov, Oktay; Aydemir, Kadriye
2016-08-01
We investigate a discontinuous boundary value problem which consists of a Sturm-Liouville equation with piece-wise continuous potential together with eigenparameter-dependent boundary conditions and supplementary transmission conditions. We establish some spectral properties of the considered problem. In particular it is shown that the generalized eigen-functions form a Riesz basis of the adequate Hilbert space.
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
On an Inverse Eigenvalue Problem for a Semilinear Sturm-Liouville Operator
Zhidkov, P E
2005-01-01
The following problem is considered: $-u''+f(u)=\\lambda u, x\\in (0,1), u=u(x), u(0)=1, u'(0)=u(1)=0,$ where $\\lambda $ is a spectral parameter. We study the inverse problem: for a given part of the spectrum $\\lambda _n\\to +\\infty $ we seek odd $f$. We obtain a description of the whole class of solutions of this problem. In addition, we show that there exists at most one function $f$ such that an auxiliary function is nondecreasing.
Wenner, Michael T.
Obtaining the solution to the linear Boltzmann equation is often is often a daunting task. The time-independent form is an equation of six independent variables which cannot be solved analytically in all but some special problems. Instead, numerical approaches have been devised. This work focuses on improving Monte Carlo methods for its solution in eigenvalue form. First, a statistical method of stationarity detection called the KPSS test adapted as a Monte Carlo eigenvalue source convergence test. The KPSS test analyzes the source center of mass series which was chosen since it should be indicative of overall source behavior, and is physically easy to understand. A source center of mass plot alone serves as a good visual source convergence diagnostic. The KPSS test and three different information theoretic diagnostics were implemented into the well known KENOV.a code inside of the SCALE (version 5) code package from Oak Ridge National Laboratory and compared through analysis of a simple problem and several difficult source convergence benchmarks. Results showed that the KPSS test can add to the overall confidence by identifying more problematic simulations than without its usage. Not only this, the source center of mass information on hand visually aids in the understanding of the problem physics. The second major focus of this dissertation concerned variance reduction methodologies for Monte Carlo eigenvalue problems. The CADIS methodology, based on importance sampling, was adapted to the eigenvalue problems. It was shown that the straight adaption of importance sampling can provide a significant variance reduction in determination of keff (in cases studied up to 30%?). A modified version of this methodology was developed which utilizes independent deterministic importance simulations. In this new methodology, each particle is simulated multiple times, once to every other discretized source region utilizing the importance for that region only. Since each particle
Hamiltonian矩阵特征值问题的Lanczos-型算法%Lanczos Algorithms-Type for Hamiltonian Eigenvalue Problems
Institute of Scientific and Technical Information of China (English)
郭蔚
2001-01-01
In the paper,we applicate Lanczos algorithms-type to Hamiltonian eigenvalue problems and give an error analysis in iterative procedure.%应用Lanczos-型算法求Hamiltonian矩阵的特征根问题，并且给出了在迭代过程中的误差估计．
Institute of Scientific and Technical Information of China (English)
张俊
2011-01-01
This paper discusses Wilson nonconforming element of eigenvalue problem of SchrSdinger equation and its error estimates.%讨论三维Schrǒdinger方程的特征值问题的Wilson元离散，并给出相应的误差估计．
Khapaev, M. M.; Khapaeva, T. M.
2016-10-01
A functional-based variational method is proposed for finding the eigenfunctions and eigenvalues in the Sturm-Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint. Computations are performed for three potentials: sin(( x-π)2/π), cos(4 x), and a high nonisosceles triangle.
Parallel Sparse Linear System and Eigenvalue Problem Solvers: From Multicore to Petascale Computing
2015-06-01
problems that achieve high performance on a single multicore node and clusters of many multicore nodes. Further, we demonstrate both the superior ...the superior robustness and parallel scalability of our solvers compared to other publicly available parallel solvers for these two fundamental...LU‐ and algebraic multigrid‐preconditioned Krylov subspace methods. This has been demonstrated in previous annual reports of this
Directory of Open Access Journals (Sweden)
G. V. Levina
2000-01-01
Full Text Available The work is concerned with the results of theoretical and laboratory modelling the processes of the large-scale structure generation under turbulent convection in the rotating-plane horizontal layer of an incompressible fluid with unstable stratification. The theoretical model describes three alternative ways of creating unstable stratification: a layer heating from below, a volumetric heating of a fluid with internal heat sources and combination of both factors. The analysis of the model equations show that under conditions of high intensity of the small-scale convection and low level of heat loss through the horizontal layer boundaries a long wave instability may arise. The condition for the existence of an instability and criterion identifying the threshold of its initiation have been determined. The principle of action of the discovered instability mechanism has been described. Theoretical predictions have been verified by a series of experiments on a laboratory model. The horizontal dimensions of the experimentally-obtained long-lived vortices are 4÷6 times larger than the thickness of the fluid layer. This work presents a description of the laboratory setup and experimental procedure. From the geophysical viewpoint the examined mechanism of the long wave instability is supposed to be adequate to allow a description of the initial step in the evolution of such large-scale vortices as tropical cyclones - a transition form the small-scale cumulus clouds to the state of the atmosphere involving cloud clusters (the stage of initial tropical perturbation.
Hamed, Haikel Ben; Bennacer, Rachid
2008-08-01
This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh-Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).
Gkoulalas-Divanis, Aris
2014-01-01
Provides cutting-edge research in large-scale data analytics from diverse scientific areas Surveys varied subject areas and reports on individual results of research in the field Shares many tips and insights into large-scale data analytics from authors and editors with long-term experience and specialization in the field
Inverse eigenvalue problems in vibration absorption: Passive modification and active control
Mottershead, John E.; Ram, Yitshak M.
2006-01-01
The abiding problem of vibration absorption has occupied engineering scientists for over a century and there remain abundant examples of the need for vibration suppression in many industries. For example, in the automotive industry the resolution of noise, vibration and harshness (NVH) problems is of extreme importance to customer satisfaction. In rotorcraft it is vital to avoid resonance close to the blade passing speed and its harmonics. An objective of the greatest importance, and extremely difficult to achieve, is the isolation of the pilot's seat in a helicopter. It is presently impossible to achieve the objectives of vibration absorption in these industries at the design stage because of limitations inherent in finite element models. Therefore, it is necessary to develop techniques whereby the dynamic of the system (possibly a car or a helicopter) can be adjusted after it has been built. There are two main approaches: structural modification by passive elements and active control. The state of art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples.
An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra
Rundell, William
2013-04-23
A classical inverse problem is "can you hear the density of a string clamped at both ends?" The mathematical model gives rise to an inverse Sturm-Liouville problem for the unknown density ñ, and it is well known that the answer is negative: the Dirichlet spectrum from the clamped end-point conditions is insufficient. There are many known ways to add additional information to gain a positive answer, and these include changing one of the boundary conditions and recomputing the spectrum or giving the energy in each eigenmode-the so-called norming constants. We make the assumption that neither of these changes are possible. Instead we will add known mass-densities to the string in a way we can prescribe and remeasure the Dirichlet spectrum. We will not be able to answer the uniqueness question in its most general form, but will give some insight to what "added masses" should be chosen and how this can lead to a reconstruction of the original string density. © 2013 Society for Industrial and Applied Mathematics.
Aktosun, Tuncay; Gintides, Drossos; Papanicolaou, Vassilis G.
2011-11-01
The recovery of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of the corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, it is shown that v is uniquely determined by the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the ‘multiplicity’ is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique recovery is obtained when the data contain one additional piece of information. Some similar results are presented for the unique determination of the potential from the transmission eigenvalues with ‘multiplicities’ for a related Schrödinger equation.
Haidar, Azzam
2011-01-01
This paper introduces a novel implementation in reducing a symmetric dense matrix to tridiagonal form, which is the preprocessing step toward solving symmetric eigenvalue problems. Based on tile algorithms, the reduction follows a two-stage approach, where the tile matrix is first reduced to symmetric band form prior to the final condensed structure. The challenging trade-off between algorithmic performance and task granularity has been tackled through a grouping technique, which consists of aggregating fine-grained and memory-aware computational tasks during both stages, while sustaining the application\\'s overall high performance. A dynamic runtime environment system then schedules the different tasks in an out-of-order fashion. The performance for the tridiagonal reduction reported in this paper is unprecedented. Our implementation results in up to 50-fold and 12-fold improvement (130 Gflop/s) compared to the equivalent routines from LAPACK V3.2 and Intel MKL V10.3, respectively, on an eight socket hexa-core AMD Opteron multicore shared-memory system with a matrix size of 24000×24000. Copyright 2011 ACM.
Energy Technology Data Exchange (ETDEWEB)
Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics
1997-11-01
The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.
The Schrodinger Eigenvalue March
Tannous, C.; Langlois, J.
2011-01-01
A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…
Large scale cluster computing workshop
Energy Technology Data Exchange (ETDEWEB)
Dane Skow; Alan Silverman
2002-12-23
Recent revolutions in computer hardware and software technologies have paved the way for the large-scale deployment of clusters of commodity computers to address problems heretofore the domain of tightly coupled SMP processors. Near term projects within High Energy Physics and other computing communities will deploy clusters of scale 1000s of processors and be used by 100s to 1000s of independent users. This will expand the reach in both dimensions by an order of magnitude from the current successful production facilities. The goals of this workshop were: (1) to determine what tools exist which can scale up to the cluster sizes foreseen for the next generation of HENP experiments (several thousand nodes) and by implication to identify areas where some investment of money or effort is likely to be needed. (2) To compare and record experimences gained with such tools. (3) To produce a practical guide to all stages of planning, installing, building and operating a large computing cluster in HENP. (4) To identify and connect groups with similar interest within HENP and the larger clustering community.
Large Scale Magnetostrictive Valve Actuator
Richard, James A.; Holleman, Elizabeth; Eddleman, David
2008-01-01
Marshall Space Flight Center's Valves, Actuators and Ducts Design and Development Branch developed a large scale magnetostrictive valve actuator. The potential advantages of this technology are faster, more efficient valve actuators that consume less power and provide precise position control and deliver higher flow rates than conventional solenoid valves. Magnetostrictive materials change dimensions when a magnetic field is applied; this property is referred to as magnetostriction. Magnetostriction is caused by the alignment of the magnetic domains in the material s crystalline structure and the applied magnetic field lines. Typically, the material changes shape by elongating in the axial direction and constricting in the radial direction, resulting in no net change in volume. All hardware and testing is complete. This paper will discuss: the potential applications of the technology; overview of the as built actuator design; discuss problems that were uncovered during the development testing; review test data and evaluate weaknesses of the design; and discuss areas for improvement for future work. This actuator holds promises of a low power, high load, proportionally controlled actuator for valves requiring 440 to 1500 newtons load.
Computing in Large-Scale Dynamic Systems
Pruteanu, A.S.
2013-01-01
Software applications developed for large-scale systems have always been difficult to de- velop due to problems caused by the large number of computing devices involved. Above a certain network size (roughly one hundred), necessary services such as code updating, topol- ogy discovery and data dissem
Diagonalizable quadratic eigenvalue problems
Lancaster, Peter; Zaballa, Ion
2009-05-01
A system is defined to be an n×n matrix function L(λ)=λ2M+λD+K where M,D,K∈C and M is nonsingular. First, a careful review is made of the possibility of direct decoupling to a diagonal (real or complex) system by applying congruence or strict equivalence transformations to L(λ). However, the main contribution is a complete description of the much wider class of systems which can be decoupled by applying congruence or strict equivalence transformations to a linearization of a system while preserving the structure of L(λ). The theory is liberally illustrated with examples.
Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Weichung
2016-10-01
We study how to efficiently solve the eigenvalue problems in computing band structure of three-dimensional dispersive metallic photonic crystals with face-centered cubic lattices based on the lossless Drude model. The discretized Maxwell equations result in large-scale standard eigenvalue problems whose spectrum contains many zero and cluster eigenvalues, both prevent existed eigenvalue solver from being efficient. To tackle this computational difficulties, we propose a hybrid Jacobi-Davidson method (hHybrid) that integrates harmonic Rayleigh-Ritz extraction, a new and hybrid way to compute the correction vectors, and a FFT-based preconditioner. Intensive numerical experiments show that the hHybrid outperforms existed eigenvalue solvers in terms of timing and convergence behaviors.
Generalized Inverse Eigenvalue Problem for Centrohermitian Matrices%关于中心厄米特矩阵的广义反特征值问题
Institute of Scientific and Technical Information of China (English)
刘仲云; 谭艳祥; 田兆录
2004-01-01
In this paper we first consider the existence and the general form of solution to the following generalized inverse eigenvalue problem(GIEP): given a set of n-dimension complex vectors {xj}mj= 1 and a set of complex numbers {λj}jm=1, find two n × n centrohermitian matrices A, B such that {xj}jm = 1 and {λj}jm= 1 are the generalized eigenvectors and generalized eigenvalues of Ax = λBx, respectively. We then discuss the optimal approximation problem for the GIEP. More concretely, given two arbitrary matrices, A, E ∈Cn×n, we find two matrices A* and B* such that the matrix (A* ,B* ) is closest to (A ,B) in the Frobenius norm, where the matrix (A *,B*) is the solution to the GIEP. We show that the expression of the solution of the optimal approximation is unique and derive the expression for it.
球面区域上buckling特征值的万有估计%UNIVERSAL BOUNDS ON EIGENVALUES OF THE BUCKLING PROBLEM ON SPHERICAL DOMAINS
Institute of Scientific and Technical Information of China (English)
黄广月; 李兴校; 曹林芬
2011-01-01
We study the eigenvalues of buckling problem on domains in the unit sphere.By introducing a new parameter and using Cauchy inequality,we optimize the inequality obtained by Wang and Xia in[12].%本文研究了球面域上的buckling特征值问题.通过引入新的参数和使用Cauchy不等式,优化了Wang-Xia在文献[1 2]中的不等式.
Workshop report on large-scale matrix diagonalization methods in chemistry theory institute
Energy Technology Data Exchange (ETDEWEB)
Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S. [eds.
1996-10-01
The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems as well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of
Large-Scale Information Systems
Energy Technology Data Exchange (ETDEWEB)
D. M. Nicol; H. R. Ammerlahn; M. E. Goldsby; M. M. Johnson; D. E. Rhodes; A. S. Yoshimura
2000-12-01
Large enterprises are ever more dependent on their Large-Scale Information Systems (LSLS), computer systems that are distinguished architecturally by distributed components--data sources, networks, computing engines, simulations, human-in-the-loop control and remote access stations. These systems provide such capabilities as workflow, data fusion and distributed database access. The Nuclear Weapons Complex (NWC) contains many examples of LSIS components, a fact that motivates this research. However, most LSIS in use grew up from collections of separate subsystems that were not designed to be components of an integrated system. For this reason, they are often difficult to analyze and control. The problem is made more difficult by the size of a typical system, its diversity of information sources, and the institutional complexities associated with its geographic distribution across the enterprise. Moreover, there is no integrated approach for analyzing or managing such systems. Indeed, integrated development of LSIS is an active area of academic research. This work developed such an approach by simulating the various components of the LSIS and allowing the simulated components to interact with real LSIS subsystems. This research demonstrated two benefits. First, applying it to a particular LSIS provided a thorough understanding of the interfaces between the system's components. Second, it demonstrated how more rapid and detailed answers could be obtained to questions significant to the enterprise by interacting with the relevant LSIS subsystems through simulated components designed with those questions in mind. In a final, added phase of the project, investigations were made on extending this research to wireless communication networks in support of telemetry applications.
Vishniac, Ethan T.
2015-01-01
We show that a differentially rotating conducting fluid automatically creates a magnetic helicity flux with components along the rotation axis and in the direction of the local vorticity. This drives a rapid growth in the local density of current helicity, which in turn drives a large scale dynamo. The dynamo growth rate derived from this process is not constant, but depends inversely on the large scale magnetic field strength. This dynamo saturates when buoyant losses of magnetic flux compete with the large scale dynamo, providing a simple prediction for magnetic field strength as a function of Rossby number in stars. Increasing anisotropy in the turbulence produces a decreasing magnetic helicity flux, which explains the flattening of the B/Rossby number relation at low Rossby numbers. We also show that the kinetic helicity is always a subdominant effect. There is no kinematic dynamo in real stars.
Large-scale circuit simulation
Wei, Y. P.
1982-12-01
The simulation of VLSI (Very Large Scale Integration) circuits falls beyond the capabilities of conventional circuit simulators like SPICE. On the other hand, conventional logic simulators can only give the results of logic levels 1 and 0 with the attendent loss of detail in the waveforms. The aim of developing large-scale circuit simulation is to bridge the gap between conventional circuit simulation and logic simulation. This research is to investigate new approaches for fast and relatively accurate time-domain simulation of MOS (Metal Oxide Semiconductors), LSI (Large Scale Integration) and VLSI circuits. New techniques and new algorithms are studied in the following areas: (1) analysis sequencing (2) nonlinear iteration (3) modified Gauss-Seidel method (4) latency criteria and timestep control scheme. The developed methods have been implemented into a simulation program PREMOS which could be used as a design verification tool for MOS circuits.
Energy Technology Data Exchange (ETDEWEB)
CREUTZ, M.
2006-01-26
It is popular to discuss low energy physics in lattice gauge theory ill terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra. In short, thinking about the eigenvalues of the Dirac operator in the presence of gauge fields can give some insight, for example the elegant Banks-Casher picture for chiral symmetry breaking. Nevertheless, care is necessary because the problem is highly non-linear. This manifests itself in the non-intuitive example of how adding flavors enhances rather than suppresses low eigenvalues. Issues involving zero mode suppression represent one facet of a set of connected unresolved issues. Are there non-perturbative ambiguities in quantities such as the topological susceptibility? How essential are rough gauge fields, i.e. gauge fields on which the winding number is ambiguous? How do these issues interplay with the quark masses? I hope the puzzles presented here will stimulate more thought along these lines.
求解大规模旅行商问题的改进大洪水算法%Modified Great Deluge Algorithm for Large-scale Travelling Salesman Problem
Institute of Scientific and Technical Information of China (English)
盛虹平; 马良
2012-01-01
Great deluge algorithm is one of heuristics by simulating the process of flood rising to search global optimization. r-Opt algorithm is usually applied in path optimization. For the travelling salesman problem, this paper gives a modified great deluge algorithm which mainly combines great deluge algorithm with r-opt algorithm, and it can be used to solve the large-scale and super large-scale travelling salesman problem. The algorithm is programmed in Delphi 7, and is tested through series of standard instances from TSPLIB. The errors between the algorithm results and the best results published in TSPLIB are almost below \\%. The algorithm is proved to be a kind of new method to solve the difficult large-scale travelling salesman problem.%大洪水算法是通过模拟洪水上涨过程来进行全局寻优的启发式算法,r-opt算法是一类常用的路径改进算法.本文针对旅行商问题,提出一种将二者有机融合的改进大洪水算法,可用于快速求解大规模和超大规模的TSP问题.算法在Delphi7环境下编程实现,经过大量TSPLIB中的数据实例进行测试和验证,求解结果与已公布的最好结果误差基本都在1％以下,为困难的大规模旅行商问题提供了新的求解手段.
S.Y.M. Mérelle (Saskia); A. Kleiboer (Annet); M. Schotanus (Miriam); T.L.M. Cluitmans (Theresia L. M.); C.M. Waardenburg (Cornelia M.); D. Kramer (Danielle); H. van de Mheen (Dike); A.J. van Rooij (Antonius)
2017-01-01
markdownabstract_Objective:_ Problematic video-gaming or social media use may seriously affect adolescents’ health status. However, it is not very well known which health-related problems are most strongly related to these issues. To inform the development of prevention and intervention strategies,
The origin and nature of spurious eigenvalues in the spectral tau method
Energy Technology Data Exchange (ETDEWEB)
Dawkins, P.T. [Lamar Univ., Beaumont, TX (United States). Dept. of Mathematics; Dunbar, S.R. [Univ. of Nebraska, Lincoln, NE (United States). Dept. of Mathematics and Statistics; Douglass, R.W. [Idaho National Engineering Lab., Idaho Falls, ID (United States)
1998-12-10
The Chebyshev-tau spectral method for approximating eigenvalues of boundary value problems may produce spurious eigenvalues with large positive real parts, even when all true eigenvalues of the problem are known to have negative real parts. The authors explain the origin and nature of the spurious eigenvalues in an example problem. The explanation will demonstrate that the large positive eigenvalues are an approximation of infinite eigenvalues in a nearby generalized eigenvalue problem.
Very Large Scale Integration (VLSI).
Yeaman, Andrew R. J.
Very Large Scale Integration (VLSI), the state-of-the-art production techniques for computer chips, promises such powerful, inexpensive computing that, in the future, people will be able to communicate with computer devices in natural language or even speech. However, before full-scale VLSI implementation can occur, certain salient factors must be…
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...... project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...
Institute of Scientific and Technical Information of China (English)
于萌
2013-01-01
近来我国北方“雾霾天气”的出现使人们更加关注环境问题，各行各业纷纷自我检视。作为现代社会活动的一种---大型体育赛事的生态环境问题理应再次引起人们的注意。大型体育赛事的生态环境问题是协同进化环境伦理基本原则的要求、是环境道德主要规范的要求、是人类社会文明转型的要求。在生态文明观照下的体育赛事与城市生态环境问题更应该引起全社会的关注。尤其是体育场馆规划建设选址问题、建材的使用及处理问题、城市环境污染问题，其中包括空气污染、水质污染、电磁污染、噪声污染等，只有全社会的关注才能使大型体育赛事为城市发展带来积极效应，避免隐形的生态环境消极效应。%Recently in North China“haze” has made people pay more attention to environmental prob-lems ,all walks of life begin to have the self-examination .As a kind of modern social activities---the ecological environment problem of large scale sports events should aroused people′s attention once a-gain .T he ecological environment problems of large scale sports events are the basic principles of envi-ronmental ethics of collaborative evolution requirements ,the main specifications of environment mor-al ,the requirement of human society civilization .Sports and city ecological environment problems in ecological civilization perspective should arouse the attention of the w hole society .Especially the sports venues location problem ,building materials and its processing issues ,city environmental pollu-tion problem (including air pollution ,water pollution ,electromagnetic pollution ,noise pollution and so on) .Only arousing the attention of the w hole society ,it could make large-scale sports events have a positive effect to city development ,and avoid the negative and invisible effects of ecological environ-ment at the same time .
Institute of Scientific and Technical Information of China (English)
汪靖; 吴志健
2011-01-01
本文通过对传统粒子群算法(PSO)的分析,在GPU(Graphic Process Unit)上设计了基于一般反向学习策略的粒子群算法,并用于求解大规模优化问题.主要思想是通过一般反向学习策略转化当前解空间,提高算法找到最优解的几率,同时使用GPU大量线程并行来加速收敛速度.对比数值实验表明,对于求解大规模高维的优化问题,本文算法比其他智能算法具有更好的精度和更快的收敛速度.%Through an analysis of the traditional particle swarm algorithm, this paper presents particle swarm algorithm based on the generalized opposition-based particle (GOBL) swarm algorithm on Graphic Processing Unit (GPU), and applies it to solve large scale optimization problem.The generalized opposition learning strategies transforms the current solution space to provide more chances of finding better solutions, and GPU in parallel accelerates the convergence rate.Experiment shows that this algorithm has better accuracy and convergence speed than other algorithm for solving large-scale and high-dimensional problems.
Energy Technology Data Exchange (ETDEWEB)
Tolonen, J.; Konttinen, P.; Lund, P. [Helsinki Univ. of Technology, Otaniemi (Finland). Dept. of Engineering Physics and Mathematics
1998-12-31
In this project a large domestic solar heating system was built and a solar district heating system was modelled and simulated. Objectives were to improve the performance and reduce costs of a large-scale solar heating system. As a result of the project the benefit/cost ratio can be increased by 40 % through dimensioning and optimising the system at the designing stage. (orig.)
Testing gravity on Large Scales
Raccanelli Alvise
2013-01-01
We show how it is possible to test general relativity and different models of gravity via Redshift-Space Distortions using forthcoming cosmological galaxy surveys. However, the theoretical models currently used to interpret the data often rely on simplifications that make them not accurate enough for precise measurements. We will discuss improvements to the theoretical modeling at very large scales, including wide-angle and general relativistic corrections; we then show that for wide and deep...
Large-Scale Visual Data Analysis
Johnson, Chris
2014-04-01
Modern high performance computers have speeds measured in petaflops and handle data set sizes measured in terabytes and petabytes. Although these machines offer enormous potential for solving very large-scale realistic computational problems, their effectiveness will hinge upon the ability of human experts to interact with their simulation results and extract useful information. One of the greatest scientific challenges of the 21st century is to effectively understand and make use of the vast amount of information being produced. Visual data analysis will be among our most most important tools in helping to understand such large-scale information. Our research at the Scientific Computing and Imaging (SCI) Institute at the University of Utah has focused on innovative, scalable techniques for large-scale 3D visual data analysis. In this talk, I will present state- of-the-art visualization techniques, including scalable visualization algorithms and software, cluster-based visualization methods and innovate visualization techniques applied to problems in computational science, engineering, and medicine. I will conclude with an outline for a future high performance visualization research challenges and opportunities.
On eigenvectors of multiple eigenvalues obtained in NASTRAN
Pamidi, P. R.; Brown, W. K.
1975-01-01
In the case of nonmultiple eigenvalues, each of the three real eigenvalue extraction methods available in NASTRAN will, for a given type of normalization, give essentially the same eigenvectors, but this is not so in the case of multiple eigenvalues. This discrepancy is explained and illustrated by considering the example of a NASTRAN demonstration problem that has both multiple and nonmultiple eigenvalues.
Growth Limits in Large Scale Networks
DEFF Research Database (Denmark)
Knudsen, Thomas Phillip
the fundamental technological resources in network technologies are analysed for scalability. Here several technological limits to continued growth are presented. The third step involves a survey of major problems in managing large scale networks given the growth of user requirements and the technological...... limitations. The rising complexity of network management with the convergence of communications platforms is shown as problematic for both automatic management feasibility and for manpower resource management. In the fourth step the scope is extended to include the present society with the DDN project as its...... main focus. Here the general perception of the nature and role in society of large scale networks as a fundamental infrastructure is analysed. This analysis focuses on the effects of the technical DDN projects and on the perception of network infrastructure as expressed by key decision makers...
Institute of Scientific and Technical Information of China (English)
张立
2014-01-01
During the production process of the cement vibration of the equipment is large,the dead load of the building is high,the ambient temperature is high and there is some corrosion at the same time,which can easily cause damage to the building structures.As to the design of large-scale cement plant,we discuss the features of structural de-sign in the first part of the article.In the latter part we discuss the treatment of common problems of large-scale cement plant and analysis its causes.%水泥厂厂房在水泥生产过程中受振动冲击大，建筑物荷载高，生产过程温度高且要承受一定的腐蚀，极易对建筑结构造成损坏。该文从大型水泥厂建筑结构设计的角度出发，简述了大型水泥厂结构设计要点，并对大型水泥厂结构设计中的常见问题进行分析并提出相应的解决方案。
Strings and large scale magnetohydrodynamics
Olesen, P
1995-01-01
From computer simulations of magnetohydrodynamics one knows that a turbulent plasma becomes very intermittent, with the magnetic fields concentrated in thin flux tubes. This situation looks very "string-like", so we investigate whether strings could be solutions of the magnetohydrodynamics equations in the limit of infinite conductivity. We find that the induction equation is satisfied, and we discuss the Navier-Stokes equation (without viscosity) with the Lorentz force included. We argue that the string equations (with non-universal maximum velocity) should describe the large scale motion of narrow magnetic flux tubes, because of a large reparametrization (gauge) invariance of the magnetic and electric string fields.
Japanese large-scale interferometers
Kuroda, K; Miyoki, S; Ishizuka, H; Taylor, C T; Yamamoto, K; Miyakawa, O; Fujimoto, M K; Kawamura, S; Takahashi, R; Yamazaki, T; Arai, K; Tatsumi, D; Ueda, A; Fukushima, M; Sato, S; Shintomi, T; Yamamoto, A; Suzuki, T; Saitô, Y; Haruyama, T; Sato, N; Higashi, Y; Uchiyama, T; Tomaru, T; Tsubono, K; Ando, M; Takamori, A; Numata, K; Ueda, K I; Yoneda, H; Nakagawa, K; Musha, M; Mio, N; Moriwaki, S; Somiya, K; Araya, A; Kanda, N; Telada, S; Sasaki, M; Tagoshi, H; Nakamura, T; Tanaka, T; Ohara, K
2002-01-01
The objective of the TAMA 300 interferometer was to develop advanced technologies for kilometre scale interferometers and to observe gravitational wave events in nearby galaxies. It was designed as a power-recycled Fabry-Perot-Michelson interferometer and was intended as a step towards a final interferometer in Japan. The present successful status of TAMA is presented. TAMA forms a basis for LCGT (large-scale cryogenic gravitational wave telescope), a 3 km scale cryogenic interferometer to be built in the Kamioka mine in Japan, implementing cryogenic mirror techniques. The plan of LCGT is schematically described along with its associated R and D.
Algorithms for Large-Scale Astronomical Problems
2013-08-01
steps. First, when calculating how many objects are within distance r of an object pi, we do not consider a ball centered at pi with radius r, but...Ankeny, Ryan Armstrong, Brian O’Shea, Paul M. Ricker, Volker Springel, Joachim Stadel, and Hy Trac. The cosmic code comparison project. Computational
Institute of Scientific and Technical Information of China (English)
凌莉芸; 凌晨
2016-01-01
For a class of eigenvalue complementarity problem with strictly semi-positive tensors,we study the symbolic features of Pareto-eigenvalue.On this based,we obtain the upper and lower bounds of Pareto-eigenvalue for eigenvalue complementarity problem with strictly semi-positive tensors by using the constant definition and operator definition of strictly semi-positive tensors.%针对一类严格半正张量特征值互补问题，研究了其 Pareto-特征值的符号特征。在此基础上，利用严格半正张量的常量定义和算子定义，得到了严格半正张量特征值互补问题的 Pareto-特征值的上下界估计。
Models of large scale structure
Energy Technology Data Exchange (ETDEWEB)
Frenk, C.S. (Physics Dept., Univ. of Durham (UK))
1991-01-01
The ingredients required to construct models of the cosmic large scale structure are discussed. Input from particle physics leads to a considerable simplification by offering concrete proposals for the geometry of the universe, the nature of the dark matter and the primordial fluctuations that seed the growth of structure. The remaining ingredient is the physical interaction that governs dynamical evolution. Empirical evidence provided by an analysis of a redshift survey of IRAS galaxies suggests that gravity is the main agent shaping the large-scale structure. In addition, this survey implies large values of the mean cosmic density, {Omega}> or approx.0.5, and is consistent with a flat geometry if IRAS galaxies are somewhat more clustered than the underlying mass. Together with current limits on the density of baryons from Big Bang nucleosynthesis, this lends support to the idea of a universe dominated by non-baryonic dark matter. Results from cosmological N-body simulations evolved from a variety of initial conditions are reviewed. In particular, neutrino dominated and cold dark matter dominated universes are discussed in detail. Finally, it is shown that apparent periodicities in the redshift distributions in pencil-beam surveys arise frequently from distributions which have no intrinsic periodicity but are clustered on small scales. (orig.).
Cacuci, Dan G.
2015-03-01
This work presents an illustrative application of the second-order adjoint sensitivity analysis methodology (2nd-ASAM) to a paradigm neutron diffusion problem, which is sufficiently simple to admit an exact solution, thereby making transparent the underlying mathematical derivations. The general theory underlying 2nd-ASAM indicates that, for a physical system comprising Nα parameters, the computation of all of the first- and second-order response sensitivities requires (per response) at most (2Nα + 1) "large-scale" computations using the first-level and, respectively, second-level adjoint sensitivity systems (1st-LASS and 2nd-LASS). Very importantly, however, the illustrative application presented in this work shows that the actual number of adjoint computations needed for computing all of the first- and second-order response sensitivities may be significantly less than (2Nα + 1) per response. For this illustrative problem, four "large-scale" adjoint computations sufficed for the complete and exact computations of all 4 first- and 10 distinct second-order derivatives. Furthermore, the construction and solution of the 2nd-LASS requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities. Very significantly, only the sources on the right-sides of the diffusion (differential) operator needed to be modified; the left-side of the differential equations (and hence the "solver" in large-scale practical applications) remained unchanged. All of the first-order relative response sensitivities to the model parameters have significantly large values, of order unity. Also importantly, most of the second-order relative sensitivities are just as large, and some even up to twice as large as the first-order sensitivities. In the illustrative example presented in this work, the second-order sensitivities contribute little to the response variances and covariances. However, they have the
Performance Engineering of the Kernel Polynomial Method on Large-Scale CPU-GPU Systems
Kreutzer, Moritz; Wellein, Gerhard; Pieper, Andreas; Alvermann, Andreas; Fehske, Holger
2014-01-01
The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show that it is possible to decouple the sparse matrix problem posed by KPM from main memory bandwidth both on CPU and GPU. To alleviate the effects of scattered data access we combine loosely coupled outer iterations with tightly coupled block sparse matrix multiple vector operations, which enables pure data streaming. All optimizations are guided by a performance analysis and modelling process that indicates how the computational bottlenecks change with each optimization step. Finally we use the optimized node-level KPM with a hybrid-parallel framework to perform large scale heterogeneous electronic structure calculations for novel topological materials on a pet...
Liu, Tianyu; Du, Xining; Ji, Wei; Xu, X. George; Brown, Forrest B.
2014-06-01
For nuclear reactor analysis such as the neutron eigenvalue calculations, the time consuming Monte Carlo (MC) simulations can be accelerated by using graphics processing units (GPUs). However, traditional MC methods are often history-based, and their performance on GPUs is affected significantly by the thread divergence problem. In this paper we describe the development of a newly designed event-based vectorized MC algorithm for solving the neutron eigenvalue problem. The code was implemented using NVIDIA's Compute Unified Device Architecture (CUDA), and tested on a NVIDIA Tesla M2090 GPU card. We found that although the vectorized MC algorithm greatly reduces the occurrence of thread divergence thus enhancing the warp execution efficiency, the overall simulation speed is roughly ten times slower than the history-based MC code on GPUs. Profiling results suggest that the slow speed is probably due to the memory access latency caused by the large amount of global memory transactions. Possible solutions to improve the code efficiency are discussed.
Desjacques, Vincent; Schmidt, Fabian
2016-01-01
This review presents a comprehensive overview of galaxy bias, that is, the statistical relation between the distribution of galaxies and matter. We focus on large scales where cosmic density fields are quasi-linear. On these scales, the clustering of galaxies can be described by a perturbative bias expansion, and the complicated physics of galaxy formation is absorbed by a finite set of coefficients of the expansion, called bias parameters. The review begins with a pedagogical proof of this very important result, which forms the basis of the rigorous perturbative description of galaxy clustering, under the assumptions of General Relativity and Gaussian, adiabatic initial conditions. Key components of the bias expansion are all leading local gravitational observables, which includes the matter density but also tidal fields and their time derivatives. We hence expand the definition of local bias to encompass all these contributions. This derivation is followed by a presentation of the peak-background split in i...
Large scale biomimetic membrane arrays
DEFF Research Database (Denmark)
Hansen, Jesper Søndergaard; Perry, Mark; Vogel, Jörg
2009-01-01
To establish planar biomimetic membranes across large scale partition aperture arrays, we created a disposable single-use horizontal chamber design that supports combined optical-electrical measurements. Functional lipid bilayers could easily and efficiently be established across CO2 laser micro......-structured 8 x 8 aperture partition arrays with average aperture diameters of 301 +/- 5 mu m. We addressed the electro-physical properties of the lipid bilayers established across the micro-structured scaffold arrays by controllable reconstitution of biotechnological and physiological relevant membrane...... peptides and proteins. Next, we tested the scalability of the biomimetic membrane design by establishing lipid bilayers in rectangular 24 x 24 and hexagonal 24 x 27 aperture arrays, respectively. The results presented show that the design is suitable for further developments of sensitive biosensor assays...
Testing gravity on Large Scales
Directory of Open Access Journals (Sweden)
Raccanelli Alvise
2013-09-01
Full Text Available We show how it is possible to test general relativity and different models of gravity via Redshift-Space Distortions using forthcoming cosmological galaxy surveys. However, the theoretical models currently used to interpret the data often rely on simplifications that make them not accurate enough for precise measurements. We will discuss improvements to the theoretical modeling at very large scales, including wide-angle and general relativistic corrections; we then show that for wide and deep surveys those corrections need to be taken into account if we want to measure the growth of structures at a few percent level, and so perform tests on gravity, without introducing systematic errors. Finally, we report the results of some recent cosmological model tests carried out using those precise models.
Conference on Large Scale Optimization
Hearn, D; Pardalos, P
1994-01-01
On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida. The con ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com puting Research Center, and Argonne National Laboratory. In addition, the NSF sponsored attendance of thirteen graduate students from universities in the United States and abro...
Colloquium: Large scale simulations on GPU clusters
Bernaschi, Massimo; Bisson, Mauro; Fatica, Massimiliano
2015-06-01
Graphics processing units (GPU) are currently used as a cost-effective platform for computer simulations and big-data processing. Large scale applications require that multiple GPUs work together but the efficiency obtained with cluster of GPUs is, at times, sub-optimal because the GPU features are not exploited at their best. We describe how it is possible to achieve an excellent efficiency for applications in statistical mechanics, particle dynamics and networks analysis by using suitable memory access patterns and mechanisms like CUDA streams, profiling tools, etc. Similar concepts and techniques may be applied also to other problems like the solution of Partial Differential Equations.
考虑装卸频率的大规模车辆路径问题研究%Research on large scale vehicle routing problem with handling frequency
Institute of Scientific and Technical Information of China (English)
马汉武; 徐森; 朱维
2011-01-01
Trough analyzing the characteristics of the large scale vehicle routing problem (LSVRP) and the solving difficulties, introduced the concept of handling frequency. Based on the conception, considered LSVRP in a new version, and established a multiple objectives planning model with the handling frequency. Proposed an improved hybrid genetic algorithm to solve the problem efficiently. Finally, introduced the improved hybrid genetic algorithm to solve the problem efficiently. The test proves that the algorithm, with practical value and broad application prospect, may greatly reduce the distribution cost and the handling frequency.%通过分析大规模车辆路径问题的特点和求解难点,从我国的配送实践出发,引入装卸频率的概念,从新的视角认识大规模车辆路径问题,建立了考虑装卸频率的车辆路径优化多目标规划模型,并设计了改进的混合遗传算法进行求解.实验结果表明,该算法能够大幅降低企业配送成本和配送的装卸频率,具有实际参考价值和应用前景.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Institute of Scientific and Technical Information of China (English)
焦宝宝
2016-01-01
在116 Sn原子核壳模型结构下，利用广义辛弱数截断多体空间得到的哈密顿矩阵是一个大型的实对称非正交归一基稀疏矩阵，因此求解大型矩阵的能量特征值和能量特征向量是原子核物理上的一个重要问题。为此，利用重正交化Lanczos法与Cholesky分解法和Elementary transformation法相结合的方法，实现了用内存较小的计算机求解大型实对称非正交归一基稀疏矩阵的特征值和特征向量。用这种方法计算小型矩阵得到的特征值和精确值符合得较好，且运用这个方法计算了116Sn壳模型截断后的大型非正交归一基稀疏矩阵的能量特征值，得到的原子核低态能量与实验测量能量相吻合，计算结果表明Lanczos法在Matlab编程和大型壳模型计算中的精确性和可行性。此方法也有助于求解一些中质核或者重核的低态能量，同时也有利于用内存稍大的计算机求解更大的非正交归一基矩阵的特征值问题。%Using shell model to calculate the nuclear systems in a large model space is an important method in the field of nuclear physics. On the basis of the nuclear shell model, a large symmetric non-orthonormal sparse Hamiltonian matrix is generated when adopting the generalized seniority method to truncate the many-body space. Calculating the energy eigenvalues and energy eigenvectors of the large symmetric non-orthonormal sparse Hamiltonian matrix is of indispensable steps before energies of nucleus are further calculated. In the mean time, some low-lying energy eigenvalues are always the focus of attention on the occasion of large scale shell model calculation. In this paper, by combining reorthogonalization Lanczos method with Cholesky decomposition method and Elementary transformation method, converting the generalized eigenvalue problems into the standard eigenvalue problems, and transforming the large standard eigenvalue problems into the small standard
On the sensitivities of multiple eigenvalues
DEFF Research Database (Denmark)
Gravesen, Jens; Evgrafov, Anton; Nguyen, Dang Manh
2011-01-01
We consider the generalized symmetric eigenvalue problem where matrices depend smoothly on a parameter. It is well known that in general individual eigenvalues, when sorted in accordance with the usual ordering on the real line, do not depend smoothly on the parameter. Nevertheless, symmetric...... a shape of a vibrating membrane with a smallest perimeter and with prescribed four lowest eigenvalues, only two of which have algebraic multiplicity one....
Institute of Scientific and Technical Information of China (English)
胡亚萍; 解惠青
2012-01-01
A new method is presented for synchro calculation of eigenpairs and their derivatives of large-scale eigenvalue problems based on Lanczos method. The convergence theory of the proposed method is established. Eigenpairs and their derivatives are computed simultaneously. The systems of equations that are solved for eigenvector derivatives can be greatly reduced from the original matrix size, thus the efficiency of computing eigenvector derivatives is improved. Numerical results show the efficiency.
Directory of Open Access Journals (Sweden)
Steinhaus Thomas
2007-01-01
Full Text Available A review of research into the burning behavior of large pool fires and fuel spill fires is presented. The features which distinguish such fires from smaller pool fires are mainly associated with the fire dynamics at low source Froude numbers and the radiative interaction with the fire source. In hydrocarbon fires, higher soot levels at increased diameters result in radiation blockage effects around the perimeter of large fire plumes; this yields lower emissive powers and a drastic reduction in the radiative loss fraction; whilst there are simplifying factors with these phenomena, arising from the fact that soot yield can saturate, there are other complications deriving from the intermittency of the behavior, with luminous regions of efficient combustion appearing randomly in the outer surface of the fire according the turbulent fluctuations in the fire plume. Knowledge of the fluid flow instabilities, which lead to the formation of large eddies, is also key to understanding the behavior of large-scale fires. Here modeling tools can be effectively exploited in order to investigate the fluid flow phenomena, including RANS- and LES-based computational fluid dynamics codes. The latter are well-suited to representation of the turbulent motions, but a number of challenges remain with their practical application. Massively-parallel computational resources are likely to be necessary in order to be able to adequately address the complex coupled phenomena to the level of detail that is necessary.
Handbook of Large-Scale Random Networks
Bollobas, Bela; Miklos, Dezso
2008-01-01
Covers various aspects of large-scale networks, including mathematical foundations and rigorous results of random graph theory, modeling and computational aspects of large-scale networks, as well as areas in physics, biology, neuroscience, sociology and technical areas
Constructing sites on a large scale
DEFF Research Database (Denmark)
Braae, Ellen Marie; Tietjen, Anne
2011-01-01
for setting the design brief in a large scale urban landscape in Norway, the Jaeren region around the city of Stavanger. In this paper, we first outline the methodological challenges and then present and discuss the proposed method based on our teaching experiences. On this basis, we discuss aspects...... within the development of our urban landscapes. At the same time, urban and landscape designers are confronted with new methodological problems. Within a strategic transformation perspective, the formulation of the design problem or brief becomes an integrated part of the design process. This paper...... discusses new design (education) methods based on a relational concept of urban sites and design processes. Within this logic site survey is not simply a pre-design activity nor is it a question of comprehensive analysis. Site survey is an integrated part of the design process. By means of active site...
Conundrum of the Large Scale Streaming
Malm, T M
1999-01-01
The etiology of the large scale peculiar velocity (large scale streaming motion) of clusters would increasingly seem more tenuous, within the context of the gravitational instability hypothesis. Are there any alternative testable models possibly accounting for such large scale streaming of clusters?
Mathematics Mechanization in the Eigenvalue Problem of Application%数学机械化方法在特征值问题中的应用
Institute of Scientific and Technical Information of China (English)
白根柱; 乌仁高娃; 冀爱萍
2011-01-01
Mathematics mechanization theory and method will be applied to solve to algebraic eigenvalue problem which was developed by our country mathematician who called WU Wenjun in the 1970 s and the modern mathematics view was reflected in mathematics teaching.It will help student to improve the mathematical thinking level,development innovation consciousness and practical ability.%将我国数学家吴文俊在二十世纪七十年代倡导的并发展起来的数学机械化理论和方法应用到代数特征值问题中,把现代的数学观点反映到数学教学中来,这对于提高学生的数学思维层次,发展创新意识和实践能力会有一定的帮助.
Distribution probability of large-scale landslides in central Nepal
Timilsina, Manita; Bhandary, Netra P.; Dahal, Ranjan Kumar; Yatabe, Ryuichi
2014-12-01
Large-scale landslides in the Himalaya are defined as huge, deep-seated landslide masses that occurred in the geological past. They are widely distributed in the Nepal Himalaya. The steep topography and high local relief provide high potential for such failures, whereas the dynamic geology and adverse climatic conditions play a key role in the occurrence and reactivation of such landslides. The major geoscientific problems related with such large-scale landslides are 1) difficulties in their identification and delineation, 2) sources of small-scale failures, and 3) reactivation. Only a few scientific publications have been published concerning large-scale landslides in Nepal. In this context, the identification and quantification of large-scale landslides and their potential distribution are crucial. Therefore, this study explores the distribution of large-scale landslides in the Lesser Himalaya. It provides simple guidelines to identify large-scale landslides based on their typical characteristics and using a 3D schematic diagram. Based on the spatial distribution of landslides, geomorphological/geological parameters and logistic regression, an equation of large-scale landslide distribution is also derived. The equation is validated by applying it to another area. For the new area, the area under the receiver operating curve of the landslide distribution probability in the new area is 0.699, and a distribution probability value could explain > 65% of existing landslides. Therefore, the regression equation can be applied to areas of the Lesser Himalaya of central Nepal with similar geological and geomorphological conditions.
Accelerated large-scale multiple sequence alignment
Directory of Open Access Journals (Sweden)
Lloyd Scott
2011-12-01
Full Text Available Abstract Background Multiple sequence alignment (MSA is a fundamental analysis method used in bioinformatics and many comparative genomic applications. Prior MSA acceleration attempts with reconfigurable computing have only addressed the first stage of progressive alignment and consequently exhibit performance limitations according to Amdahl's Law. This work is the first known to accelerate the third stage of progressive alignment on reconfigurable hardware. Results We reduce subgroups of aligned sequences into discrete profiles before they are pairwise aligned on the accelerator. Using an FPGA accelerator, an overall speedup of up to 150 has been demonstrated on a large data set when compared to a 2.4 GHz Core2 processor. Conclusions Our parallel algorithm and architecture accelerates large-scale MSA with reconfigurable computing and allows researchers to solve the larger problems that confront biologists today. Program source is available from http://dna.cs.byu.edu/msa/.
Hybrid Heuristic Algorithm for the Large-scale VRP Optimizaton Problem%混合超启发式法求解大规模VRP的优化研究
Institute of Scientific and Technical Information of China (English)
杜玲玲
2011-01-01
Vehicle routing is a NP-complete problem. It is of theoretical and practical significance to study good quality heuristic algorithm for solving the vehicle routing problem. In order to solve the vehicle routing problem with capacity constraint, the paper presents a new and effective hybrid rnetaheuristic algorithm which combines the strengths of the well-known nearest neighbor search and tabu search. Nearest neighbor search is used to construet initial routes in the first stage, and then tabu search is utilized to optimize the intra-route and the inter-route in the second stage. The computational experiments are carried out on a standard benchmark and a real dataset with 6772 tobacco customers. The results demonstrate that the suggested method is highly competitive in reducing the total distance. It provides a new idea to solve the large scale vehicle routing problem.%车辆路径是一类NP(non-deteministic polynomial)完全问题,研究解决车辆路径问题的高质量启发式算法有着重要理论价值和现实意义.提出一种将最近邻搜索法和禁忌搜索法优势相结合的混合超启发式算法,用来解决带容量约束的车辆路径问题.先利用最近邻搜索法构建初步路线,再利用禁忌搜索法对内部线路和互跨线路进行优化.通过对基于标准数据集和6 772个烟草客户真实数据集进行应用验证,新算法在减少线路的总路程上具有显著效果,为大规模车辆路径问题的求解提供了新的求解思路.
Institute of Scientific and Technical Information of China (English)
陈小潘; 党兰学; 孔云峰
2013-01-01
校车调度问题（SBSP）是通过调度使一辆校车服务完一个学校后继续服务其他学校，以减少一个地区所需的校车总数，进而降低校车采购成本和运营成本。目前的SBSP求解方法是将其转化为指派问题或运输问题，使用混合整型规划算法或者简单启发式算法进行求解，但求解性能有局限。本文在单校校车路径规划的基础上，将单校路径抽象为虚拟站点，进而将SBSP转换为带有时间窗的车辆路径问题（VRPTW），设计元启发算法进行求解。使用构造启发式算法获得初始解后，在模拟退火算法框架中通过典型的局部搜索算子搜索邻域解，逐步改善求解质量。搜索算子包括单点移动、两点交换、2-OPT和Cross-Exchange。迭代优化过程中以校车路径数为主要目标，路径长度为次要目标。为避免邻域搜索陷入局部最优，算法以一定的概率接受部分使路径长度增加的解。15个案例实验验证了本算法的有效性，与现有算法相比，能够获得更好的优化目标，适用于大规模的校车调度。%Given school bus trips for each school in a school district, if a school bus can serve multiple trips, the efficiency of school bus service can be improved in terms of the number of buses needed and the total travel cost. The school bus scheduling problem (SBSP), a class of school bus routing problem (SBRP), is concerned with assigning a fleet of buses to serve all the given trips and aims to get optimal bus schedules. Each school has its xed time window within which school bus must arrive at the destination school of the trip. In existing litera-tures, SBSP is usually formulated as a transportation problem (TP) or an assignment problem (AP). However, many existing algorithms for vehicle routing problem (VRP) have not been fully utilized to solve the problem ef-fectively. This paper proposes a meta-heuristic algorithm for large-scale SBSP
用Lanczos算法进行周期结构固有特性分析的研究%The Analysis of Eigenvalue Problem of Periodic Structures byLanczos Method
Institute of Scientific and Technical Information of China (English)
王翔
2000-01-01
In the FEM dynamic analysis of large flexible spacestructure (LFSS), the solution of frequencies and corresponding modelsis actually a general eigenvalue and eigenvector problem. In thisarticle, Lanczos method was applied to this type of problem. Innumerical examples, the convergency, accuracy-time relation andmulti-root problem of Lanczos method for beam structure were analyzed.Considering the characteristic of the stiffness matrix of beam structure, theauthor also present some ideas to improve Lanczos method byiteration method.
Computing the eigenvalues and eigenvectors of a fuzzy matrix
Directory of Open Access Journals (Sweden)
A. Kumar
2012-08-01
Full Text Available Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.$
1988-04-01
Moreover, if e2 > 61 and we further assume (f.1) f(x,y) is locally Lipschitz continuous in y then inequalities (1.37) and (1.38) are strict. 17 Proof MI...Univ. Math. J. 20 (1971), 983-996.[I 124 18. J. A. Hempel, Superlinear variational boundary value problems and nonuniqueness , Thesis, University of
Large Scale Computations in Air Pollution Modelling
DEFF Research Database (Denmark)
Zlatev, Z.; Brandt, J.; Builtjes, P. J. H.
Proceedings of the NATO Advanced Research Workshop on Large Scale Computations in Air Pollution Modelling, Sofia, Bulgaria, 6-10 July 1998......Proceedings of the NATO Advanced Research Workshop on Large Scale Computations in Air Pollution Modelling, Sofia, Bulgaria, 6-10 July 1998...
Large Scale Computations in Air Pollution Modelling
DEFF Research Database (Denmark)
Zlatev, Z.; Brandt, J.; Builtjes, P. J. H.
Proceedings of the NATO Advanced Research Workshop on Large Scale Computations in Air Pollution Modelling, Sofia, Bulgaria, 6-10 July 1998......Proceedings of the NATO Advanced Research Workshop on Large Scale Computations in Air Pollution Modelling, Sofia, Bulgaria, 6-10 July 1998...
[Issues of large scale tissue culture of medicinal plant].
Lv, Dong-Mei; Yuan, Yuan; Zhan, Zhi-Lai
2014-09-01
In order to increase the yield and quality of the medicinal plant and enhance the competitive power of industry of medicinal plant in our country, this paper analyzed the status, problem and countermeasure of the tissue culture of medicinal plant on large scale. Although the biotechnology is one of the most efficient and promising means in production of medicinal plant, it still has problems such as stability of the material, safety of the transgenic medicinal plant and optimization of cultured condition. Establishing perfect evaluation system according to the characteristic of the medicinal plant is the key measures to assure the sustainable development of the tissue culture of medicinal plant on large scale.
Inverse problems of generalized eigenvalue for H-(anti) symmetric mtrices%H-(反)对称矩阵的广义特征值反问题
Institute of Scientific and Technical Information of China (English)
燕列雅; 任学明; 王艳
2012-01-01
讨论H矩阵的性质,给出H-对称矩阵和H-反对称矩阵的结构,证明若x是H-对称矩阵或H-反对称矩阵A -λB的特征向量,则x是H-对称向量或H-反对称向量,或者x可以由H-对称向量及H-反对称向量线性表示,并根据A-λB的特征向量的上述特点,得到H-对称矩阵和H-反对称矩阵的广义特征值反问题AX=BXA解的表达式.%Properties of H-matrices were discussed, the structures of H-symmetric and H-antisymmetric matrices were given, and it was proven that when x was an eigenvector of H-symmetric matrices or H-antisymmetric matrices A-λB, x would be either an H-symmetric vector, or H-antisymmetric vector, or x could be expressed by linear combination of H-symmetric vector with H-antisymmetric vector. Based on a-bove-mentioned feature of eigenvector of A-λB, the expression of solution to inverse problem AX=BXA of generalized eigenvalue of H-symmetric matrices and H-antisymmetric matrices were obtained.
Large scale network-centric distributed systems
Sarbazi-Azad, Hamid
2014-01-01
A highly accessible reference offering a broad range of topics and insights on large scale network-centric distributed systems Evolving from the fields of high-performance computing and networking, large scale network-centric distributed systems continues to grow as one of the most important topics in computing and communication and many interdisciplinary areas. Dealing with both wired and wireless networks, this book focuses on the design and performance issues of such systems. Large Scale Network-Centric Distributed Systems provides in-depth coverage ranging from ground-level hardware issu
Network robustness under large-scale attacks
Zhou, Qing; Liu, Ruifang; Cui, Shuguang
2014-01-01
Network Robustness under Large-Scale Attacks provides the analysis of network robustness under attacks, with a focus on large-scale correlated physical attacks. The book begins with a thorough overview of the latest research and techniques to analyze the network responses to different types of attacks over various network topologies and connection models. It then introduces a new large-scale physical attack model coined as area attack, under which a new network robustness measure is introduced and applied to study the network responses. With this book, readers will learn the necessary tools to evaluate how a complex network responds to random and possibly correlated attacks.
Transmission eigenvalues for operators with constant coefficients
Hitrik, Michael; Ola, Petri; Päivärinta, Lassi
2010-01-01
In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\\ge 2$ with constant real coefficients. Under suitable growth conditions on the symbol of the operator and the perturbation, we show the discreteness of the set of transmission eigenvalues and derive sufficient conditions on the existence of transmission eigenvalues. We apply these techniques to the case of the biharmonic operator and the Dirac system. In the hypoelliptic case we present a connection to scattering theory.
Large scale mechanical metamaterials as seismic shields
Miniaci, Marco; Krushynska, Anastasiia; Bosia, Federico; Pugno, Nicola M.
2016-08-01
Earthquakes represent one of the most catastrophic natural events affecting mankind. At present, a universally accepted risk mitigation strategy for seismic events remains to be proposed. Most approaches are based on vibration isolation of structures rather than on the remote shielding of incoming waves. In this work, we propose a novel approach to the problem and discuss the feasibility of a passive isolation strategy for seismic waves based on large-scale mechanical metamaterials, including for the first time numerical analysis of both surface and guided waves, soil dissipation effects, and adopting a full 3D simulations. The study focuses on realistic structures that can be effective in frequency ranges of interest for seismic waves, and optimal design criteria are provided, exploring different metamaterial configurations, combining phononic crystals and locally resonant structures and different ranges of mechanical properties. Dispersion analysis and full-scale 3D transient wave transmission simulations are carried out on finite size systems to assess the seismic wave amplitude attenuation in realistic conditions. Results reveal that both surface and bulk seismic waves can be considerably attenuated, making this strategy viable for the protection of civil structures against seismic risk. The proposed remote shielding approach could open up new perspectives in the field of seismology and in related areas of low-frequency vibration damping or blast protection.
Management of large-scale multimedia conferencing
Cidon, Israel; Nachum, Youval
1998-12-01
The goal of this work is to explore management strategies and algorithms for large-scale multimedia conferencing over a communication network. Since the use of multimedia conferencing is still limited, the management of such systems has not yet been studied in depth. A well organized and human friendly multimedia conference management should utilize efficiently and fairly its limited resources as well as take into account the requirements of the conference participants. The ability of the management to enforce fair policies and to quickly take into account the participants preferences may even lead to a conference environment that is more pleasant and more effective than a similar face to face meeting. We suggest several principles for defining and solving resource sharing problems in this context. The conference resources which are addressed in this paper are the bandwidth (conference network capacity), time (participants' scheduling) and limitations of audio and visual equipment. The participants' requirements for these resources are defined and translated in terms of Quality of Service requirements and the fairness criteria.
Large-scale wind turbine structures
Spera, David A.
1988-01-01
The purpose of this presentation is to show how structural technology was applied in the design of modern wind turbines, which were recently brought to an advanced stage of development as sources of renewable power. Wind turbine structures present many difficult problems because they are relatively slender and flexible; subject to vibration and aeroelastic instabilities; acted upon by loads which are often nondeterministic; operated continuously with little maintenance in all weather; and dominated by life-cycle cost considerations. Progress in horizontal-axis wind turbines (HAWT) development was paced by progress in the understanding of structural loads, modeling of structural dynamic response, and designing of innovative structural response. During the past 15 years a series of large HAWTs was developed. This has culminated in the recent completion of the world's largest operating wind turbine, the 3.2 MW Mod-5B power plane installed on the island of Oahu, Hawaii. Some of the applications of structures technology to wind turbine will be illustrated by referring to the Mod-5B design. First, a video overview will be presented to provide familiarization with the Mod-5B project and the important components of the wind turbine system. Next, the structural requirements for large-scale wind turbines will be discussed, emphasizing the difficult fatigue-life requirements. Finally, the procedures used to design the structure will be presented, including the use of the fracture mechanics approach for determining allowable fatigue stresses.
Large Scale Metal Additive Techniques Review
Energy Technology Data Exchange (ETDEWEB)
Nycz, Andrzej [ORNL; Adediran, Adeola I [ORNL; Noakes, Mark W [ORNL; Love, Lonnie J [ORNL
2016-01-01
In recent years additive manufacturing made long strides toward becoming a main stream production technology. Particularly strong progress has been made in large-scale polymer deposition. However, large scale metal additive has not yet reached parity with large scale polymer. This paper is a review study of the metal additive techniques in the context of building large structures. Current commercial devices are capable of printing metal parts on the order of several cubic feet compared to hundreds of cubic feet for the polymer side. In order to follow the polymer progress path several factors are considered: potential to scale, economy, environment friendliness, material properties, feedstock availability, robustness of the process, quality and accuracy, potential for defects, and post processing as well as potential applications. This paper focuses on current state of art of large scale metal additive technology with a focus on expanding the geometric limits.
Dual Decomposition for Large-Scale Power Balancing
DEFF Research Database (Denmark)
Halvgaard, Rasmus; Jørgensen, John Bagterp; Vandenberghe, Lieven
2013-01-01
Dual decomposition is applied to power balancing of exible thermal storage units. The centralized large-scale problem is decomposed into smaller subproblems and solved locallyby each unit in the Smart Grid. Convergence is achieved by coordinating the units consumption through a negotiation...
Sensitivity technologies for large scale simulation.
Energy Technology Data Exchange (ETDEWEB)
Collis, Samuel Scott; Bartlett, Roscoe Ainsworth; Smith, Thomas Michael; Heinkenschloss, Matthias (Rice University, Houston, TX); Wilcox, Lucas C. (Brown University, Providence, RI); Hill, Judith C. (Carnegie Mellon University, Pittsburgh, PA); Ghattas, Omar (Carnegie Mellon University, Pittsburgh, PA); Berggren, Martin Olof (University of UppSala, Sweden); Akcelik, Volkan (Carnegie Mellon University, Pittsburgh, PA); Ober, Curtis Curry; van Bloemen Waanders, Bart Gustaaf; Keiter, Eric Richard
2005-01-01
Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification,reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective through the development of hybrid automatic differentiation tools, standard linear algebra interfaces for numerical algorithms, time domain decomposition algorithms and two level Newton methods. We attempt to accomplish the second goal by presenting the results of several case studies in which direct sensitivities and adjoint methods have been effectively applied, in addition to an investigation of h-p adaptivity using adjoint based a posteriori error estimation. A mathematical overview is provided of direct sensitivities and adjoint methods for both steady state and transient simulations. Two case studies are presented to demonstrate the utility of these methods. A direct sensitivity method is implemented to solve a source inversion problem for steady state internal flows subject to convection diffusion. Real time performance is achieved using novel decomposition into offline and online calculations. Adjoint methods are used to reconstruct initial conditions of a contamination event in an external flow. We demonstrate an adjoint based transient solution. In addition, we investigated time domain decomposition algorithms in an attempt to improve the efficiency of transient simulations. Because derivative calculations are at the root of sensitivity calculations, we have developed hybrid automatic differentiation methods and implemented this approach for shape optimization for gas dynamics using the Euler equations. The hybrid automatic differentiation method was applied to a first
Sensitivity technologies for large scale simulation.
Energy Technology Data Exchange (ETDEWEB)
Collis, Samuel Scott; Bartlett, Roscoe Ainsworth; Smith, Thomas Michael; Heinkenschloss, Matthias (Rice University, Houston, TX); Wilcox, Lucas C. (Brown University, Providence, RI); Hill, Judith C. (Carnegie Mellon University, Pittsburgh, PA); Ghattas, Omar (Carnegie Mellon University, Pittsburgh, PA); Berggren, Martin Olof (University of UppSala, Sweden); Akcelik, Volkan (Carnegie Mellon University, Pittsburgh, PA); Ober, Curtis Curry; van Bloemen Waanders, Bart Gustaaf; Keiter, Eric Richard
2005-01-01
Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification,reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective through the development of hybrid automatic differentiation tools, standard linear algebra interfaces for numerical algorithms, time domain decomposition algorithms and two level Newton methods. We attempt to accomplish the second goal by presenting the results of several case studies in which direct sensitivities and adjoint methods have been effectively applied, in addition to an investigation of h-p adaptivity using adjoint based a posteriori error estimation. A mathematical overview is provided of direct sensitivities and adjoint methods for both steady state and transient simulations. Two case studies are presented to demonstrate the utility of these methods. A direct sensitivity method is implemented to solve a source inversion problem for steady state internal flows subject to convection diffusion. Real time performance is achieved using novel decomposition into offline and online calculations. Adjoint methods are used to reconstruct initial conditions of a contamination event in an external flow. We demonstrate an adjoint based transient solution. In addition, we investigated time domain decomposition algorithms in an attempt to improve the efficiency of transient simulations. Because derivative calculations are at the root of sensitivity calculations, we have developed hybrid automatic differentiation methods and implemented this approach for shape optimization for gas dynamics using the Euler equations. The hybrid automatic differentiation method was applied to a first
Generation Expansion Planning Considering Integrating Large-scale Wind Generation
DEFF Research Database (Denmark)
Zhang, Chunyu; Ding, Yi; Østergaard, Jacob
2013-01-01
Generation expansion planning (GEP) is the problem of finding the optimal strategy to plan the Construction of new generation while satisfying technical and economical constraints. In the deregulated and competitive environment, large-scale integration of wind generation (WG) in power system has...... necessitated the inclusion of more innovative and sophisticated approaches in power system investment planning. A bi-level generation expansion planning approach considering large-scale wind generation was proposed in this paper. The first phase is investment decision, while the second phase is production...
Fast paths in large-scale dynamic road networks
Nannicini, Giacomo; Barbier, Gilles; Krob, Daniel; Liberti, Leo
2007-01-01
Efficiently computing fast paths in large scale dynamic road networks (where dynamic traffic information is known over a part of the network) is a practical problem faced by several traffic information service providers who wish to offer a realistic fast path computation to GPS terminal enabled vehicles. The heuristic solution method we propose is based on a highway hierarchy-based shortest path algorithm for static large-scale networks; we maintain a static highway hierarchy and perform each query on the dynamically evaluated network.
Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Jacobi - Davidson, and FEAST), establishing the competitiveness of my methods . Graduate School Form 30 Updated 1/15/2015 PURDUE UNIVERSITY GRADUATE...LOBPCG, Jacobi -Davidson, and FEAST), establishing the competitiveness of our methods . 1 1 INTRODUCTION Many applications in science and engineering give...though SLEPc’s Jacobi -Davidson is the fastest method ; it is roughly twice as fast as TraceMin-Davidson. However, since it uses a block size 90 of 1
Institute of Scientific and Technical Information of China (English)
秦佩华
2012-01-01
Elliptic eigenvalue problems in nonsmooth domain by using of discontinuous galerkin (DG) methods were analyzed. From many numerical results we find that for elliptic eigenvalue problems in nonsmooth domain DG methods provide better approximation than other methods, such as conforming or nonconforming finite element method, and finite element defect correction scheme.%本文针对非光滑区域上椭圆特征值特征值问题利用间断有限元方法(DG)近似.利用大量的数值算例发现,DG方法对非光滑区域(凹角,裂缝等问题)上Laplace特征值问题的近似比协调有限元、非协调元(如C-R元),甚至比有限元校正格式有着更好的效果.
Eigenvalues of singular differential operators by finite difference methods. I.
Baxley, J. V.
1972-01-01
Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.
One-dimensional adhesion model for large scale structures
Directory of Open Access Journals (Sweden)
Kayyunnapara Thomas Joseph
2010-05-01
Full Text Available We discuss initial value problems and initial boundary value problems for some systems of partial differential equations appearing in the modelling for the large scale structure formation in the universe. We restrict the initial data to be bounded measurable and locally bounded variation function and use Volpert product to justify the product which appear in the equation. For more general initial data in the class of generalized functions of Colombeau, we construct the solution in the sense of association.
Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.
2009-08-01
A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Commun. 179 (2008) 685-693]. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials, a 3D-model of a hydrogen atom in a homogeneous magnetic field and a hydrogen atom on a three-dimensional sphere. Program summaryProgram title: ODPEVP Catalogue identifier: AEDV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3001 No. of bytes in distributed program, including test data, etc.: 24 195 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on the number and order of finite
Accelerating sustainability in large-scale facilities
Marina Giampietro
2011-01-01
Scientific research centres and large-scale facilities are intrinsically energy intensive, but how can big science improve its energy management and eventually contribute to the environmental cause with new cleantech? CERN’s commitment to providing tangible answers to these questions was sealed in the first workshop on energy management for large scale scientific infrastructures held in Lund, Sweden, on the 13-14 October. Participants at the energy management for large scale scientific infrastructures workshop. The workshop, co-organised with the European Spallation Source (ESS) and the European Association of National Research Facilities (ERF), tackled a recognised need for addressing energy issues in relation with science and technology policies. It brought together more than 150 representatives of Research Infrastrutures (RIs) and energy experts from Europe and North America. “Without compromising our scientific projects, we can ...
Large-Scale Analysis of Art Proportions
DEFF Research Database (Denmark)
Jensen, Karl Kristoffer
2014-01-01
While literature often tries to impute mathematical constants into art, this large-scale study (11 databases of paintings and photos, around 200.000 items) shows a different truth. The analysis, consisting of the width/height proportions, shows a value of rarely if ever one (square) and with majo......While literature often tries to impute mathematical constants into art, this large-scale study (11 databases of paintings and photos, around 200.000 items) shows a different truth. The analysis, consisting of the width/height proportions, shows a value of rarely if ever one (square...
Large-scale Complex IT Systems
Sommerville, Ian; Calinescu, Radu; Keen, Justin; Kelly, Tim; Kwiatkowska, Marta; McDermid, John; Paige, Richard
2011-01-01
This paper explores the issues around the construction of large-scale complex systems which are built as 'systems of systems' and suggests that there are fundamental reasons, derived from the inherent complexity in these systems, why our current software engineering methods and techniques cannot be scaled up to cope with the engineering challenges of constructing such systems. It then goes on to propose a research and education agenda for software engineering that identifies the major challenges and issues in the development of large-scale complex, software-intensive systems. Central to this is the notion that we cannot separate software from the socio-technical environment in which it is used.
Topological Routing in Large-Scale Networks
DEFF Research Database (Denmark)
Pedersen, Jens Myrup; Knudsen, Thomas Phillip; Madsen, Ole Brun
2004-01-01
A new routing scheme, Topological Routing, for large-scale networks is proposed. It allows for efficient routing without large routing tables as known from traditional routing schemes. It presupposes a certain level of order in the networks, known from Structural QoS. The main issues in applying...... Topological Routing to large-scale networks are discussed. Hierarchical extensions are presented along with schemes for shortest path routing, fault handling and path restoration. Further reserach in the area is discussed and perspectives on the prerequisites for practical deployment of Topological Routing...
Topological Routing in Large-Scale Networks
DEFF Research Database (Denmark)
Pedersen, Jens Myrup; Knudsen, Thomas Phillip; Madsen, Ole Brun
A new routing scheme, Topological Routing, for large-scale networks is proposed. It allows for efficient routing without large routing tables as known from traditional routing schemes. It presupposes a certain level of order in the networks, known from Structural QoS. The main issues in applying...... Topological Routing to large-scale networks are discussed. Hierarchical extensions are presented along with schemes for shortest path routing, fault handling and path restoration. Further reserach in the area is discussed and perspectives on the prerequisites for practical deployment of Topological Routing...
Large scale topic modeling made practical
DEFF Research Database (Denmark)
Wahlgreen, Bjarne Ørum; Hansen, Lars Kai
2011-01-01
Topic models are of broad interest. They can be used for query expansion and result structuring in information retrieval and as an important component in services such as recommender systems and user adaptive advertising. In large scale applications both the size of the database (number of docume......Topic models are of broad interest. They can be used for query expansion and result structuring in information retrieval and as an important component in services such as recommender systems and user adaptive advertising. In large scale applications both the size of the database (number...... topics at par with a much larger case specific vocabulary....
Optimization of Survivability Analysis for Large-Scale Engineering Networks
Poroseva, S V
2012-01-01
Engineering networks fall into the category of large-scale networks with heterogeneous nodes such as sources and sinks. The survivability analysis of such networks requires the analysis of the connectivity of the network components for every possible combination of faults to determine a network response to each combination of faults. From the computational complexity point of view, the problem belongs to the class of exponential time problems at least. Partially, the problem complexity can be reduced by mapping the initial topology of a complex large-scale network with multiple sources and multiple sinks onto a set of smaller sub-topologies with multiple sources and a single sink connected to the network of sources by a single link. In this paper, the mapping procedure is applied to the Florida power grid.
Large-scale multimedia modeling applications
Energy Technology Data Exchange (ETDEWEB)
Droppo, J.G. Jr.; Buck, J.W.; Whelan, G.; Strenge, D.L.; Castleton, K.J.; Gelston, G.M.
1995-08-01
Over the past decade, the US Department of Energy (DOE) and other agencies have faced increasing scrutiny for a wide range of environmental issues related to past and current practices. A number of large-scale applications have been undertaken that required analysis of large numbers of potential environmental issues over a wide range of environmental conditions and contaminants. Several of these applications, referred to here as large-scale applications, have addressed long-term public health risks using a holistic approach for assessing impacts from potential waterborne and airborne transport pathways. Multimedia models such as the Multimedia Environmental Pollutant Assessment System (MEPAS) were designed for use in such applications. MEPAS integrates radioactive and hazardous contaminants impact computations for major exposure routes via air, surface water, ground water, and overland flow transport. A number of large-scale applications of MEPAS have been conducted to assess various endpoints for environmental and human health impacts. These applications are described in terms of lessons learned in the development of an effective approach for large-scale applications.
Evaluating Large-Scale Interactive Radio Programmes
Potter, Charles; Naidoo, Gordon
2009-01-01
This article focuses on the challenges involved in conducting evaluations of interactive radio programmes in South Africa with large numbers of schools, teachers, and learners. It focuses on the role such large-scale evaluation has played during the South African radio learning programme's development stage, as well as during its subsequent…
Configuration management in large scale infrastructure development
Rijn, T.P.J. van; Belt, H. van de; Los, R.H.
2000-01-01
Large Scale Infrastructure (LSI) development projects such as the construction of roads, rail-ways and other civil engineering (water)works is tendered differently today than a decade ago. Traditional workflow requested quotes from construction companies for construction works where the works to be
Large-scale perspective as a challenge
Plomp, M.G.A.
2012-01-01
1. Scale forms a challenge for chain researchers: when exactly is something ‘large-scale’? What are the underlying factors (e.g. number of parties, data, objects in the chain, complexity) that determine this? It appears to be a continuum between small- and large-scale, where positioning on that cont
DEFF Research Database (Denmark)
Arler, Finn
2006-01-01
, which kind of attitude is appropriate when dealing with large-scale changes like these from an ethical point of view. Three kinds of approaches are discussed: Aldo Leopold's mountain thinking, the neoclassical economists' approach, and finally the so-called Concentric Circle Theories approach...
Inflation, large scale structure and particle physics
Indian Academy of Sciences (India)
S F King
2004-02-01
We review experimental and theoretical developments in inflation and its application to structure formation, including the curvation idea. We then discuss a particle physics model of supersymmetric hybrid inflation at the intermediate scale in which the Higgs scalar field is responsible for large scale structure, show how such a theory is completely natural in the framework extra dimensions with an intermediate string scale.
Eigenvector derivatives of repeated eigenvalues using singular value decomposition
Lim, Kyong B.; Juang, Jer-Nan; Ghaemmaghami, Peiman
1989-01-01
An explicit formula is obtained for the first-order eigenvector derivative that corresponds to the eigenvector of a repeated eigenvalue, in the case of the nonself-adjoint eigenvalue problem. This method applies to the class of nondefective problems whose first eigenvalue derivatives of the repeated eigenvalues are distinct. A singular-value decomposition approach is used to compute four requisite bases for eigenspaces, as well as to keep track of the dimensions of state variables and the conditioning of the state equations.
Extremal eigenvalues of measure differential equations with fixed variation
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely continuous.By taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth functionals.These results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.
Simplicity of extremal eigenvalues of the Klein-Gordon equation
Koppen, Mario; Winklmeier, Monika
2010-01-01
We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that these extremal eigenvalues are simple and possess strictly positive eigenfunctions. Examples of electric potentials satisfying these assumptions are given.
Systematic Literature Review of Agile Scalability for Large Scale Projects
Directory of Open Access Journals (Sweden)
Hina saeeda
2015-09-01
Full Text Available In new methods, “agile” has come out as the top approach in software industry for the development of the soft wares. With different shapes agile is applied for handling the issues such as low cost, tight time to market schedule continuously changing requirements, Communication & Coordination, team size and distributed environment. Agile has proved to be successful in the small and medium size project, however, it have several limitations when applied on large size projects. The purpose of this study is to know agile techniques in detail, finding and highlighting its restrictions for large size projects with the help of systematic literature review. The systematic literature review is going to find answers for the Research questions: 1 How to make agile approaches scalable and adoptable for large projects?2 What are the existing methods, approaches, frameworks and practices support agile process in large scale projects? 3 What are limitations of existing agile approaches, methods, frameworks and practices with reference to large scale projects? This study will identify the current research problems of the agile scalability for large size projects by giving a detail literature review of the identified problems, existed work for providing solution to these problems and will find out limitations of the existing work for covering the identified problems in the agile scalability. All the results gathered will be summarized statistically based on these finding remedial work will be planned in future for handling the identified limitations of agile approaches for large scale projects.
Directory of Open Access Journals (Sweden)
Akimov Pavel Alekseevich
2012-10-01
Full Text Available The proposed paper covers the operator-related formulation of the eigenvalue problem of analysis of a three-dimensional structure that has piecewise-constant physical and geometrical parameters alongside the so-called basic direction within the framework of a discrete-continual approach (a discrete-continual finite element method, a discrete-continual variation method. Generally, discrete-continual formulations represent contemporary mathematical models that become available for computer implementation. They make it possible for a researcher to consider the boundary effects whenever particular components of the solution represent rapidly varying functions. Another feature of discrete-continual methods is the absence of any limitations imposed on lengths of structures. The three-dimensional problem of elasticity is used as the design model of a structure. In accordance with the so-called method of extended domain, the domain in question is embordered by an extended one of an arbitrary shape. At the stage of numerical implementation, relative key features of discrete-continual methods include convenient mathematical formulas, effective computational patterns and algorithms, simple data processing, etc. The authors present their formulation of the problem in question for an isotropic medium with allowance for supports restrained by elastic elements while standard boundary conditions are also taken into consideration.
Eigenvalue approximation from below using non-conforming finite elements
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,with emphasis on obtaining lower bounds. In addition,this article also contains some new materials for eigenvalue approximations of the Laplace operator,which include:1) the proof of the fact that the non-conforming Crouzeix-Raviart element approximates eigenvalues associated with smooth eigenfunctions from below;2) the proof of the fact that the non-conforming EQ rot1 element approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements;3) the explanation of the phenomena that numerical eigenvalues λ 1,h and λ 3,h of the non-conforming Q rot1 element approximate the true eigenvalues from below for the L-shaped domain. Finally,we list several unsolved problems.
EXISTENCE AND UNIQUENESS OF POSITIVE EIGENVALUES FOR CERTAIN EIGENVALUE SYSTEMS
Institute of Scientific and Technical Information of China (English)
XUE Ruying; QIN Yuchun
1999-01-01
In this paper we consider certain eigenvalue systems.Imposing some reasonable hypotheses, we prove that theeigenvalue system has a unique eigenvalue with positiveeigenfunctions, and that the eigenfunction is unique upto a scalar multiple.
A Study on the Problems of EigenValue and Eigenvectors%特征值与特征向量相关问题的研究
Institute of Scientific and Technical Information of China (English)
王新武
2011-01-01
特征值与特征向量是代数研究的中心问题之一，是两个密切相关的概念．在理论和实际应用中，特征值与特征向量都有举足轻重的地位．本文主要是对矩阵特征值与特征向量进行讨论，给出关于特征值与特征向量的相关命题．并对有关特征值与特征向量的题型做了解析以及解题的错误做出相应分析．%Eigenvalue and Eigenvectors are one of key items in Algebra study and closely related concepts. In theory and practice, Eigenvalue and Eigenvectors have important function. The paper discusses on Matrix Eigen value and Eigenvectors, listing and solving related propositions on Matrix Eigenvalue and Eigenvectors, and analyzing the corresponding causes on errors.
Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues
Shakir, Muhammad
2011-01-01
Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach. © 2011 ICST.
The large-scale structure of vacuum
Albareti, F D; Maroto, A L
2014-01-01
The vacuum state in quantum field theory is known to exhibit an important number of fundamental physical features. In this work we explore the possibility that this state could also present a non-trivial space-time structure on large scales. In particular, we will show that by imposing the renormalized vacuum energy-momentum tensor to be conserved and compatible with cosmological observations, the vacuum energy of sufficiently heavy fields behaves at late times as non-relativistic matter rather than as a cosmological constant. In this limit, the vacuum state supports perturbations whose speed of sound is negligible and accordingly allows the growth of structures in the vacuum energy itself. This large-scale structure of vacuum could seed the formation of galaxies and clusters very much in the same way as cold dark matter does.
Quantum Signature of Cosmological Large Scale Structures
Capozziello, S; De Siena, S; Illuminati, F; Capozziello, Salvatore; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio
1998-01-01
We demonstrate that to all large scale cosmological structures where gravitation is the only overall relevant interaction assembling the system (e.g. galaxies), there is associated a characteristic unit of action per particle whose order of magnitude coincides with the Planck action constant $h$. This result extends the class of physical systems for which quantum coherence can act on macroscopic scales (as e.g. in superconductivity) and agrees with the absence of screening mechanisms for the gravitational forces, as predicted by some renormalizable quantum field theories of gravity. It also seems to support those lines of thought invoking that large scale structures in the Universe should be connected to quantum primordial perturbations as requested by inflation, that the Newton constant should vary with time and distance and, finally, that gravity should be considered as an effective interaction induced by quantization.
Process Principles for Large-Scale Nanomanufacturing.
Behrens, Sven H; Breedveld, Victor; Mujica, Maritza; Filler, Michael A
2017-06-07
Nanomanufacturing-the fabrication of macroscopic products from well-defined nanoscale building blocks-in a truly scalable and versatile manner is still far from our current reality. Here, we describe the barriers to large-scale nanomanufacturing and identify routes to overcome them. We argue for nanomanufacturing systems consisting of an iterative sequence of synthesis/assembly and separation/sorting unit operations, analogous to those used in chemicals manufacturing. In addition to performance and economic considerations, phenomena unique to the nanoscale must guide the design of each unit operation and the overall process flow. We identify and discuss four key nanomanufacturing process design needs: (a) appropriately selected process break points, (b) synthesis techniques appropriate for large-scale manufacturing, (c) new structure- and property-based separations, and (d) advances in stabilization and packaging.
Condition Monitoring of Large-Scale Facilities
Hall, David L.
1999-01-01
This document provides a summary of the research conducted for the NASA Ames Research Center under grant NAG2-1182 (Condition-Based Monitoring of Large-Scale Facilities). The information includes copies of view graphs presented at NASA Ames in the final Workshop (held during December of 1998), as well as a copy of a technical report provided to the COTR (Dr. Anne Patterson-Hine) subsequent to the workshop. The material describes the experimental design, collection of data, and analysis results associated with monitoring the health of large-scale facilities. In addition to this material, a copy of the Pennsylvania State University Applied Research Laboratory data fusion visual programming tool kit was also provided to NASA Ames researchers.
Large-scale structure of the Universe
Energy Technology Data Exchange (ETDEWEB)
Shandarin, S.F.; Doroshkevich, A.G.; Zel' dovich, Ya.B. (Inst. Prikladnoj Matematiki, Moscow, USSR)
1983-01-01
A review of theory of the large-scale structure of the Universe is given, including formation of clusters and superclusters of galaxies as well as large voids. Particular attention is paid to the theory of neutrino dominated Universe - the cosmological model where neutrinos with the rest mass of several tens eV dominate the mean density. Evolution of small perturbations is discussed, estimates of microwave backgorund radiation fluctuations is given for different angular scales. Adiabatic theory of the Universe structure formation, known as ''cake'' scenario and their successive fragmentation is given. This scenario is based on approximate nonlinear theory of gravitation instability. Results of numerical experiments, modeling the processes of large-scale structure formation are discussed.
Large-scale structure of the universe
Energy Technology Data Exchange (ETDEWEB)
Shandarin, S.F.; Doroshkevich, A.G.; Zel' dovich, Y.B.
1983-01-01
A survey is given of theories for the origin of large-scale structure in the universe: clusters and superclusters of galaxies, and vast black regions practically devoid of galaxies. Special attention is paid to the theory of a neutrino-dominated universe: a cosmology in which electron neutrinos with a rest mass of a few tens of electron volts would contribute the bulk of the mean density. The evolution of small perturbations is discussed, and estimates are made for the temperature anisotropy of the microwave background radiation on various angular scales. The nonlinear stage in the evolution of smooth irrotational perturbations in a low-pressure medium is described in detail. Numerical experiments simulating large-scale structure formation processes are discussed, as well as their interpretation in the context of catastrophe theory.
Wireless Secrecy in Large-Scale Networks
Pinto, Pedro C; Win, Moe Z
2011-01-01
The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper provides an overview of the main properties of this new class of random graphs. We first analyze the local properties of the iS-graph, namely the degree distributions and their dependence on fading, target secrecy rate, and eavesdropper collusion. To mitigate the effect of the eavesdroppers, we propose two techniques that improve secure connectivity. Then, we analyze the global properties of the iS-graph, namely percolation on the infinite plane, and full connectivity on a finite region. These results help clarify how the presence of eavesdroppers can compromise secure communication in a large-scale network.
ELASTIC: A Large Scale Dynamic Tuning Environment
Directory of Open Access Journals (Sweden)
Andrea Martínez
2014-01-01
Full Text Available The spectacular growth in the number of cores in current supercomputers poses design challenges for the development of performance analysis and tuning tools. To be effective, such analysis and tuning tools must be scalable and be able to manage the dynamic behaviour of parallel applications. In this work, we present ELASTIC, an environment for dynamic tuning of large-scale parallel applications. To be scalable, the architecture of ELASTIC takes the form of a hierarchical tuning network of nodes that perform a distributed analysis and tuning process. Moreover, the tuning network topology can be configured to adapt itself to the size of the parallel application. To guide the dynamic tuning process, ELASTIC supports a plugin architecture. These plugins, called ELASTIC packages, allow the integration of different tuning strategies into ELASTIC. We also present experimental tests conducted using ELASTIC, showing its effectiveness to improve the performance of large-scale parallel applications.
Measuring Bulk Flows in Large Scale Surveys
Feldman, H A; Feldman, Hume A.; Watkins, Richard
1993-01-01
We follow a formalism presented by Kaiser to calculate the variance of bulk flows in large scale surveys. We apply the formalism to a mock survey of Abell clusters \\'a la Lauer \\& Postman and find the variance in the expected bulk velocities in a universe with CDM, MDM and IRAS--QDOT power spectra. We calculate the velocity variance as a function of the 1--D velocity dispersion of the clusters and the size of the survey.
Statistical characteristics of Large Scale Structure
Demianski; Doroshkevich
2002-01-01
We investigate the mass functions of different elements of the Large Scale Structure -- walls, pancakes, filaments and clouds -- and the impact of transverse motions -- expansion and/or compression -- on their statistical characteristics. Using the Zel'dovich theory of gravitational instability we show that the mass functions of all structure elements are approximately the same and the mass of all elements is found to be concentrated near the corresponding mean mass. At high redshifts, both t...
Topologies for large scale photovoltaic power plants
Cabrera Tobar, Ana; Bullich Massagué, Eduard; Aragüés Peñalba, Mònica; Gomis Bellmunt, Oriol
2016-01-01
© 2016 Elsevier Ltd. All rights reserved. The concern of increasing renewable energy penetration into the grid together with the reduction of prices of photovoltaic solar panels during the last decade have enabled the development of large scale solar power plants connected to the medium and high voltage grid. Photovoltaic generation components, the internal layout and the ac collection grid are being investigated for ensuring the best design, operation and control of these power plants. This ...
Multitree Algorithms for Large-Scale Astrostatistics
March, William B.; Ozakin, Arkadas; Lee, Dongryeol; Riegel, Ryan; Gray, Alexander G.
2012-03-01
this number every week, resulting in billions of objects. At such scales, even linear-time analysis operations present challenges, particularly since statistical analyses are inherently interactive processes, requiring that computations complete within some reasonable human attention span. The quadratic (or worse) runtimes of straightforward implementations become quickly unbearable. Examples of applications. These analysis subroutines occur ubiquitously in astrostatistical work. We list just a few examples. The need to cross-match objects across different catalogs has led to various algorithms, which at some point perform an AllNN computation. 2-point and higher-order spatial correlations for the basis of spatial statistics, and are utilized in astronomy to compare the spatial structures of two datasets, such as an observed sample and a theoretical sample, for example, forming the basis for two-sample hypothesis testing. Friends-of-friends clustering is often used to identify halos in data from astrophysical simulations. Minimum spanning tree properties have also been proposed as statistics of large-scale structure. Comparison of the distributions of different kinds of objects requires accurate density estimation, for which KDE is the overall statistical method of choice. The prediction of redshifts from optical data requires accurate regression, for which kernel regression is a powerful method. The identification of objects of various types in astronomy, such as stars versus galaxies, requires accurate classification, for which KDA is a powerful method. Overview. In this chapter, we will briefly sketch the main ideas behind recent fast algorithms which achieve, for example, linear runtimes for pairwise-distance problems, or similarly dramatic reductions in computational growth. In some cases, the runtime orders for these algorithms are mathematically provable statements, while in others we have only conjectures backed by experimental observations for the time being
Large-scale instabilities of helical flows
Cameron, Alexandre; Brachet, Marc-Étienne
2016-01-01
Large-scale hydrodynamic instabilities of periodic helical flows are investigated using $3$D Floquet numerical computations. A minimal three-modes analytical model that reproduce and explains some of the full Floquet results is derived. The growth-rate $\\sigma$ of the most unstable modes (at small scale, low Reynolds number $Re$ and small wavenumber $q$) is found to scale differently in the presence or absence of anisotropic kinetic alpha (\\AKA{}) effect. When an $AKA$ effect is present the scaling $\\sigma \\propto q\\; Re\\,$ predicted by the $AKA$ effect theory [U. Frisch, Z. S. She, and P. L. Sulem, Physica D: Nonlinear Phenomena 28, 382 (1987)] is recovered for $Re\\ll 1$ as expected (with most of the energy of the unstable mode concentrated in the large scales). However, as $Re$ increases, the growth-rate is found to saturate and most of the energy is found at small scales. In the absence of \\AKA{} effect, it is found that flows can still have large-scale instabilities, but with a negative eddy-viscosity sca...
Economically viable large-scale hydrogen liquefaction
Cardella, U.; Decker, L.; Klein, H.
2017-02-01
The liquid hydrogen demand, particularly driven by clean energy applications, will rise in the near future. As industrial large scale liquefiers will play a major role within the hydrogen supply chain, production capacity will have to increase by a multiple of today’s typical sizes. The main goal is to reduce the total cost of ownership for these plants by increasing energy efficiency with innovative and simple process designs, optimized in capital expenditure. New concepts must ensure a manageable plant complexity and flexible operability. In the phase of process development and selection, a dimensioning of key equipment for large scale liquefiers, such as turbines and compressors as well as heat exchangers, must be performed iteratively to ensure technological feasibility and maturity. Further critical aspects related to hydrogen liquefaction, e.g. fluid properties, ortho-para hydrogen conversion, and coldbox configuration, must be analysed in detail. This paper provides an overview on the approach, challenges and preliminary results in the development of efficient as well as economically viable concepts for large-scale hydrogen liquefaction.
Large-scale neuromorphic computing systems
Furber, Steve
2016-10-01
Neuromorphic computing covers a diverse range of approaches to information processing all of which demonstrate some degree of neurobiological inspiration that differentiates them from mainstream conventional computing systems. The philosophy behind neuromorphic computing has its origins in the seminal work carried out by Carver Mead at Caltech in the late 1980s. This early work influenced others to carry developments forward, and advances in VLSI technology supported steady growth in the scale and capability of neuromorphic devices. Recently, a number of large-scale neuromorphic projects have emerged, taking the approach to unprecedented scales and capabilities. These large-scale projects are associated with major new funding initiatives for brain-related research, creating a sense that the time and circumstances are right for progress in our understanding of information processing in the brain. In this review we present a brief history of neuromorphic engineering then focus on some of the principal current large-scale projects, their main features, how their approaches are complementary and distinct, their advantages and drawbacks, and highlight the sorts of capabilities that each can deliver to neural modellers.
Large-Scale Optimization for Bayesian Inference in Complex Systems
Energy Technology Data Exchange (ETDEWEB)
Willcox, Karen [MIT; Marzouk, Youssef [MIT
2013-11-12
The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to
The Least Eigenvalue of Graphs
Institute of Scientific and Technical Information of China (English)
Guidong YU; Yizheng FAN; Yi WANG
2012-01-01
In this paper we investigate the least eigenvalue of a graph whose complement is connected,and present a lower bound for the least eigenvalue of such graph.We also characterize the unique graph whose least eigenvalue attains the second minimum among all graphs of fixed order.
Critical thinking, politics on a large scale and media democracy
Directory of Open Access Journals (Sweden)
José Antonio IBÁÑEZ-MARTÍN
2015-06-01
Full Text Available The first approximation to the social current reality offers us numerous motives for the worry. The spectacle of violence and of immorality can scare us easily. But more worrying still it is to verify that the horizon of conviviality, peace and wellbeing that Europe had been developing from the Treaty of Rome of 1957 has compromised itself seriously for the economic crisis. Today we are before an assault to the democratic politics, which is qualified, on the part of the media democracy, as an exhausted system, which is required to be changed into a new and great politics, a politics on a large scale. The article analyses the concept of a politics on a large scale, primarily attending to Nietzsche, and noting its union with the great philosophy and the great education. The study of the texts of Nietzsche leads us to the conclusion of how in them we often find an interesting analysis of the problems and a misguided proposal for solutions. We cannot think to suggest solutions to all the problems, but we outline various proposals about changes of political activity, that reasonably are defended from the media democracy. In conclusion, we point out that a politics on a large scale requires statesmen, able to suggest modes of life in common that can structure a long-term coexistence.
A visualization framework for large-scale virtual astronomy
Fu, Chi-Wing
Motivated by advances in modern positional astronomy, this research attempts to digitally model the entire Universe through computer graphics technology. Our first challenge is space itself. The gigantic size of the Universe makes it impossible to put everything into a typical graphics system at its own scale. The graphics rendering process can easily fail because of limited computational precision, The second challenge is that the enormous amount of data could slow down the graphics; we need clever techniques to speed up the rendering. Third, since the Universe is dominated by empty space, objects are widely separated; this makes navigation difficult. We attempt to tackle these problems through various techniques designed to extend and optimize the conventional graphics framework, including the following: power homogeneous coordinates for large-scale spatial representations, generalized large-scale spatial transformations, and rendering acceleration via environment caching and object disappearance criteria. Moreover, we implemented an assortment of techniques for modeling and rendering a variety of astronomical bodies, ranging from the Earth up to faraway galaxies, and attempted to visualize cosmological time; a method we call the Lightcone representation was introduced to visualize the whole space-time of the Universe at a single glance. In addition, several navigation models were developed to handle the large-scale navigation problem. Our final results include a collection of visualization tools, two educational animations appropriate for planetarium audiences, and state-of-the-art-advancing rendering techniques that can be transferred to practice in digital planetarium systems.
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....
Large-Scale Self-Consistent Nuclear Mass Calculations
Stoitsov, M V; Dobaczewski, J; Nazarewicz, W
2006-01-01
The program of systematic large-scale self-consistent nuclear mass calculations that is based on the nuclear density functional theory represents a rich scientific agenda that is closely aligned with the main research directions in modern nuclear structure and astrophysics, especially the radioactive nuclear beam physics. The quest for the microscopic understanding of the phenomenon of nuclear binding represents, in fact, a number of fundamental and crucial questions of the quantum many-body problem, including the proper treatment of correlations and dynamics in the presence of symmetry breaking. Recent advances and open problems in the field of nuclear mass calculations are presented and discussed.
RESTRUCTURING OF THE LARGE-SCALE SPRINKLERS
Directory of Open Access Journals (Sweden)
Paweł Kozaczyk
2016-09-01
Full Text Available One of the best ways for agriculture to become independent from shortages of precipitation is irrigation. In the seventies and eighties of the last century a number of large-scale sprinklers in Wielkopolska was built. At the end of 1970’s in the Poznan province 67 sprinklers with a total area of 6400 ha were installed. The average size of the sprinkler reached 95 ha. In 1989 there were 98 sprinklers, and the area which was armed with them was more than 10 130 ha. The study was conducted on 7 large sprinklers with the area ranging from 230 to 520 hectares in 1986÷1998. After the introduction of the market economy in the early 90’s and ownership changes in agriculture, large-scale sprinklers have gone under a significant or total devastation. Land on the State Farms of the State Agricultural Property Agency has leased or sold and the new owners used the existing sprinklers to a very small extent. This involved a change in crop structure, demand structure and an increase in operating costs. There has also been a threefold increase in electricity prices. Operation of large-scale irrigation encountered all kinds of barriers in practice and limitations of system solutions, supply difficulties, high levels of equipment failure which is not inclined to rational use of available sprinklers. An effect of a vision of the local area was to show the current status of the remaining irrigation infrastructure. The adopted scheme for the restructuring of Polish agriculture was not the best solution, causing massive destruction of assets previously invested in the sprinkler system.
Aeroelastic stability analysis of wind turbines using an eigenvalue approach
DEFF Research Database (Denmark)
Hansen, M.H.
2004-01-01
. To eliminate the periodic coefficients and avoid using the Floquet Theory, the multi-blade transformation is utilized. From the corresponding eigenvalue problem, the eigenvalues and eigenvectors can be computed at any operation condition to give the aeroelastic modal properties: Natural frequencies, damping...
Large-Scale PV Integration Study
Energy Technology Data Exchange (ETDEWEB)
Lu, Shuai; Etingov, Pavel V.; Diao, Ruisheng; Ma, Jian; Samaan, Nader A.; Makarov, Yuri V.; Guo, Xinxin; Hafen, Ryan P.; Jin, Chunlian; Kirkham, Harold; Shlatz, Eugene; Frantzis, Lisa; McClive, Timothy; Karlson, Gregory; Acharya, Dhruv; Ellis, Abraham; Stein, Joshua; Hansen, Clifford; Chadliev, Vladimir; Smart, Michael; Salgo, Richard; Sorensen, Rahn; Allen, Barbara; Idelchik, Boris
2011-07-29
This research effort evaluates the impact of large-scale photovoltaic (PV) and distributed generation (DG) output on NV Energy’s electric grid system in southern Nevada. It analyzes the ability of NV Energy’s generation to accommodate increasing amounts of utility-scale PV and DG, and the resulting cost of integrating variable renewable resources. The study was jointly funded by the United States Department of Energy and NV Energy, and conducted by a project team comprised of industry experts and research scientists from Navigant Consulting Inc., Sandia National Laboratories, Pacific Northwest National Laboratory and NV Energy.
Conformal Anomaly and Large Scale Gravitational Coupling
Salehi, H
2000-01-01
We present a model in which the breackdown of conformal symmetry of a quantum stress-tensor due to the trace anomaly is related to a cosmological effect in a gravitational model. This is done by characterizing the traceless part of the quantum stress-tensor in terms of the stress-tensor of a conformal invariant classical scalar field. We introduce a conformal frame in which the anomalous trace is identified with a cosmological constant. In this conformal frame we establish the Einstein field equations by connecting the quantum stress-tensor with the large scale distribution of matter in the universe.
Large Scale Quantum Simulations of Nuclear Pasta
Fattoyev, Farrukh J.; Horowitz, Charles J.; Schuetrumpf, Bastian
2016-03-01
Complex and exotic nuclear geometries collectively referred to as ``nuclear pasta'' are expected to naturally exist in the crust of neutron stars and in supernovae matter. Using a set of self-consistent microscopic nuclear energy density functionals we present the first results of large scale quantum simulations of pasta phases at baryon densities 0 . 03 pasta configurations. This work is supported in part by DOE Grants DE-FG02-87ER40365 (Indiana University) and DE-SC0008808 (NUCLEI SciDAC Collaboration).
Large scale wind power penetration in Denmark
DEFF Research Database (Denmark)
Karnøe, Peter
2013-01-01
he Danish electricity generating system prepared to adopt nuclear power in the 1970s, yet has become the world's front runner in wind power with a national plan for 50% wind power penetration by 2020. This paper deploys a sociotechnical perspective to explain the historical transformation of "net...... expertise evolves and contributes to the normalization and large-scale penetration of wind power in the electricity generating system. The analysis teaches us how technological paths become locked-in, but also indicates keys for locking them out....
Nigro, G.; Pongkitiwanichakul, P.; Cattaneo, F.; Tobias, S. M.
2017-01-01
We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number (Rm). We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations.
Large scale phononic metamaterials for seismic isolation
Energy Technology Data Exchange (ETDEWEB)
Aravantinos-Zafiris, N. [Department of Sound and Musical Instruments Technology, Ionian Islands Technological Educational Institute, Stylianou Typaldou ave., Lixouri 28200 (Greece); Sigalas, M. M. [Department of Materials Science, University of Patras, Patras 26504 (Greece)
2015-08-14
In this work, we numerically examine structures that could be characterized as large scale phononic metamaterials. These novel structures could have band gaps in the frequency spectrum of seismic waves when their dimensions are chosen appropriately, thus raising the belief that they could be serious candidates for seismic isolation structures. Different and easy to fabricate structures were examined made from construction materials such as concrete and steel. The well-known finite difference time domain method is used in our calculations in order to calculate the band structures of the proposed metamaterials.
Hiearchical Engine for Large Scale Infrastructure Simulation
Energy Technology Data Exchange (ETDEWEB)
2017-03-15
HELICS ls a new open-source, cyber-physlcal-energy co-simulation framework for electric power systems. HELICS Is designed to support very-large-scale (100,000+ federates) cosimulations with off-the-shelf power-system, communication, market, and end-use tools. Other key features Include cross platform operating system support, the integration of both eventdrlven (e.g., packetlzed communication) and time-series (e.g.,power flow) simulations, and the ability to co-Iterate among federates to ensure physical model convergence at each time step.
On the Phenomenology of an Accelerated Large-Scale Universe
Directory of Open Access Journals (Sweden)
Martiros Khurshudyan
2016-10-01
Full Text Available In this review paper, several new results towards the explanation of the accelerated expansion of the large-scale universe is discussed. On the other hand, inflation is the early-time accelerated era and the universe is symmetric in the sense of accelerated expansion. The accelerated expansion of is one of the long standing problems in modern cosmology, and physics in general. There are several well defined approaches to solve this problem. One of them is an assumption concerning the existence of dark energy in recent universe. It is believed that dark energy is responsible for antigravity, while dark matter has gravitational nature and is responsible, in general, for structure formation. A different approach is an appropriate modification of general relativity including, for instance, f ( R and f ( T theories of gravity. On the other hand, attempts to build theories of quantum gravity and assumptions about existence of extra dimensions, possible variability of the gravitational constant and the speed of the light (among others, provide interesting modifications of general relativity applicable to problems of modern cosmology, too. In particular, here two groups of cosmological models are discussed. In the first group the problem of the accelerated expansion of large-scale universe is discussed involving a new idea, named the varying ghost dark energy. On the other hand, the second group contains cosmological models addressed to the same problem involving either new parameterizations of the equation of state parameter of dark energy (like varying polytropic gas, or nonlinear interactions between dark energy and dark matter. Moreover, for cosmological models involving varying ghost dark energy, massless particle creation in appropriate radiation dominated universe (when the background dynamics is due to general relativity is demonstrated as well. Exploring the nature of the accelerated expansion of the large-scale universe involving generalized
Numerical pole assignment by eigenvalue Jacobian inversion
Sevaston, George E.
1986-01-01
A numerical procedure for solving the linear pole placement problem is developed which operates by the inversion of an analytically determined eigenvalue Jacobian matrix. Attention is given to convergence characteristics and pathological situations. It is not concluded that the algorithm developed is suitable for computer-aided control system design with particular reference to the scan platform pointing control system for the Galileo spacecraft.
On the sensitivities of multiple eigenvalues
DEFF Research Database (Denmark)
Gravesen, Jens; Evgrafov, Anton; Nguyen, Dang Manh
2011-01-01
polynomials of a number of eigenvalues, regardless of their multiplicity, which are known to be isolated from the rest depend smoothly on the parameter. We present explicit readily computable expressions for their first derivatives. Finally, we demonstrate the utility of our approach on a problem of finding...
Eigenvalues of the -Laplacian and disconjugacy criteria
Directory of Open Access Journals (Sweden)
Pinasco Juan P
2006-01-01
Full Text Available We derive oscillation and nonoscillation criteria for the one-dimensional -Laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willett, and the proof is based on a Picone-type identity.
Robust large-scale parallel nonlinear solvers for simulations.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any
Murthy, D. V.
1989-01-01
This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.
Internationalization Measures in Large Scale Research Projects
Soeding, Emanuel; Smith, Nancy
2017-04-01
Internationalization measures in Large Scale Research Projects Large scale research projects (LSRP) often serve as flagships used by universities or research institutions to demonstrate their performance and capability to stakeholders and other interested parties. As the global competition among universities for the recruitment of the brightest brains has increased, effective internationalization measures have become hot topics for universities and LSRP alike. Nevertheless, most projects and universities are challenged with little experience on how to conduct these measures and make internationalization an cost efficient and useful activity. Furthermore, those undertakings permanently have to be justified with the Project PIs as important, valuable tools to improve the capacity of the project and the research location. There are a variety of measures, suited to support universities in international recruitment. These include e.g. institutional partnerships, research marketing, a welcome culture, support for science mobility and an effective alumni strategy. These activities, although often conducted by different university entities, are interlocked and can be very powerful measures if interfaced in an effective way. On this poster we display a number of internationalization measures for various target groups, identify interfaces between project management, university administration, researchers and international partners to work together, exchange information and improve processes in order to be able to recruit, support and keep the brightest heads to your project.
Large-scale Globally Propagating Coronal Waves
Directory of Open Access Journals (Sweden)
Alexander Warmuth
2015-09-01
Full Text Available Large-scale, globally propagating wave-like disturbances have been observed in the solar chromosphere and by inference in the corona since the 1960s. However, detailed analysis of these phenomena has only been conducted since the late 1990s. This was prompted by the availability of high-cadence coronal imaging data from numerous spaced-based instruments, which routinely show spectacular globally propagating bright fronts. Coronal waves, as these perturbations are usually referred to, have now been observed in a wide range of spectral channels, yielding a wealth of information. Many findings have supported the “classical” interpretation of the disturbances: fast-mode MHD waves or shocks that are propagating in the solar corona. However, observations that seemed inconsistent with this picture have stimulated the development of alternative models in which “pseudo waves” are generated by magnetic reconfiguration in the framework of an expanding coronal mass ejection. This has resulted in a vigorous debate on the physical nature of these disturbances. This review focuses on demonstrating how the numerous observational findings of the last one and a half decades can be used to constrain our models of large-scale coronal waves, and how a coherent physical understanding of these disturbances is finally emerging.
BILGO: Bilateral greedy optimization for large scale semidefinite programming
Hao, Zhifeng
2013-10-03
Many machine learning tasks (e.g. metric and manifold learning problems) can be formulated as convex semidefinite programs. To enable the application of these tasks on a large-scale, scalability and computational efficiency are considered as desirable properties for a practical semidefinite programming algorithm. In this paper, we theoretically analyze a new bilateral greedy optimization (denoted BILGO) strategy in solving general semidefinite programs on large-scale datasets. As compared to existing methods, BILGO employs a bilateral search strategy during each optimization iteration. In such an iteration, the current semidefinite matrix solution is updated as a bilateral linear combination of the previous solution and a suitable rank-1 matrix, which can be efficiently computed from the leading eigenvector of the descent direction at this iteration. By optimizing for the coefficients of the bilateral combination, BILGO reduces the cost function in every iteration until the KKT conditions are fully satisfied, thus, it tends to converge to a global optimum. In fact, we prove that BILGO converges to the global optimal solution at a rate of O(1/k), where k is the iteration counter. The algorithm thus successfully combines the efficiency of conventional rank-1 update algorithms and the effectiveness of gradient descent. Moreover, BILGO can be easily extended to handle low rank constraints. To validate the effectiveness and efficiency of BILGO, we apply it to two important machine learning tasks, namely Mahalanobis metric learning and maximum variance unfolding. Extensive experimental results clearly demonstrate that BILGO can solve large-scale semidefinite programs efficiently.
An Effective Method of Monitoring the Large-Scale Traffic Pattern Based on RMT and PCA
Directory of Open Access Journals (Sweden)
Jia Liu
2010-01-01
Full Text Available Mechanisms to extract the characteristics of network traffic play a significant role in traffic monitoring, offering helpful information for network management and control. In this paper, a method based on Random Matrix Theory (RMT and Principal Components Analysis (PCA is proposed for monitoring and analyzing large-scale traffic patterns in the Internet. Besides the analysis of the largest eigenvalue in RMT, useful information is also extracted from small eigenvalues by a method based on PCA. And then an appropriate approach is put forward to select some observation points on the base of the eigen analysis. Finally, some experiments about peer-to-peer traffic pattern recognition and backbone aggregate flow estimation are constructed. The simulation results show that using about 10% of nodes as observation points, our method can monitor and extract key information about Internet traffic patterns.
Analysis using large-scale ringing data
Directory of Open Access Journals (Sweden)
Baillie, S. R.
2004-06-01
survival and recruitment estimates from the French CES scheme to assess the relative contributions of survival and recruitment to overall population changes. He develops a novel approach to modelling survival rates from such multi–site data by using within–year recaptures to provide a covariate of between–year recapture rates. This provided parsimonious models of variation in recapture probabilities between sites and years. The approach provides promising results for the four species investigated and can potentially be extended to similar data from other CES/MAPS schemes. The final paper by Blandine Doligez, David Thomson and Arie van Noordwijk (Doligez et al., 2004 illustrates how large-scale studies of population dynamics can be important for evaluating the effects of conservation measures. Their study is concerned with the reintroduction of White Stork populations to the Netherlands where a re–introduction programme started in 1969 had resulted in a breeding population of 396 pairs by 2000. They demonstrate the need to consider a wide range of models in order to account for potential age, time, cohort and “trap–happiness” effects. As the data are based on resightings such trap–happiness must reflect some form of heterogeneity in resighting probabilities. Perhaps surprisingly, the provision of supplementary food did not influence survival, but it may havehad an indirect effect via the alteration of migratory behaviour. Spatially explicit modelling of data gathered at many sites inevitably results in starting models with very large numbers of parameters. The problem is often complicated further by having relatively sparse data at each site, even where the total amount of data gathered is very large. Both Julliard (2004 and Doligez et al. (2004 give explicit examples of problems caused by needing to handle very large numbers of parameters and show how they overcame them for their particular data sets. Such problems involve both the choice of appropriate
Split Bregman method for large scale fused Lasso
Ye, Gui-Bo
2010-01-01
rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\\ell_1$ norm regularizer. However, due to nonseparability and nonsmoothness of the regularization term, solving the fused Lasso problem is computationally demanding. Existing solvers can only deal with problems of small or medium size, or a special case of the fused Lasso problem in which the predictor matrix is identity matrix. In this paper, we propose an iterative algorithm based on split Bregman method to solve a class of large-scale fused Lasso problems, including a generalized fused Lasso and a fused Lasso support vector classifier. We derive our algorithm using augmented Lagrangian method and prove its convergence properties. The performance of our method is tested on both artificial data and real-world applications including proteomic data from mass spectrometry and genomic data from array...
Planning under uncertainty solving large-scale stochastic linear programs
Energy Technology Data Exchange (ETDEWEB)
Infanger, G. (Stanford Univ., CA (United States). Dept. of Operations Research Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft)
1992-12-01
For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.
Large-Scale Astrophysical Visualization on Smartphones
Becciani, U.; Massimino, P.; Costa, A.; Gheller, C.; Grillo, A.; Krokos, M.; Petta, C.
2011-07-01
Nowadays digital sky surveys and long-duration, high-resolution numerical simulations using high performance computing and grid systems produce multidimensional astrophysical datasets in the order of several Petabytes. Sharing visualizations of such datasets within communities and collaborating research groups is of paramount importance for disseminating results and advancing astrophysical research. Moreover educational and public outreach programs can benefit greatly from novel ways of presenting these datasets by promoting understanding of complex astrophysical processes, e.g., formation of stars and galaxies. We have previously developed VisIVO Server, a grid-enabled platform for high-performance large-scale astrophysical visualization. This article reviews the latest developments on VisIVO Web, a custom designed web portal wrapped around VisIVO Server, then introduces VisIVO Smartphone, a gateway connecting VisIVO Web and data repositories for mobile astrophysical visualization. We discuss current work and summarize future developments.
Clumps in large scale relativistic jets
Tavecchio, F; Celotti, A
2003-01-01
The relatively intense X-ray emission from large scale (tens to hundreds kpc) jets discovered with Chandra likely implies that jets (at least in powerful quasars) are still relativistic at that distances from the active nucleus. In this case the emission is due to Compton scattering off seed photons provided by the Cosmic Microwave Background, and this on one hand permits to have magnetic fields close to equipartition with the emitting particles, and on the other hand minimizes the requirements about the total power carried by the jet. The emission comes from compact (kpc scale) knots, and we here investigate what we can predict about the possible emission between the bright knots. This is motivated by the fact that bulk relativistic motion makes Compton scattering off the CMB photons efficient even when electrons are cold or mildly relativistic in the comoving frame. This implies relatively long cooling times, dominated by adiabatic losses. Therefore the relativistically moving plasma can emit, by Compton sc...
Large-scale parametric survival analysis.
Mittal, Sushil; Madigan, David; Cheng, Jerry Q; Burd, Randall S
2013-10-15
Survival analysis has been a topic of active statistical research in the past few decades with applications spread across several areas. Traditional applications usually consider data with only a small numbers of predictors with a few hundreds or thousands of observations. Recent advances in data acquisition techniques and computation power have led to considerable interest in analyzing very-high-dimensional data where the number of predictor variables and the number of observations range between 10(4) and 10(6). In this paper, we present a tool for performing large-scale regularized parametric survival analysis using a variant of the cyclic coordinate descent method. Through our experiments on two real data sets, we show that application of regularized models to high-dimensional data avoids overfitting and can provide improved predictive performance and calibration over corresponding low-dimensional models.
Curvature constraints from Large Scale Structure
Di Dio, Enea; Raccanelli, Alvise; Durrer, Ruth; Kamionkowski, Marc; Lesgourgues, Julien
2016-01-01
We modified the CLASS code in order to include relativistic galaxy number counts in spatially curved geometries; we present the formalism and study the effect of relativistic corrections on spatial curvature. The new version of the code is now publicly available. Using a Fisher matrix analysis, we investigate how measurements of the spatial curvature parameter $\\Omega_K$ with future galaxy surveys are affected by relativistic effects, which influence observations of the large scale galaxy distribution. These effects include contributions from cosmic magnification, Doppler terms and terms involving the gravitational potential. As an application, we consider angle and redshift dependent power spectra, which are especially well suited for model independent cosmological constraints. We compute our results for a representative deep, wide and spectroscopic survey, and our results show the impact of relativistic corrections on the spatial curvature parameter estimation. We show that constraints on the curvature para...
Large-scale simulations of reionization
Energy Technology Data Exchange (ETDEWEB)
Kohler, Katharina; /JILA, Boulder /Fermilab; Gnedin, Nickolay Y.; /Fermilab; Hamilton, Andrew J.S.; /JILA, Boulder
2005-11-01
We use cosmological simulations to explore the large-scale effects of reionization. Since reionization is a process that involves a large dynamic range--from galaxies to rare bright quasars--we need to be able to cover a significant volume of the universe in our simulation without losing the important small scale effects from galaxies. Here we have taken an approach that uses clumping factors derived from small scale simulations to approximate the radiative transfer on the sub-cell scales. Using this technique, we can cover a simulation size up to 1280h{sup -1} Mpc with 10h{sup -1} Mpc cells. This allows us to construct synthetic spectra of quasars similar to observed spectra of SDSS quasars at high redshifts and compare them to the observational data. These spectra can then be analyzed for HII region sizes, the presence of the Gunn-Peterson trough, and the Lyman-{alpha} forest.
Large-Scale Tides in General Relativity
Ip, Hiu Yan
2016-01-01
Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lema\\^itre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the "separate universe" paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effects are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation ...
Grid sensitivity capability for large scale structures
Nagendra, Gopal K.; Wallerstein, David V.
1989-01-01
The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.
Large scale water lens for solar concentration.
Mondol, A S; Vogel, B; Bastian, G
2015-06-01
Properties of large scale water lenses for solar concentration were investigated. These lenses were built from readily available materials, normal tap water and hyper-elastic linear low density polyethylene foil. Exposed to sunlight, the focal lengths and light intensities in the focal spot were measured and calculated. Their optical properties were modeled with a raytracing software based on the lens shape. We have achieved a good match of experimental and theoretical data by considering wavelength dependent concentration factor, absorption and focal length. The change in light concentration as a function of water volume was examined via the resulting load on the foil and the corresponding change of shape. The latter was extracted from images and modeled by a finite element simulation.
Supporting large-scale computational science
Energy Technology Data Exchange (ETDEWEB)
Musick, R
1998-10-01
A study has been carried out to determine the feasibility of using commercial database management systems (DBMSs) to support large-scale computational science. Conventional wisdom in the past has been that DBMSs are too slow for such data. Several events over the past few years have muddied the clarity of this mindset: 1. 2. 3. 4. Several commercial DBMS systems have demonstrated storage and ad-hoc quer access to Terabyte data sets. Several large-scale science teams, such as EOSDIS [NAS91], high energy physics [MM97] and human genome [Kin93] have adopted (or make frequent use of) commercial DBMS systems as the central part of their data management scheme. Several major DBMS vendors have introduced their first object-relational products (ORDBMSs), which have the potential to support large, array-oriented data. In some cases, performance is a moot issue. This is true in particular if the performance of legacy applications is not reduced while new, albeit slow, capabilities are added to the system. The basic assessment is still that DBMSs do not scale to large computational data. However, many of the reasons have changed, and there is an expiration date attached to that prognosis. This document expands on this conclusion, identifies the advantages and disadvantages of various commercial approaches, and describes the studies carried out in exploring this area. The document is meant to be brief, technical and informative, rather than a motivational pitch. The conclusions within are very likely to become outdated within the next 5-7 years, as market forces will have a significant impact on the state of the art in scientific data management over the next decade.
Introducing Large-Scale Innovation in Schools
Sotiriou, Sofoklis; Riviou, Katherina; Cherouvis, Stephanos; Chelioti, Eleni; Bogner, Franz X.
2016-08-01
Education reform initiatives tend to promise higher effectiveness in classrooms especially when emphasis is given to e-learning and digital resources. Practical changes in classroom realities or school organization, however, are lacking. A major European initiative entitled Open Discovery Space (ODS) examined the challenge of modernizing school education via a large-scale implementation of an open-scale methodology in using technology-supported innovation. The present paper describes this innovation scheme which involved schools and teachers all over Europe, embedded technology-enhanced learning into wider school environments and provided training to teachers. Our implementation scheme consisted of three phases: (1) stimulating interest, (2) incorporating the innovation into school settings and (3) accelerating the implementation of the innovation. The scheme's impact was monitored for a school year using five indicators: leadership and vision building, ICT in the curriculum, development of ICT culture, professional development support, and school resources and infrastructure. Based on about 400 schools, our study produced four results: (1) The growth in digital maturity was substantial, even for previously high scoring schools. This was even more important for indicators such as vision and leadership" and "professional development." (2) The evolution of networking is presented graphically, showing the gradual growth of connections achieved. (3) These communities became core nodes, involving numerous teachers in sharing educational content and experiences: One out of three registered users (36 %) has shared his/her educational resources in at least one community. (4) Satisfaction scores ranged from 76 % (offer of useful support through teacher academies) to 87 % (good environment to exchange best practices). Initiatives such as ODS add substantial value to schools on a large scale.
Application of methanol synthesis reactor to large-scale plants
Institute of Scientific and Technical Information of China (English)
LOU Ren; XU Rong-liang; LOU Shou-lin
2006-01-01
The developing status of world large-scale methanol production technology is analyzed and Linda's JW low-pressure methanol synthesis reactor with uniform temperature is described. JW serial reactors have been successfully introduced in and applied in Harbin Gasification Plant and the productivity has been increased by 50% and now nine sets of equipments are successfully running in Harbin Gasification Plant,Jiangsu Xinya, Shandong Kenli,Henan Zhongyuan, Handan Xinyangguang,' Shanxi Weihua and Inner Mongolia Tianye. Now it has manufacturing the reactors of 300,000 t/a for Liaoning Dahua. Some solutions for the structure problems of 1000 ～5000 t/d methanol synthesis rectors are put forward.
Large-scale magnetic fields from inflation in teleparallel gravity
Bamba, Kazuharu; Luo, Ling-Wei
2013-01-01
Generation of large-scale magnetic fields in inflationary cosmology is studied in teleparallelism, where instead of the scalar curvature in general relativity, the torsion scalar describes the gravity theory. In particular, we investigate a coupling of the electromagnetic field to the torsion scalar during inflation, which leads to the breaking of conformal invariance of the electromagnetic field. We demonstrate that for a power-law type coupling, the current magnetic field strength of $\\sim 10^{-9}$ G on 1 Mpc scale can be generated, if the backreaction effects and strong coupling problem are not taken into consideration.
Petascale computations for Large-scale Atomic and Molecular collisions
McLaughlin, Brendan M
2014-01-01
Petaflop architectures are currently being utilized efficiently to perform large scale computations in Atomic, Molecular and Optical Collisions. We solve the Schroedinger or Dirac equation for the appropriate collision problem using the R-matrix or R-matrix with pseudo-states approach. We briefly outline the parallel methodology used and implemented for the current suite of Breit-Pauli and DARC codes. Various examples are shown of our theoretical results compared with those obtained from Synchrotron Radiation facilities and from Satellite observations. We also indicate future directions and implementation of the R-matrix codes on emerging GPU architectures.
Highly Scalable Trip Grouping for Large Scale Collective Transportation Systems
DEFF Research Database (Denmark)
Gidofalvi, Gyozo; Pedersen, Torben Bach; Risch, Tore
2008-01-01
Transportation-related problems, like road congestion, parking, and pollution, are increasing in most cities. In order to reduce traffic, recent work has proposed methods for vehicle sharing, for example for sharing cabs by grouping "closeby" cab requests and thus minimizing transportation cost...... and utilizing cab space. However, the methods published so far do not scale to large data volumes, which is necessary to facilitate large-scale collective transportation systems, e.g., ride-sharing systems for large cities. This paper presents highly scalable trip grouping algorithms, which generalize previous...
Less is more: regularization perspectives on large scale machine learning
CERN. Geneva
2017-01-01
Deep learning based techniques provide a possible solution at the expanse of theoretical guidance and, especially, of computational requirements. It is then a key challenge for large scale machine learning to devise approaches guaranteed to be accurate and yet computationally efficient. In this talk, we will consider a regularization perspectives on machine learning appealing to classical ideas in linear algebra and inverse problems to scale-up dramatically nonparametric methods such as kernel methods, often dismissed because of prohibitive costs. Our analysis derives optimal theoretical guarantees while providing experimental results at par or out-performing state of the art approaches.
SPIN ALIGNMENTS OF SPIRAL GALAXIES WITHIN THE LARGE-SCALE STRUCTURE FROM SDSS DR7
Energy Technology Data Exchange (ETDEWEB)
Zhang, Youcai; Yang, Xiaohu; Luo, Wentao [Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Nandan Road 80, Shanghai 200030 (China); Wang, Huiyuan [Key Laboratory for Research in Galaxies and Cosmology, University of Science and Technology of China, Hefei, Anhui 230026 (China); Wang, Lei [Purple Mountain Observatory, The Partner Group of MPI für Astronomie, 2 West Beijing Road, Nanjing 210008 (China); Mo, H. J. [Department of Astronomy, University of Massachusetts, Amherst, MA 01003-9305 (United States); Van den Bosch, Frank C., E-mail: yczhang@shao.ac.cn, E-mail: xyang@sjtu.edu.cn [Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT 06520-8101 (United States)
2015-01-01
Using a sample of spiral galaxies selected from the Sloan Digital Sky Survey Data Release 7 and Galaxy Zoo 2, we investigate the alignment of spin axes of spiral galaxies with their surrounding large-scale structure, which is characterized by the large-scale tidal field reconstructed from the data using galaxy groups above a certain mass threshold. We find that the spin axes only have weak tendencies to be aligned with (or perpendicular to) the intermediate (or minor) axis of the local tidal tensor. The signal is the strongest in a cluster environment where all three eigenvalues of the local tidal tensor are positive. Compared to the alignments between halo spins and the local tidal field obtained in N-body simulations, the above observational results are in best agreement with those for the spins of inner regions of halos, suggesting that the disk material traces the angular momentum of dark matter halos in the inner regions.
Foundational perspectives on causality in large-scale brain networks
Mannino, Michael; Bressler, Steven L.
2015-12-01
likelihood that a change in the activity of one neuronal population affects the activity in another. We argue that these measures access the inherently probabilistic nature of causal influences in the brain, and are thus better suited for large-scale brain network analysis than are DC-based measures. Our work is consistent with recent advances in the philosophical study of probabilistic causality, which originated from inherent conceptual problems with deterministic regularity theories. It also resonates with concepts of stochasticity that were involved in establishing modern physics. In summary, we argue that probabilistic causality is a conceptually appropriate foundation for describing neural causality in the brain.
Foundational perspectives on causality in large-scale brain networks.
Mannino, Michael; Bressler, Steven L
2015-12-01
likelihood that a change in the activity of one neuronal population affects the activity in another. We argue that these measures access the inherently probabilistic nature of causal influences in the brain, and are thus better suited for large-scale brain network analysis than are DC-based measures. Our work is consistent with recent advances in the philosophical study of probabilistic causality, which originated from inherent conceptual problems with deterministic regularity theories. It also resonates with concepts of stochasticity that were involved in establishing modern physics. In summary, we argue that probabilistic causality is a conceptually appropriate foundation for describing neural causality in the brain.
Distributions of Dirac Operator Eigenvalues
Akemann, G
2004-01-01
The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions which are stated. As a special case, we give examples of the lowest-lying eigenvalue distributions for QCD-like gauge theories without making use of earlier results based on the relation to Random Matrix Theory.
Pro website development and operations streamlining DevOps for large-scale websites
Sacks, Matthew
2012-01-01
Pro Website Development and Operations gives you the experience you need to create and operate a large-scale production website. Large-scale websites have their own unique set of problems regarding their design-problems that can get worse when agile methodologies are adopted for rapid results. Managing large-scale websites, deploying applications, and ensuring they are performing well often requires a full scale team involving the development and operations sides of the company-two departments that don't always see eye to eye. When departments struggle with each other, it adds unnecessary comp
Institute of Scientific and Technical Information of China (English)
徐娟; 孙大伟
2012-01-01
Aiming at the problems of the security and stability of power network caused by load undulation or power quality not good when wind power and photoelectric power generation connected with power network on a large scale.Through analyzing and comparing to find out： the smart grid with powerful capacity,facility and compatibility,con fit multiform power supply to connect with and contain it.The result of research shows that developing the smart grid maybe is the best of all scheme to solve the bottleneck problems of wind power and photoelectric power generation connected with power network on a large scale.%针对大规模风、光发电集中接入电网后产生的负荷波动性及电能质量较差,给电网带来的安全性和稳定性问题,通过分析对比发现,智能电网具有很好的智能性、灵活性和兼容性,不但成功地解决了上述问题还可以适应多种形式的电源接入并能将其成功消纳。研究表明：发展智能电网是解决大规模风、光发电并网瓶颈问题的最佳方案。
Dual variational formulas for the first Dirichlet eigenvalue on half-line
Institute of Scientific and Technical Information of China (English)
Chen; Mufa(陈木法); ZHANG; Yuhui(张余辉); ZHAO; Xiaoliang(赵晓亮)
2003-01-01
The aim of the paper is to establish two dual variational formulas for the first Dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the coefficients of the operators are presented. Moreover, the corresponding problems in the discrete case and the higher-order eigenvalues in the continuous case are also studied.
On the design derivatives of eigenvalues and eigenvectors for distributed parameter systems
Reiss, R.
1985-01-01
In this paper, analytic expressions are obtained for the design derivatives of eigenvalues and eigenfunctions of self-adjoint linear distributed parameter systems. Explicit treatment of boundary conditions is avoided by casting the eigenvalue equation into integral form. Results are expressed in terms of the linear operators defining the eigenvalue problem, and are therefore quite general. Sufficiency conditions appropriate to structural optimization of eigenvalues are obtained.
Maximization of eigenvalues using topology optimization
DEFF Research Database (Denmark)
Pedersen, Niels Leergaard
2000-01-01
Topology optimization is used to optimize the eigenvalues of plates. The results are intended especially for MicroElectroMechanical Systems (MEMS) but call be seen as more general. The problem is not formulated as a case of reinforcement of an existing structure, so there is a problem related...... to localized modes in low density areas. The topology optimization problem is formulated using the SIMP method. Special attention is paid to a numerical method for removing localized eigenmodes in low density areas. The method is applied to numerical examples of maximizing the first eigenfrequency, One example...... is a practical MEMS application; a probe used in an Atomic Force Microscope (AFM). For the AFM probe the optimization is complicated by a constraint on the stiffness and constraints on higher order eigenvalues....
On the distribution of eigenvalues of non-selfadjoint operators
Demuth, Michael; Katriel, Guy
2008-01-01
We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.
Numerical methods for evaluating the derivatives of eigenvalues and eigenvectors
Rudisill, C. S.; Chu, Y.-Y.
1975-01-01
Two numerical methods are presented for computing the derivatives of eigenvalues and eigenvectors which do not require complete solution of the eigenvalue problem if only a few derivatives are sought. The 'iterative' method may be used to find the first derivative of one or all of the eigenvectors together with the second derivative of their eigenvalues in a self-adjoint system. If the left- and right-hand eigenvectors are known, the first derivative of the eigenvector corresponding to the largest eigenvalue and the second derivative of the largest eigenvalue may be obtained for a nonself-adjoint system. The 'algebraic' method may be used to find all orders of the derivatives, provided they exist, without requiring the left-hand eigenvectors.
Eigenvalue based Spectrum Sensing Algorithms for Cognitive Radio
Zeng, Yonghong
2008-01-01
Spectrum sensing is a fundamental component is a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based ...
Extreme eigenvalues of sample covariance and correlation matrices
DEFF Research Database (Denmark)
Heiny, Johannes
This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... of the problem at hand. We develop a theory for the point process of the normalized eigenvalues of the sample covariance matrix in the case where rows and columns of the data are linearly dependent. Based on the weak convergence of this point process we derive the limit laws of various functionals...... of the eigenvalues. In the second part, we show that the largest and smallest eigenvalues of a highdimensional sample correlation matrix possess almost sure non-random limits if the truncated variance of the entry distribution is “almost slowly varying”, a condition we describe via moment properties of self...
Cold flows and large scale tides
van de Weygaert, R.; Hoffman, Y.
1999-01-01
Within the context of the general cosmological setting it has remained puzzling that the local Universe is a relatively cold environment, in the sense of small-scale peculiar velocities being relatively small. Indeed, it has since long figured as an important argument for the Universe having a low Ω, or if the Universe were to have a high Ω for the existence of a substantial bias between the galaxy and the matter distribution. Here we investigate the dynamical impact of neighbouring matter concentrations on local small-scale characteristics of cosmic flows. While regions where huge nearby matter clumps represent a dominating component in the local dynamics and kinematics may experience a faster collapse on behalf of the corresponding tidal influence, the latter will also slow down or even prevent a thorough mixing and virialization of the collapsing region. By means of N-body simulations starting from constrained realizations of regions of modest density surrounded by more pronounced massive structures, we have explored the extent to which the large scale tidal fields may indeed suppress the `heating' of the small-scale cosmic velocities. Amongst others we quantify the resulting cosmic flows through the cosmic Mach number. This allows us to draw conclusions about the validity of estimates of global cosmological parameters from local cosmic phenomena and the necessity to take into account the structure and distribution of mass in the local Universe.
Large-scale autostereoscopic outdoor display
Reitterer, Jörg; Fidler, Franz; Saint Julien-Wallsee, Ferdinand; Schmid, Gerhard; Gartner, Wolfgang; Leeb, Walter; Schmid, Ulrich
2013-03-01
State-of-the-art autostereoscopic displays are often limited in size, effective brightness, number of 3D viewing zones, and maximum 3D viewing distances, all of which are mandatory requirements for large-scale outdoor displays. Conventional autostereoscopic indoor concepts like lenticular lenses or parallax barriers cannot simply be adapted for these screens due to the inherent loss of effective resolution and brightness, which would reduce both image quality and sunlight readability. We have developed a modular autostereoscopic multi-view laser display concept with sunlight readable effective brightness, theoretically up to several thousand 3D viewing zones, and maximum 3D viewing distances of up to 60 meters. For proof-of-concept purposes a prototype display with two pixels was realized. Due to various manufacturing tolerances each individual pixel has slightly different optical properties, and hence the 3D image quality of the display has to be calculated stochastically. In this paper we present the corresponding stochastic model, we evaluate the simulation and measurement results of the prototype display, and we calculate the achievable autostereoscopic image quality to be expected for our concept.
Large-scale tides in general relativity
Ip, Hiu Yan; Schmidt, Fabian
2017-02-01
Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the "separate universe" paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effects are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation of Hui and Bertschinger [1]. We also show that this very simple set of equations matches the exact evolution of the density field at second order, but fails at third and higher order. This provides a useful, easy-to-use framework for computing the fully relativistic growth of structure at second order.
Large scale probabilistic available bandwidth estimation
Thouin, Frederic; Rabbat, Michael
2010-01-01
The common utilization-based definition of available bandwidth and many of the existing tools to estimate it suffer from several important weaknesses: i) most tools report a point estimate of average available bandwidth over a measurement interval and do not provide a confidence interval; ii) the commonly adopted models used to relate the available bandwidth metric to the measured data are invalid in almost all practical scenarios; iii) existing tools do not scale well and are not suited to the task of multi-path estimation in large-scale networks; iv) almost all tools use ad-hoc techniques to address measurement noise; and v) tools do not provide enough flexibility in terms of accuracy, overhead, latency and reliability to adapt to the requirements of various applications. In this paper we propose a new definition for available bandwidth and a novel framework that addresses these issues. We define probabilistic available bandwidth (PAB) as the largest input rate at which we can send a traffic flow along a pa...
Gravitational redshifts from large-scale structure
Croft, Rupert A C
2013-01-01
The recent measurement of the gravitational redshifts of galaxies in galaxy clusters by Wojtak et al. has opened a new observational window on dark matter and modified gravity. By stacking clusters this determination effectively used the line of sight distortion of the cross-correlation function of massive galaxies and lower mass galaxies to estimate the gravitational redshift profile of clusters out to 4 Mpc/h. Here we use a halo model of clustering to predict the distortion due to gravitational redshifts of the cross-correlation function on scales from 1 - 100 Mpc/h. We compare our predictions to simulations and use the simulations to make mock catalogues relevant to current and future galaxy redshift surveys. Without formulating an optimal estimator, we find that the full BOSS survey should be able to detect gravitational redshifts from large-scale structure at the ~4 sigma level. Upcoming redshift surveys will greatly increase the number of galaxies useable in such studies and the BigBOSS and Euclid exper...
Food appropriation through large scale land acquisitions
Rulli, Maria Cristina; D'Odorico, Paolo
2014-05-01
The increasing demand for agricultural products and the uncertainty of international food markets has recently drawn the attention of governments and agribusiness firms toward investments in productive agricultural land, mostly in the developing world. The targeted countries are typically located in regions that have remained only marginally utilized because of lack of modern technology. It is expected that in the long run large scale land acquisitions (LSLAs) for commercial farming will bring the technology required to close the existing crops yield gaps. While the extent of the acquired land and the associated appropriation of freshwater resources have been investigated in detail, the amount of food this land can produce and the number of people it could feed still need to be quantified. Here we use a unique dataset of land deals to provide a global quantitative assessment of the rates of crop and food appropriation potentially associated with LSLAs. We show how up to 300-550 million people could be fed by crops grown in the acquired land, should these investments in agriculture improve crop production and close the yield gap. In contrast, about 190-370 million people could be supported by this land without closing of the yield gap. These numbers raise some concern because the food produced in the acquired land is typically exported to other regions, while the target countries exhibit high levels of malnourishment. Conversely, if used for domestic consumption, the crops harvested in the acquired land could ensure food security to the local populations.
Large-scale clustering of cosmic voids
Chan, Kwan Chuen; Hamaus, Nico; Desjacques, Vincent
2014-11-01
We study the clustering of voids using N -body simulations and simple theoretical models. The excursion-set formalism describes fairly well the abundance of voids identified with the watershed algorithm, although the void formation threshold required is quite different from the spherical collapse value. The void cross bias bc is measured and its large-scale value is found to be consistent with the peak background split results. A simple fitting formula for bc is found. We model the void auto-power spectrum taking into account the void biasing and exclusion effect. A good fit to the simulation data is obtained for voids with radii ≳30 Mpc h-1 , especially when the void biasing model is extended to 1-loop order. However, the best-fit bias parameters do not agree well with the peak-background results. Being able to fit the void auto-power spectrum is particularly important not only because it is the direct observable in galaxy surveys, but also our method enables us to treat the bias parameters as nuisance parameters, which are sensitive to the techniques used to identify voids.
Large scale digital atlases in neuroscience
Hawrylycz, M.; Feng, D.; Lau, C.; Kuan, C.; Miller, J.; Dang, C.; Ng, L.
2014-03-01
Imaging in neuroscience has revolutionized our current understanding of brain structure, architecture and increasingly its function. Many characteristics of morphology, cell type, and neuronal circuitry have been elucidated through methods of neuroimaging. Combining this data in a meaningful, standardized, and accessible manner is the scope and goal of the digital brain atlas. Digital brain atlases are used today in neuroscience to characterize the spatial organization of neuronal structures, for planning and guidance during neurosurgery, and as a reference for interpreting other data modalities such as gene expression and connectivity data. The field of digital atlases is extensive and in addition to atlases of the human includes high quality brain atlases of the mouse, rat, rhesus macaque, and other model organisms. Using techniques based on histology, structural and functional magnetic resonance imaging as well as gene expression data, modern digital atlases use probabilistic and multimodal techniques, as well as sophisticated visualization software to form an integrated product. Toward this goal, brain atlases form a common coordinate framework for summarizing, accessing, and organizing this knowledge and will undoubtedly remain a key technology in neuroscience in the future. Since the development of its flagship project of a genome wide image-based atlas of the mouse brain, the Allen Institute for Brain Science has used imaging as a primary data modality for many of its large scale atlas projects. We present an overview of Allen Institute digital atlases in neuroscience, with a focus on the challenges and opportunities for image processing and computation.
Efficient algorithms for large-scale quantum transport calculations
Brück, Sascha; Calderara, Mauro; Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost; Luisier, Mathieu
2017-08-01
Massively parallel algorithms are presented in this paper to reduce the computational burden associated with quantum transport simulations from first-principles. The power of modern hybrid computer architectures is harvested in order to determine the open boundary conditions that connect the simulation domain with its environment and to solve the resulting Schrödinger equation. While the former operation takes the form of an eigenvalue problem that is solved by a contour integration technique on the available central processing units (CPUs), the latter can be cast into a linear system of equations that is simultaneously processed by SplitSolve, a two-step algorithm, on general-purpose graphics processing units (GPUs). A significant decrease of the computational time by up to two orders of magnitude is obtained as compared to standard solution methods.
Developing Large-Scale Bayesian Networks by Composition
National Aeronautics and Space Administration — In this paper, we investigate the use of Bayesian networks to construct large-scale diagnostic systems. In particular, we consider the development of large-scale...
Distributed large-scale dimensional metrology new insights
Franceschini, Fiorenzo; Maisano, Domenico
2011-01-01
Focuses on the latest insights into and challenges of distributed large scale dimensional metrology Enables practitioners to study distributed large scale dimensional metrology independently Includes specific examples of the development of new system prototypes
Nonlinear evolution of large-scale structure in the universe
Energy Technology Data Exchange (ETDEWEB)
Frenk, C.S.; White, S.D.M.; Davis, M.
1983-08-15
Using N-body simulations we study the nonlinear development of primordial density perturbation in an Einstein--de Sitter universe. We compare the evolution of an initial distribution without small-scale density fluctuations to evolution from a random Poisson distribution. These initial conditions mimic the assumptions of the adiabatic and isothermal theories of galaxy formation. The large-scale structures which form in the two cases are markedly dissimilar. In particular, the correlation function xi(r) and the visual appearance of our adiabatic (or ''pancake'') models match better the observed distribution of galaxies. This distribution is characterized by large-scale filamentary structure. Because the pancake models do not evolve in a self-similar fashion, the slope of xi(r) steepens with time; as a result there is a unique epoch at which these models fit the galaxy observations. We find the ratio of cutoff length to correlation length at this time to be lambda/sub min//r/sub 0/ = 5.1; its expected value in a neutrino dominated universe is 4(..cap omega..h)/sup -1/ (H/sub 0/ = 100h km s/sup -1/ Mpc/sup -1/). At early epochs these models predict a negligible amplitude for xi(r) and could explain the lack of measurable clustering in the Ly..cap alpha.. absorption lines of high-redshift quasars. However, large-scale structure in our models collapses after z = 2. If this collapse precedes galaxy formation as in the usual pancake theory, galaxies formed uncomfortably recently. The extent of this problem may depend on the cosmological model used; the present series of experiments should be extended in the future to include models with ..cap omega..<1.
Large Scale Flame Spread Environmental Characterization Testing
Clayman, Lauren K.; Olson, Sandra L.; Gokoghi, Suleyman A.; Brooker, John E.; Ferkul, Paul V.; Kacher, Henry F.
2013-01-01
Under the Advanced Exploration Systems (AES) Spacecraft Fire Safety Demonstration Project (SFSDP), as a risk mitigation activity in support of the development of a large-scale fire demonstration experiment in microgravity, flame-spread tests were conducted in normal gravity on thin, cellulose-based fuels in a sealed chamber. The primary objective of the tests was to measure pressure rise in a chamber as sample material, burning direction (upward/downward), total heat release, heat release rate, and heat loss mechanisms were varied between tests. A Design of Experiments (DOE) method was imposed to produce an array of tests from a fixed set of constraints and a coupled response model was developed. Supplementary tests were run without experimental design to additionally vary select parameters such as initial chamber pressure. The starting chamber pressure for each test was set below atmospheric to prevent chamber overpressure. Bottom ignition, or upward propagating burns, produced rapid acceleratory turbulent flame spread. Pressure rise in the chamber increases as the amount of fuel burned increases mainly because of the larger amount of heat generation and, to a much smaller extent, due to the increase in gaseous number of moles. Top ignition, or downward propagating burns, produced a steady flame spread with a very small flat flame across the burning edge. Steady-state pressure is achieved during downward flame spread as the pressure rises and plateaus. This indicates that the heat generation by the flame matches the heat loss to surroundings during the longer, slower downward burns. One heat loss mechanism included mounting a heat exchanger directly above the burning sample in the path of the plume to act as a heat sink and more efficiently dissipate the heat due to the combustion event. This proved an effective means for chamber overpressure mitigation for those tests producing the most total heat release and thusly was determined to be a feasible mitigation
GPU-based large-scale visualization
Hadwiger, Markus
2013-11-19
Recent advances in image and volume acquisition as well as computational advances in simulation have led to an explosion of the amount of data that must be visualized and analyzed. Modern techniques combine the parallel processing power of GPUs with out-of-core methods and data streaming to enable the interactive visualization of giga- and terabytes of image and volume data. A major enabler for interactivity is making both the computational and the visualization effort proportional to the amount of data that is actually visible on screen, decoupling it from the full data size. This leads to powerful display-aware multi-resolution techniques that enable the visualization of data of almost arbitrary size. The course consists of two major parts: An introductory part that progresses from fundamentals to modern techniques, and a more advanced part that discusses details of ray-guided volume rendering, novel data structures for display-aware visualization and processing, and the remote visualization of large online data collections. You will learn how to develop efficient GPU data structures and large-scale visualizations, implement out-of-core strategies and concepts such as virtual texturing that have only been employed recently, as well as how to use modern multi-resolution representations. These approaches reduce the GPU memory requirements of extremely large data to a working set size that fits into current GPUs. You will learn how to perform ray-casting of volume data of almost arbitrary size and how to render and process gigapixel images using scalable, display-aware techniques. We will describe custom virtual texturing architectures as well as recent hardware developments in this area. We will also describe client/server systems for distributed visualization, on-demand data processing and streaming, and remote visualization. We will describe implementations using OpenGL as well as CUDA, exploiting parallelism on GPUs combined with additional asynchronous
Deep Feature Learning and Cascaded Classifier for Large Scale Data
DEFF Research Database (Denmark)
Prasoon, Adhish
from data rather than having a predefined feature set. We explore deep learning approach of convolutional neural network (CNN) for segmenting three dimensional medical images. We propose a novel system integrating three 2D CNNs, which have a one-to-one association with the xy, yz and zx planes of 3D......This thesis focuses on voxel/pixel classification based approaches for image segmentation. The main application is segmentation of articular cartilage in knee MRIs. The first major contribution of the thesis deals with large scale machine learning problems. Many medical imaging problems need huge...... amount of training data to cover sufficient biological variability. Learning methods scaling badly with number of training data points cannot be used in such scenarios. This may restrict the usage of many powerful classifiers having excellent generalization ability. We propose a cascaded classifier which...
Applications of large-scale density functional theory in biology
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
Deep Feature Learning and Cascaded Classifier for Large Scale Data
DEFF Research Database (Denmark)
Prasoon, Adhish
This thesis focuses on voxel/pixel classification based approaches for image segmentation. The main application is segmentation of articular cartilage in knee MRIs. The first major contribution of the thesis deals with large scale machine learning problems. Many medical imaging problems need huge...... to a state-of-the-art method for cartilage segmentation using one stage nearest neighbour classifier. Our method achieved better results than the state-of-the-art method for tibial as well as femoral cartilage segmentation. The next main contribution of the thesis deals with learning features autonomously...... image, respectively and this system is referred as triplanar convolutional neural network in the thesis. We applied the triplanar CNN for segmenting articular cartilage in knee MRI and compared its performance with the same state-of-the-art method which was used as a benchmark for cascaded classifier...
Performance Health Monitoring of Large-Scale Systems
Energy Technology Data Exchange (ETDEWEB)
Rajamony, Ram [IBM Research, Austin, TX (United States)
2014-11-20
This report details the progress made on the ASCR funded project Performance Health Monitoring for Large Scale Systems. A large-scale application may not achieve its full performance potential due to degraded performance of even a single subsystem. Detecting performance faults, isolating them, and taking remedial action is critical for the scale of systems on the horizon. PHM aims to develop techniques and tools that can be used to identify and mitigate such performance problems. We accomplish this through two main aspects. The PHM framework encompasses diagnostics, system monitoring, fault isolation, and performance evaluation capabilities that indicates when a performance fault has been detected, either due to an anomaly present in the system itself or due to contention for shared resources between concurrently executing jobs. Software components called the PHM Control system then build upon the capabilities provided by the PHM framework to mitigate degradation caused by performance problems.
Synchronization of coupled large-scale Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Li, Fangfei, E-mail: li-fangfei@163.com [Department of Mathematics, East China University of Science and Technology, No. 130, Meilong Road, Shanghai, Shanghai 200237 (China)
2014-03-15
This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.
Synchronization of coupled large-scale Boolean networks
Li, Fangfei
2014-03-01
This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.
Second-order perturbation theory: Problems on large scales
Pound, Adam
2015-11-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time "snapshots" of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.
On the Bending Problem for Large Scale Mapping
Esteban, I.; Booij, O.; Dijk, J.; Groen, F.
2010-01-01
During Simultaneous Localization And Mapping, geometrical constraints are established between map features. These constraints, introduced through measurements and motion prediction, produce a bending effect in the event of closing a large loop. In this paper we present a discussion of the bending pr
On the bending problem for large scale mapping
I. Esteban; O. Booij; J. Dijk; F. Groen
2009-01-01
During Simultaneous Localization And Mapping, geometrical constraints are established between map features. These constraints, introduced through measurements and motion prediction, produce a bending effect in the event of closing a large loop. In this paper we present a discussion of the bending pr
On the bending problem for large scale mapping
Esteban, I.; Booij, O.; Dijk, J.; Groen, F.
2009-01-01
During Simultaneous Localization And Mapping, geometrical constraints are established between map features. These constraints, introduced through measurements and motion prediction, produce a bending effect in the event of closing a large loop. In this paper we present a discussion of the bending
Second-order perturbation theory: problems on large scales
Pound, Adam
2015-01-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long timescales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force ef...
Evaluation of the multi-sums for large scale problems
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, J.; Hasselhuhn, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2012-02-15
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter {epsilon} can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme. (orig.)
Optimal Experimental Design for Large-Scale Bayesian Inverse Problems
Ghattas, Omar
2014-01-06
We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Research Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate expressions. The control parameters are the initial mixture composition and the temperature. The approach is based on first building a polynomial based surrogate model for the observables relevant to the shock tube experiments. Based on these surrogates, a novel MAP based approach is used to estimate the expected information gain in the proposed experiments, and to select the best experimental set-ups yielding the optimal expected information gains. The validity of the approach is tested using synthetic data generated by sampling the PC surrogate. We finally outline a methodology for validation using actual laboratory experiments, and extending experimental design methodology to the cases where the control parameters are noisy.
Optimization of Large-Scale Structural Systems
DEFF Research Database (Denmark)
Jensen, F. M.
solutions to small problems with one or two variables to the optimization of large structures such as bridges, ships and offshore structures. The methods used for salving these problems have evolved from being classical differential calculus and calculus of variation to very advanced numerical techniques...
Large-scale stabilization control of input-constrained quadrotor
Directory of Open Access Journals (Sweden)
Jun Jiang
2016-10-01
Full Text Available The quadrotor has been the most popular aircraft in the last decade due to its excellent dynamics and continues to attract ever-increasing research interest. Delivering a quadrotor from a large fixed-wing aircraft is a promising application of quadrotors. In such an application, the quadrotor needs to switch from a highly unstable status, featured as large initial states, to a safe and stable flight status. This is the so-called large-scale stability control problem. In such an extreme scenario, the quadrotor is at risk of actuator saturation. This can cause the controller to update incorrectly and lead the quadrotor to spiral and crash. In this article, to safely control the quadrotor in such scenarios, the control input constraint is analyzed. The key states of a quadrotor dynamic model are selected, and a two-dimensional dynamic model is extracted based on a symmetrical body configuration. A generalized point-wise min-norm nonlinear control method is proposed based on the Lyapunov function, and large-scale stability control is hence achieved. An enhanced point-wise, min-norm control is further provided to improve the attitude control performance, with altitude performance degenerating slightly. Simulation results showed that the proposed control methods can stabilize the input-constrained quadrotor and the enhanced method can improve the performance of the quadrotor in critical states.
Large-scale Direct Targeting for Drug Repositioning and Discovery
Zheng, Chunli; Guo, Zihu; Huang, Chao; Wu, Ziyin; Li, Yan; Chen, Xuetong; Fu, Yingxue; Ru, Jinlong; Ali Shar, Piar; Wang, Yuan; Wang, Yonghua
2015-01-01
A system-level identification of drug-target direct interactions is vital to drug repositioning and discovery. However, the biological means on a large scale remains challenging and expensive even nowadays. The available computational models mainly focus on predicting indirect interactions or direct interactions on a small scale. To address these problems, in this work, a novel algorithm termed weighted ensemble similarity (WES) has been developed to identify drug direct targets based on a large-scale of 98,327 drug-target relationships. WES includes: (1) identifying the key ligand structural features that are highly-related to the pharmacological properties in a framework of ensemble; (2) determining a drug’s affiliation of a target by evaluation of the overall similarity (ensemble) rather than a single ligand judgment; and (3) integrating the standardized ensemble similarities (Z score) by Bayesian network and multi-variate kernel approach to make predictions. All these lead WES to predict drug direct targets with external and experimental test accuracies of 70% and 71%, respectively. This shows that the WES method provides a potential in silico model for drug repositioning and discovery. PMID:26155766
The large scale magnetic fields of thin accretion disks
Cao, Xinwu
2013-01-01
Large scale magnetic field threading an accretion disk is a key ingredient in the jet formation model. The most attractive scenario for the origin of such a large scale field is the advection of the field by the gas in the accretion disk from the interstellar medium or a companion star. However, it is realized that outward diffusion of the accreted field is fast compared to the inward accretion velocity in a geometrically thin accretion disk if the value of the Prandtl number Pm is around unity. In this work, we revisit this problem considering the angular momentum of the disk is removed predominantly by the magnetically driven outflows. The radial velocity of the disk is significantly increased due to the presence of the outflows. Using a simplified model for the vertical disk structure, we find that even moderately weak fields can cause sufficient angular momentum loss via a magnetic wind to balance outward diffusion. There are two equilibrium points, one at low field strengths corresponding to a plasma-bet...
The combustion behavior of large scale lithium titanate battery
Huang, Peifeng; Wang, Qingsong; Li, Ke; Ping, Ping; Sun, Jinhua
2015-01-01
Safety problem is always a big obstacle for lithium battery marching to large scale application. However, the knowledge on the battery combustion behavior is limited. To investigate the combustion behavior of large scale lithium battery, three 50 Ah Li(NixCoyMnz)O2/Li4Ti5O12 batteries under different state of charge (SOC) were heated to fire. The flame size variation is depicted to analyze the combustion behavior directly. The mass loss rate, temperature and heat release rate are used to analyze the combustion behavior in reaction way deeply. Based on the phenomenon, the combustion process is divided into three basic stages, even more complicated at higher SOC with sudden smoke flow ejected. The reason is that a phase change occurs in Li(NixCoyMnz)O2 material from layer structure to spinel structure. The critical temperatures of ignition are at 112–121°C on anode tab and 139 to 147°C on upper surface for all cells. But the heating time and combustion time become shorter with the ascending of SOC. The results indicate that the battery fire hazard increases with the SOC. It is analyzed that the internal short and the Li+ distribution are the main causes that lead to the difference. PMID:25586064
Large scale dynamics of protoplanetary discs
BÃ©thune, William
2017-08-01
Planets form in the gaseous and dusty disks orbiting young stars. These protoplanetary disks are dispersed in a few million years, being accreted onto the central star or evaporated into the interstellar medium. To explain the observed accretion rates, it is commonly assumed that matter is transported through the disk by turbulence, although the mechanism sustaining turbulence is uncertain. On the other side, irradiation by the central star could heat up the disk surface and trigger a photoevaporative wind, but thermal effects cannot account for the observed acceleration and collimation of the wind into a narrow jet perpendicular to the disk plane. Both issues can be solved if the disk is sensitive to magnetic fields. Weak fields lead to the magnetorotational instability, whose outcome is a state of sustained turbulence. Strong fields can slow down the disk, causing it to accrete while launching a collimated wind. However, the coupling between the disk and the neutral gas is done via electric charges, each of which is outnumbered by several billion neutral molecules. The imperfect coupling between the magnetic field and the neutral gas is described in terms of "non-ideal" effects, introducing new dynamical behaviors. This thesis is devoted to the transport processes happening inside weakly ionized and weakly magnetized accretion disks; the role of microphysical effects on the large-scale dynamics of the disk is of primary importance. As a first step, I exclude the wind and examine the impact of non-ideal effects on the turbulent properties near the disk midplane. I show that the flow can spontaneously organize itself if the ionization fraction is low enough; in this case, accretion is halted and the disk exhibits axisymmetric structures, with possible consequences on planetary formation. As a second step, I study the launching of disk winds via a global model of stratified disk embedded in a warm atmosphere. This model is the first to compute non-ideal effects from
Large-Scale Spacecraft Fire Safety Tests
Urban, David; Ruff, Gary A.; Ferkul, Paul V.; Olson, Sandra; Fernandez-Pello, A. Carlos; T'ien, James S.; Torero, Jose L.; Cowlard, Adam J.; Rouvreau, Sebastien; Minster, Olivier; Toth, Balazs; Legros, Guillaume; Eigenbrod, Christian; Smirnov, Nickolay; Fujita, Osamu; Jomaas, Grunde
2014-01-01
An international collaborative program is underway to address open issues in spacecraft fire safety. Because of limited access to long-term low-gravity conditions and the small volume generally allotted for these experiments, there have been relatively few experiments that directly study spacecraft fire safety under low-gravity conditions. Furthermore, none of these experiments have studied sample sizes and environment conditions typical of those expected in a spacecraft fire. The major constraint has been the size of the sample, with prior experiments limited to samples of the order of 10 cm in length and width or smaller. This lack of experimental data forces spacecraft designers to base their designs and safety precautions on 1-g understanding of flame spread, fire detection, and suppression. However, low-gravity combustion research has demonstrated substantial differences in flame behavior in low-gravity. This, combined with the differences caused by the confined spacecraft environment, necessitates practical scale spacecraft fire safety research to mitigate risks for future space missions. To address this issue, a large-scale spacecraft fire experiment is under development by NASA and an international team of investigators. This poster presents the objectives, status, and concept of this collaborative international project (Saffire). The project plan is to conduct fire safety experiments on three sequential flights of an unmanned ISS re-supply spacecraft (the Orbital Cygnus vehicle) after they have completed their delivery of cargo to the ISS and have begun their return journeys to earth. On two flights (Saffire-1 and Saffire-3), the experiment will consist of a flame spread test involving a meter-scale sample ignited in the pressurized volume of the spacecraft and allowed to burn to completion while measurements are made. On one of the flights (Saffire-2), 9 smaller (5 x 30 cm) samples will be tested to evaluate NASAs material flammability screening tests
Making Predictions using Large Scale Gaussian Processes
National Aeronautics and Space Administration — One of the key problems that arises in many areas is to estimate a potentially nonlinear function [tex] G(x, theta)[/tex] given input and output samples tex [/tex]...
Large Scale Emerging Properties from Non Hamiltonian Complex Systems
Directory of Open Access Journals (Sweden)
Marco Bianucci
2017-06-01
Full Text Available The concept of “large scale” depends obviously on the phenomenon we are interested in. For example, in the field of foundation of Thermodynamics from microscopic dynamics, the spatial and time large scales are order of fraction of millimetres and microseconds, respectively, or lesser, and are defined in relation to the spatial and time scales of the microscopic systems. In large scale oceanography or global climate dynamics problems the time scales of interest are order of thousands of kilometres, for space, and many years for time, and are compared to the local and daily/monthly times scales of atmosphere and ocean dynamics. In all the cases a Zwanzig projection approach is, at least in principle, an effective tool to obtain class of universal smooth “large scale” dynamics for few degrees of freedom of interest, starting from the complex dynamics of the whole (usually many degrees of freedom system. The projection approach leads to a very complex calculus with differential operators, that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, as it happens in Foundation of Thermodynamics problems. However, in geophysical Fluid Dynamics, Biology, and in most of the physical problems the building block fundamental equations of motions have a non Hamiltonian structure. Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. Then we shall apply this formalism to obtain some relevant results concerning the statistical properties of the El Niño Southern Oscillation (ENSO.
Three dimensional large scale aerodynamic shape optimization based on shape calculus
Schmidt, Stephan; Gauger, Nicolas,; Ilic, Caslav; Schulz, Volker
2011-01-01
Large-scale three-dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large-scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended-wing–bod...
A Multilevel Design Method of Large-scale Machine System Oriented Network Environment
Institute of Scientific and Technical Information of China (English)
LI Shuiping; HE Jianjun
2006-01-01
The design of large-scale machine system is a very complex problem. These design problems usually have a lot of design variables and constraints so that they are difficult to be solved rapidly and efficiently by using conventional methods. In this paper, a new multilevel design method oriented network environment is proposed, which maps the design problem of large-scale machine system into a hypergraph with degree of linking strength (DLS) between vertices. By decomposition of hypergraph, this method can divide the complex design problem into some small and simple subproblems that can be solved concurrently in a network.
Kanungo, Bikash; Gavini, Vikram
2017-01-01
We present a computationally efficient approach to perform large-scale all-electron density functional theory calculations by enriching the classical finite element basis with compactly supported atom-centered numerical basis functions that are constructed from the solution of the Kohn-Sham (KS) problem for single atoms. We term these numerical basis functions as enrichment functions, and the resultant basis as the enriched finite element basis. The compact support for the enrichment functions is obtained by using smooth cutoff functions, which enhances the conditioning and maintains the locality of the enriched finite element basis. The integrals involved in the evaluation of the discrete KS Hamiltonian and overlap matrix in the enriched finite element basis are computed using an adaptive quadrature grid that is constructed based on the characteristics of enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by using a blockwise matrix inversion in conjunction with special reduced-order quadrature rules, which is required to transform the discrete Kohn-Sham problem to a standard eigenvalue problem. Finally, we solve the resulting standard eigenvalue problem, in each self-consistent field iteration, by using a Chebyshev polynomial based filtering technique to compute the relevant eigenspectrum. We demonstrate the accuracy, efficiency, and parallel scalability of the proposed method on semiconducting and heavy-metallic systems of various sizes, with the largest system containing 8694 electrons. We obtain accuracies in the ground-state energies that are ˜1 mHa with reference ground-state energies employing classical finite element as well as Gaussian basis sets. Using the proposed formulation based on enriched finite element basis, for accuracies commensurate with chemical accuracy, we observe a staggering 50 -300 -fold reduction in the overall computational time when compared to classical finite element basis. Further, we find a
Large-scale assembly of colloidal particles
Yang, Hongta
This study reports a simple, roll-to-roll compatible coating technology for producing three-dimensional highly ordered colloidal crystal-polymer composites, colloidal crystals, and macroporous polymer membranes. A vertically beveled doctor blade is utilized to shear align silica microsphere-monomer suspensions to form large-area composites in a single step. The polymer matrix and the silica microspheres can be selectively removed to create colloidal crystals and self-standing macroporous polymer membranes. The thickness of the shear-aligned crystal is correlated with the viscosity of the colloidal suspension and the coating speed, and the correlations can be qualitatively explained by adapting the mechanisms developed for conventional doctor blade coating. Five important research topics related to the application of large-scale three-dimensional highly ordered macroporous films by doctor blade coating are covered in this study. The first topic describes the invention in large area and low cost color reflective displays. This invention is inspired by the heat pipe technology. The self-standing macroporous polymer films exhibit brilliant colors which originate from the Bragg diffractive of visible light form the three-dimensional highly ordered air cavities. The colors can be easily changed by tuning the size of the air cavities to cover the whole visible spectrum. When the air cavities are filled with a solvent which has the same refractive index as that of the polymer, the macroporous polymer films become completely transparent due to the index matching. When the solvent trapped in the cavities is evaporated by in-situ heating, the sample color changes back to brilliant color. This process is highly reversible and reproducible for thousands of cycles. The second topic reports the achievement of rapid and reversible vapor detection by using 3-D macroporous photonic crystals. Capillary condensation of a condensable vapor in the interconnected macropores leads to the
Complexity Measurement of Large-Scale Software System Based on Complex Network
Directory of Open Access Journals (Sweden)
Dali Li
2014-05-01
Full Text Available With the increase of software system complexity, the traditional measurements can not meet the requirements, for the reason that the developers need control the software quality effectively and guarantee the normal operation of software system. Hence how to measure the complexity of large-scale software system has been a challenge problem. In order to solve this problem, the developers have to obtain a good method to measure the complexity of software system first. Only through this work, the software quality and the software structure could be controlled and optimized. Note that the complex network theory has offered a new theoretical understanding and a new perspective to solve this kind of complexity problem, this work discusses the complexity phenomenon in large-scale software system. Based on this, some complexity measurements of large-scale software system are put forward from static structure and dynamic structure perspectives. Furthermore, we find some potential complexity characteristics in large-scale software networks through the numerical simulations. The proposed measurement methods have a guiding significance on the development for today's large-scale software system. In addition, this paper presents a new technique for the structural complexity measurements of large-scale software system
Planck intermediate results. XLII. Large-scale Galactic magnetic fields
Adam, R; Alves, M I R; Ashdown, M; Aumont, J; Baccigalupi, C; Banday, A J; Barreiro, R B; Bartolo, N; Battaner, E; Benabed, K; Benoit-Lévy, A; Bernard, J -P; Bersanelli, M; Bielewicz, P; Bonavera, L; Bond, J R; Borrill, J; Bouchet, F R; Boulanger, F; Bucher, M; Burigana, C; Butler, R C; Calabrese, E; Cardoso, J -F; Catalano, A; Chiang, H C; Christensen, P R; Colombo, L P L; Combet, C; Couchot, F; Crill, B P; Curto, A; Cuttaia, F; Danese, L; Davis, R J; de Bernardis, P; de Rosa, A; de Zotti, G; Delabrouille, J; Dickinson, C; Diego, J M; Dolag, K; Doré, O; Ducout, A; Dupac, X; Elsner, F; Enßlin, T A; Eriksen, H K; Ferrière, K; Finelli, F; Forni, O; Frailis, M; Fraisse, A A; Franceschi, E; Galeotta, S; Ganga, K; Ghosh, T; Giard, M; Gjerløw, E; González-Nuevo, J; Górski, K M; Gregorio, A; Gruppuso, A; Gudmundsson, J E; Hansen, F K; Harrison, D L; Hernández-Monteagudo, C; Herranz, D; Hildebrandt, S R; Hobson, M; Hornstrup, A; Hurier, G; Jaffe, A H; Jaffe, T R; Jones, W C; Juvela, M; Keihänen, E; Keskitalo, R; Kisner, T S; Knoche, J; Kunz, M; Kurki-Suonio, H; Lamarre, J -M; Lasenby, A; Lattanzi, M; Lawrence, C R; Leahy, J P; Leonardi, R; Levrier, F; Lilje, P B; Linden-Vørnle, M; López-Caniego, M; Lubin, P M; Macías-Pérez, J F; Maggio, G; Maino, D; Mandolesi, N; Mangilli, A; Maris, M; Martin, P G; Masi, S; Melchiorri, A; Mennella, A; Migliaccio, M; Miville-Deschênes, M -A; Moneti, A; Montier, L; Morgante, G; Munshi, D; Murphy, J A; Naselsky, P; Nati, F; Natoli, P; Nørgaard-Nielsen, H U; Oppermann, N; Orlando, E; Pagano, L; Pajot, F; Paladini, R; Paoletti, D; Pasian, F; Perotto, L; Pettorino, V; Piacentini, F; Piat, M; Pierpaoli, E; Plaszczynski, S; Pointecouteau, E; Polenta, G; Ponthieu, N; Pratt, G W; Prunet, S; Puget, J -L; Rachen, J P; Reinecke, M; Remazeilles, M; Renault, C; Renzi, A; Ristorcelli, I; Rocha, G; Rossetti, M; Roudier, G; Rubiño-Martín, J A; Rusholme, B; Sandri, M; Santos, D; Savelainen, M; Scott, D; Spencer, L D; Stolyarov, V; Stompor, R; Strong, A W; Sudiwala, R; Sunyaev, R; Suur-Uski, A -S; Sygnet, J -F; Tauber, J A; Terenzi, L; Toffolatti, L; Tomasi, M; Tristram, M; Tucci, M; Valenziano, L; Valiviita, J; Van Tent, B; Vielva, P; Villa, F; Wade, L A; Wandelt, B D; Wehus, I K; Yvon, D; Zacchei, A; Zonca, A
2016-01-01
Recent models for the large-scale Galactic magnetic fields in the literature were largely constrained by synchrotron emission and Faraday rotation measures. We select three different but representative models and compare their predicted polarized synchrotron and dust emission with that measured by the Planck satellite. We first update these models to match the Planck synchrotron products using a common model for the cosmic-ray leptons. We discuss the impact on this analysis of the ongoing problems of component separation in the Planck microwave bands and of the uncertain cosmic-ray spectrum. In particular, the inferred degree of ordering in the magnetic fields is sensitive to these systematic uncertainties. We then compare the resulting simulated emission to the observed dust emission and find that the dust predictions do not match the morphology in the Planck data, particularly the vertical profile in latitude. We show how the dust data can then be used to further improve these magnetic field models, particu...
Building a Large-Scale Knowledge Base for Machine Translation
Knight, K; Knight, Kevin; Luk, Steve K.
1994-01-01
Knowledge-based machine translation (KBMT) systems have achieved excellent results in constrained domains, but have not yet scaled up to newspaper text. The reason is that knowledge resources (lexicons, grammar rules, world models) must be painstakingly handcrafted from scratch. One of the hypotheses being tested in the PANGLOSS machine translation project is whether or not these resources can be semi-automatically acquired on a very large scale. This paper focuses on the construction of a large ontology (or knowledge base, or world model) for supporting KBMT. It contains representations for some 70,000 commonly encountered objects, processes, qualities, and relations. The ontology was constructed by merging various online dictionaries, semantic networks, and bilingual resources, through semi-automatic methods. Some of these methods (e.g., conceptual matching of semantic taxonomies) are broadly applicable to problems of importing/exporting knowledge from one KB to another. Other methods (e.g., bilingual match...
Computational solutions to large-scale data management and analysis.
Schadt, Eric E; Linderman, Michael D; Sorenson, Jon; Lee, Lawrence; Nolan, Garry P
2010-09-01
Today we can generate hundreds of gigabases of DNA and RNA sequencing data in a week for less than US$5,000. The astonishing rate of data generation by these low-cost, high-throughput technologies in genomics is being matched by that of other technologies, such as real-time imaging and mass spectrometry-based flow cytometry. Success in the life sciences will depend on our ability to properly interpret the large-scale, high-dimensional data sets that are generated by these technologies, which in turn requires us to adopt advances in informatics. Here we discuss how we can master the different types of computational environments that exist - such as cloud and heterogeneous computing - to successfully tackle our big data problems.
Automatic Installation and Configuration for Large Scale Farms
Novák, J
2005-01-01
Since the early appearance of commodity hardware, the utilization of computers rose rapidly, and they became essential in all areas of life. Soon it was realized that nodes are able to work cooperatively, in order to solve new, more complex tasks. This conception got materialized in coherent aggregations of computers called farms and clusters. Collective application of nodes, being efficient and economical, was adopted in education, research and industry before long. But maintainance, especially in large scale, appeared as a problem to be resolved. New challenges needed new methods and tools. Development work has been started to build farm management applications and frameworks. In the first part of the thesis, these systems are introduced. After a general description of the matter, a comparative analysis of different approaches and tools illustrates the practical aspects of the theoretical discussion. CERN, the European Organization of Nuclear Research is the largest Particle Physics laboratory in the world....