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Sample records for linear scaling solution

  1. Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems

    CERN Document Server

    Rousselet, Bernard

    2013-01-01

    We consider {\\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibration.

  2. 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...

  3. Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

    Directory of Open Access Journals (Sweden)

    Matt Challacombe

    2014-03-01

    Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

  4. FAST SOLUTION FOR LARGE SCALE LINEAR ALGEBRAIC EQUATIONS IN FINITE ELEMENT ANALYSIS

    Institute of Scientific and Technical Information of China (English)

    Qi Zhaohui; Liu Yuqi; Hu Ping

    2001-01-01

    The computational efficiency of numerical solution of linear algebraic equations in finite elements can be improved in tow wqys. One is to decrease the fill-in numbers, which are new non-ze-ro numbers in the matrix of global stiffness generated during the process of elimination.The other is to reduce the computational operation of multiplying a real number by zero.Based on the fact that the order of elimination can determine how many fill-in numbers should be generated, we present a new method for optimization of numbering nodes. This method is quite different from bandwidth optimization. Fill-in numbers can be decreased in a large scale by the use of this method. The bi-factorization method is adoted to avoid multiplying real numbers by zero.For large scale finite element analysis, the method presented in this paper is more efficient than the traditional LDLT method.

  5. Scaled Sparse Linear Regression

    CERN Document Server

    Sun, Tingni

    2011-01-01

    Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual squares and scaling the penalty in proportion to the estimated noise level. The iterative algorithm costs nearly nothing beyond the computation of a path of the sparse regression estimator for penalty levels above a threshold. For the scaled Lasso, the algorithm is a gradient descent in a convex minimization of a penalized joint loss function for the regression coefficients and noise level. Under mild regularity conditions, we prove that the method yields simultaneously an estimator for the noise level and an estimated coefficient vector in the Lasso path satisfying certain oracle inequalities for the estimation of the noise level, prediction, and the estimation of regression coefficients. These oracle inequalities provide sufficient conditions for the consistency and asymptotic...

  6. Combining Linear-Scaling DFT with Subsystem DFT in Born-Oppenheimer and Ehrenfest Molecular Dynamics Simulations: From Molecules to a Virus in Solution.

    Science.gov (United States)

    Andermatt, Samuel; Cha, Jinwoong; Schiffmann, Florian; VandeVondele, Joost

    2016-07-12

    In this work, methods for the efficient simulation of large systems embedded in a molecular environment are presented. These methods combine linear-scaling (LS) Kohn-Sham (KS) density functional theory (DFT) with subsystem (SS) DFT. LS DFT is efficient for large subsystems, while SS DFT is linear scaling with a smaller prefactor for large sets of small molecules. The combination of SS and LS, which is an embedding approach, can result in a 10-fold speedup over a pure LS simulation for large systems in aqueous solution. In addition to a ground-state Born-Oppenheimer SS+LS implementation, a time-dependent density functional theory-based Ehrenfest molecular dynamics (EMD) using density matrix propagation is presented that allows for performing nonadiabatic dynamics. Density matrix-based EMD in the SS framework is naturally linear scaling and appears suitable to study the electronic dynamics of molecules in solution. In the LS framework, linear scaling results as long as the density matrix remains sparse during time propagation. However, we generally find a less than exponential decay of the density matrix after a sufficiently long EMD run, preventing LS EMD simulations with arbitrary accuracy. The methods are tested on various systems, including spectroscopy on dyes, the electronic structure of TiO2 nanoparticles, electronic transport in carbon nanotubes, and the satellite tobacco mosaic virus in explicit solution.

  7. Quantum, classical, and hybrid QM/MM calculations in solution: General implementation of the ddCOSMO linear scaling strategy

    Energy Technology Data Exchange (ETDEWEB)

    Lipparini, Filippo, E-mail: flippari@uni-mainz.de [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); Sorbonne Universités, UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); Sorbonne Universités, UPMC Univ. Paris 06, Institut du Calcul et de la Simulation, F-75005 Paris (France); Scalmani, Giovanni; Frisch, Michael J. [Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492 (United States); Lagardère, Louis [Sorbonne Universités, UPMC Univ. Paris 06, Institut du Calcul et de la Simulation, F-75005 Paris (France); Stamm, Benjamin [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); CNRS, UMR 7598 and 7616, F-75005 Paris (France); Cancès, Eric [Université Paris-Est, CERMICS, Ecole des Ponts and INRIA, 6 and 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2 (France); Maday, Yvon [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); Institut Universitaire de France, Paris, France and Division of Applied Maths, Brown University, Providence, Rhode Island 02912 (United States); Piquemal, Jean-Philip [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); CNRS, UMR 7598 and 7616, F-75005 Paris (France); Mennucci, Benedetta [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)

    2014-11-14

    We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.

  8. A SCALED CENTRAL PATH FOR LINEAR PROGRAMMING

    Institute of Scientific and Technical Information of China (English)

    Ya-xiang Yuan

    2001-01-01

    Interior point methods are very efficient methods for solving large scale linear programming problems. The central path plays a very important role in interior point methods. In this paper we propose a new central path, which scales the variables. Thus it has the advantage of forcing the path to have roughly the same distance from each active constraint boundary near the solution.

  9. Iterative solution of linear systems

    Science.gov (United States)

    Freund, Roland W.; Golub, Gene H.; Nachtigal, Noel M.

    1992-01-01

    Recent advances in the field of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for nonHermitian matrices.

  10. Linear scaling explicitly correlated MP2-F12 and ONIOM methods for the long-range interactions of the nanoscale clusters in methanol aqueous solutions.

    Science.gov (United States)

    Li, Wei

    2013-01-07

    A linear scaling quantum chemistry method, generalized energy-based fragmentation (GEBF) approach has been extended to the explicitly correlated second-order Møller-Plesset perturbation theory F12 (MP2-F12) method and own N-layer integrated molecular orbital molecular mechanics (ONIOM) method, in which GEBF-MP2-F12, GEBF-MP2, and conventional density functional tight-binding methods could be used for different layers. Then the long-range interactions in dilute methanol aqueous solutions are studied by computing the binding energies between methanol molecule and water molecules in gas-phase and condensed phase methanol-water clusters with various sizes, which were taken from classic molecular dynamics (MD) snapshots. By comparing with the results of force field methods, including SPC, TIP3P, PCFF, and AMOEBA09, the GEBF-MP2-F12 and GEBF-ONIOM methods are shown to be powerful and efficient for studying the long-range interactions at a high level. With the GEBF-ONIOM(MP2-F12:MP2) and GEBF-ONIOM(MP2-F12:MP2:cDFTB) methods, the diameters of the largest nanoscale clusters under studies are about 2.4 nm (747 atoms and 10 209 basis functions with aug-cc-pVDZ basis set) and 4 nm (3351 atoms), respectively, which are almost impossible to be treated by conventional MP2 or MP2-F12 method. Thus, the GEBF-F12 and GEBF-ONIOM methods are expected to be a practical tool for studying the nanoscale clusters in condensed phase, providing an alternative benchmark for ab initio and density functional theory studies, and developing new force fields by combining with classic MD simulations.

  11. Exact Solutions in Nonlocal Linear Models

    OpenAIRE

    Vernov, S. Yu.

    2008-01-01

    A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.

  12. Preface: Introductory Remarks: Linear Scaling Methods

    Science.gov (United States)

    Bowler, D. R.; Fattebert, J.-L.; Gillan, M. J.; Haynes, P. D.; Skylaris, C.-K.

    2008-07-01

    implementation questions relating to parallelization (particularly with multi-core processors starting to dominate the market) and inherent scaling and basis sets (in both normal and linear scaling codes). For now, the answer seems to lie between 100-1,000 atoms, though this depends on the type of simulation used among other factors. Basis sets are still a problematic question in the area of electronic structure calculations. The linear scaling community has largely split into two camps: those using relatively small basis sets based on local atomic-like functions (where systematic convergence to the full basis set limit is hard to achieve); and those that use necessarily larger basis sets which allow convergence systematically and therefore are the localised equivalent of plane waves. Related to basis sets is the study of Wannier functions, on which some linear scaling methods are based and which give a good point of contact with traditional techniques; they are particularly interesting for modelling unoccupied states with linear scaling methods. There are, of course, as many approaches to linear scaling solution for the density matrix as there are groups in the area, though there are various broad areas: McWeeny-based methods, fragment-based methods, recursion methods, and combinations of these. While many ideas have been in development for several years, there are still improvements emerging, as shown by the rich variety of the talks below. Applications using O(N) DFT methods are now starting to emerge, though they are still clearly not trivial. Once systems to be simulated cross the 10,000 atom barrier, only linear scaling methods can be applied, even with the most efficient standard techniques. One of the most challenging problems remaining, now that ab initio methods can be applied to large systems, is the long timescale problem. Although much of the work presented was concerned with improving the performance of the codes, and applying them to scientificallyimportant

  13. Linear Rheology of Guar Gum Solutions

    NARCIS (Netherlands)

    Wientjes, Roland H.W.; Duits, Michel H.G.; Jongschaap, Rob J.J.; Mellema, Jorrit

    2000-01-01

    We have investigated the linear viscoelastic behavior of guar gum solutions as a function of frequency, temperature, polymer concentration, and molecular weight. This was done to sort out the importance of different relaxation mechanisms like reptation or the breakup of physical bonds. In the kilohe

  14. PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    FEIGUIHUA; QIUQINGJIU

    1997-01-01

    The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.

  15. Optical systolic solutions of linear algebraic equations

    Science.gov (United States)

    Neuman, C. P.; Casasent, D.

    1984-01-01

    The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

  16. A new class of scale free solutions to linear ordinary differential equations and the universality of the golden mean (Radical radicand 5 -1)/2=0.618033...

    CERN Document Server

    Datta, D P

    2003-01-01

    A new class of finitely differentiable scale free solutions to the simplest class of ordinary differential equations is presented. Consequently, the real number set gets replaced by an extended physical set, each element of which is endowed with an equivalence class of infinitesimally separated neighbours in the form of random fluctuations. We show how a sense of time and evolution is intrinsically defined by the infinite continued fraction of the golden mean irrational number (Radical radicand 5 -1)/2, which plays a key role in this extended SL(2,R) formalism of calculus analogous to El Naschie's theory of E sup ( supinfinity sup ) spacetime manifold. Time may thereby undergo random inversions generating well defined random scales, thus allowing a dynamical system to evolve self similarly over the set of multiple scales. The late time stochastic fluctuations of a dynamical system enjoys the generic 1/f spectrum. A universal form of the related probability density is also derived. We prove that the golden mea...

  17. Developments and trends in the parallel solution of linear systems

    NARCIS (Netherlands)

    Duff, I.S.; Vorst, H.A. van der

    2001-01-01

    In this review paper, we consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism. We briefly discuss the solution of dense linear systems, before studying the solution of sparse eq

  18. Minimal solution of singular LR fuzzy linear systems.

    Science.gov (United States)

    Nikuie, M; Ahmad, M Z

    2014-01-01

    In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.

  19. On almost automorphic solutions of linear operational-differential equations

    Directory of Open Access Journals (Sweden)

    Gaston M. N'Guérékata

    2004-01-01

    Full Text Available We prove almost periodicity and almost automorphy of bounded solutions of linear differential equations x′(t=Ax(t+f(t for some class of linear operators acting in a Banach space.

  20. Solution Methods for Stochastic Dynamic Linear Programs.

    Science.gov (United States)

    1980-12-01

    Linear Programming, IIASA , Laxenburg, Austria, June 2-6, 1980. [2] Aghili, P., R.H., Cramer and H.W. Thompson, "On the applicability of two- stage...Laxenburg, Austria, May, 1978. [52] Propoi, A. and V. Krivonozhko, ’The simplex method for dynamic linear programs", RR-78-14, IIASA , Vienna, Austria

  1. On Alternative Optimal Solutions to Linear Fractional Optimization Problems

    Institute of Scientific and Technical Information of China (English)

    ShengjiaXue

    2004-01-01

    The structure of the optimal solution set is derived for linear fractional optimization problems with the representation theorem of polyhedral sets.And the computational procedure in determining all optimal solutions is also given.

  2. Linear scaling algorithms: Progress and promise

    Energy Technology Data Exchange (ETDEWEB)

    Stechel, E.B.

    1996-08-01

    The goal of this laboratory-directed research and development (LDRD) project was to develop a new and efficient electronic structure algorithm that would scale linearly with system size. Since the start of the program this field has received much attention in the literature as well as in terms of focused symposia and at least one dedicated international workshop. The major success of this program is the development of a unique algorithm for minimization of the density functional energy which replaces the diagonalization of the Kohn-Sham hamiltonian with block diagonalization into explicit occupied and partially occupied (in metals) subspaces and an implicit unoccupied subspace. The progress reported here represents an important step toward the simultaneous goals of linear scaling, controlled accuracy, efficiency and transferability. The method is specifically designed to deal with localized, non-orthogonal basis sets to maximize transferability and state by state iteration to minimize any charge-sloshing instabilities and accelerate convergence. The computational demands of the algorithm do scale as the particle number, permitting applications to problems involving many inequivalent atoms. Our targeted goal is at least 10,000 inequivalent atoms on a teraflop computer. This report describes our algorithm, some proof-of-principle examples and a state of the field at the conclusion of this LDRD.

  3. A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

    Science.gov (United States)

    Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

    1992-01-01

    The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

  4. Piecewise polynomial solutions to linear inverse problems

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Mosegaard, K.

    1996-01-01

    We have presented a new algorithm PP-TSVD that computes piecewise polynomial solutions to ill-posed problems, without a priori knowledge about the positions of the break points. In particular, we can compute piecewise constant functions that describe layered models. Such solutions are useful, e.g.......g., in seismological problems, and the algorithm can also be used as a preprocessor for other methods where break points/discontinuities must be incorporated explicitly....

  5. Minimal solution of general dual fuzzy linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of)], E-mail: abbasbandy@yahoo.com; Otadi, M.; Mosleh, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh (Iran, Islamic Republic of)

    2008-08-15

    Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered.

  6. The nature of solutions to linear passive complementarity systems

    NARCIS (Netherlands)

    Camlibel, Mehmet; Heemels, W.P.M.H.; Schumacher, J.M.

    1999-01-01

    Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the

  7. 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.

  8. Iterative solution of large linear systems

    CERN Document Server

    Young, David M

    2003-01-01

    This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth

  9. Scaling Laws for $e^+ e^-$ Linear Colliders

    CERN Document Server

    Delahaye, J P; Raubenheimer, T O; Wilson, Ian H

    1999-01-01

    Design studies of a future TeV e+e- Linear Collider (TLC) are presently being made by five major laboratories within the framework of a world-wide collaboration. A figure of merit is defined which enables an objective comparison of these different designs. This figure of merit is shown to depend only on a small number of parameters. General scaling laws for the main beam parameters and linac parameters are derived and prove to be very effective when used as guidelines to optimize the linear collider design. By adopting appropriate parameters for beam stability, the figure of merit becomes nearly independent of accelerating gradient and RF frequency of the accelerating structures. In spite of the strong dependence of the wake-fields with frequency, the single bunch emittance preservation during acceleration along the linac is also shown to be independent of the RF frequency when using equivalent trajectory correction schemes. In this situation, beam acceleration using high frequency structures becomes very adv...

  10. ON MEROMORPHIC SOLUTIONS OF RICCATI AND LINEAR DIFFERENCE EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Ranran ZHANG; Zongxuan CHEN

    2013-01-01

    In this paper, meromorphic solutions of Riccati and linear difference equations are investigated. The growth and Borel exceptional values of these solutions are discussed, and the growth, zeros and poles of differences of these solutions are also investigated. Furthermore, several examples are given showing that our results are best possible in certain senses.

  11. The Uniqueness of Optimal Solution for Linear Programming Problem

    Institute of Scientific and Technical Information of China (English)

    QuanlingWei; HongYan; JunWang

    2004-01-01

    This paper investigates an old problem in operations research, the uniqueness of the optimal solution to a linear programming problem. We discuss the problem on a general polyhedron, give some equivalent conditions for uniqueness testing. In addition, we discuss the implementation issues for linear programming based decision making procedures,which motivated this research.

  12. Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System

    Directory of Open Access Journals (Sweden)

    Yue-Wen Cheng

    2013-01-01

    Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.

  13. A Novel Weak Fuzzy Solution for Fuzzy Linear System

    Directory of Open Access Journals (Sweden)

    Soheil Salahshour

    2016-03-01

    Full Text Available This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.

  14. Generating exact solutions to Einstein's equation using linearized approximations

    Science.gov (United States)

    Harte, Abraham I.; Vines, Justin

    2016-10-01

    We show that certain solutions to the linearized Einstein equation can—by the application of a particular type of linearized gauge transformation—be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.

  15. Generating exact solutions to Einstein's equation using linearized approximations

    CERN Document Server

    Harte, Abraham I

    2016-01-01

    We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.

  16. Oscillatory solutions of the Cauchy problem for linear differential equations

    Directory of Open Access Journals (Sweden)

    Gro Hovhannisyan

    2015-06-01

    Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

  17. ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

    Institute of Scientific and Technical Information of China (English)

    Xue Shengjia

    2007-01-01

    In this paper, the nonlinear programming problem with quasimonotonic ( both quasiconvex and quasiconcave )objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method,the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.

  18. Non-Liouvillian solutions for second order linear ODEs

    OpenAIRE

    Chan, L; Cheb-Terrab,E. S.

    2004-01-01

    There exist sound literature and algorithms for computing Liouvillian solutions for the important problem of linear ODEs with rational coefficients. Taking as sample the 363 second order equations of that type found in Kamke's book, for instance, 51 % of them admit Liouvillian solutions and so are solvable using Kovacic's algorithm. On the other hand, special function solutions not admitting Liouvillian form appear frequently in mathematical physics, but there are not so general algorithms fo...

  19. Analytical exact solution of the non-linear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica

    2011-07-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  20. Parallel preconditioning for the solution of nonsymmetric banded linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Amodio, P.; Mazzia, F. [Universita di Bari (Italy)

    1994-12-31

    Many computational techniques require the solution of banded linear systems. Common examples derive from the solution of partial differential equations and of boundary value problems. In particular the authors are interested in the parallel solution of block Hessemberg linear systems Gx = f, arising from the solution of ordinary differential equations by means of boundary value methods (BVMs), even if the considered preconditioning may be applied to any block banded linear system. BVMs have been extensively investigated in the last few years and their stability properties give promising results. A new class of BVMs called Reverse Adams, which are BV-A-stable for orders up to 6, and BV-A{sub 0}-stable for orders up to 9, have been studied.

  1. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  2. Out-of-Core Solutions of Complex Sparse Linear Equations

    Science.gov (United States)

    Yip, E. L.

    1982-01-01

    ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.

  3. Fundamental solutions of linear partial differential operators theory and practice

    CERN Document Server

    Ortner, Norbert

    2015-01-01

    This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics...

  4. A Note on Solutions for Asymptotically Linear Elliptic Systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, we axe concerned with the elliptic system of -△u+V(x)u=g(=x,v),x=∈RN,-△v+V(x)v=f(x, u), x∈RN, where V(x) is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods.

  5. Algebraic Framework for Linear and Morphological Scale-Spaces

    NARCIS (Netherlands)

    Heijmans, H.J.A.M.; van den Boomgaard, R.

    2002-01-01

    This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to first downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and finally resize the image to its original scale

  6. Scaling solutions for dilaton quantum gravity

    Directory of Open Access Journals (Sweden)

    T. Henz

    2017-06-01

    The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.

  7. Scaling behavior of linear polymers in disordered media

    OpenAIRE

    Janssen, Hans-Karl; Stenull, Olaf

    2006-01-01

    Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks Folklore has, that the universal scaling properties of linear polymers in disordered media are well described by the statistics of self-avoiding walks (SAWs) on percolation clusters and their critical exponent $\

  8. Periodic solutions and flip bifurcation in a linear impulsive system

    Institute of Scientific and Technical Information of China (English)

    Jiang Gui-Rong; Yang Qi-Gui

    2008-01-01

    In this paper,the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically.The existence and the stability of period-one solution are discussed by using a discrete map.The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters.Moreover,the periodic solutions,the bifurcation diagram,and the chaotic attractor,which show their consistence with the theoretical analyses,are given in an example.中图分类:O547

  9. Exact solution of some linear matrix equations using algebraic methods

    Science.gov (United States)

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  10. Initial data generating bounded solutions of linear discrete equations

    Directory of Open Access Journals (Sweden)

    Jaromír Baštinec

    2006-01-01

    Full Text Available A lot of papers are devoted to the investigation of the problem of prescribed behavior of solutions of discrete equations and in numerous results sufficient conditions for existence of at least one solution of discrete equations having prescribed asymptotic behavior are indicated. Not so much attention has been paid to the problem of determining corresponding initial data generating such solutions. We fill this gap for the case of linear equations in this paper. The initial data mentioned are constructed with use of two convergent monotone sequences. An illustrative example is considered, too.

  11. Linear iterative technique for solution of nonlinear thermal network problems

    Energy Technology Data Exchange (ETDEWEB)

    Seabourn, C.M.

    1976-11-01

    A method for rapid and accurate solution of linear and/or nonlinear thermal network problems is described. It is a matrix iterative process that converges for nodal temperatures and variations of thermal conductivity with temperature. The method is computer oriented and can be changed easily for design studies.

  12. Robust Solutions for Systems of Uncertain Linear Equations

    NARCIS (Netherlands)

    Zhen, Jianzhe; den Hertog, Dick

    2015-01-01

    Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection

  13. MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.

  14. Minimal solution of linear formed fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    Maryam Mosleh

    2012-10-01

    Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

  15. An iterative decoupling solution method for large scale Lyapunov equations

    Science.gov (United States)

    Athay, T. M.; Sandell, N. R., Jr.

    1976-01-01

    A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

  16. An iterative decoupling solution method for large scale Lyapunov equations

    Science.gov (United States)

    Athay, T. M.; Sandell, N. R., Jr.

    1976-01-01

    A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

  17. The solution space geometry of random linear equations

    CERN Document Server

    Achlioptas, Dimitris

    2011-01-01

    We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In particular, we prove that with probability that tends to 1 as the number of variables, n, grows: for every pair of solutions \\sigma, \\tau, either there exists a sequence of solutions \\sigma,...,\\tau, in which successive elements differ by O(log n) variables, or every sequence of solutions \\sigma,...,\\tau, contains a step requiring the simultaneous change of \\Omega(n) variables. Furthermore, we determine precisely which pairs of solutions are in each category. Our results are tight and highly quantitative in nature. Moreover, our proof highlights the role of unique extendability as the driving force behind the success of Low Density Parity Check codes and our techniques also apply to the problem of so-called pseudo-codewords in such codes.

  18. Decentralised stabilising controllers for a class of large-scale linear systems

    Indian Academy of Sciences (India)

    B C Jha; K Patralekh; R Singh

    2000-12-01

    A simple method for computing decentralised stabilising controllers for a class of large-scale (interconnected) linear systems has been developed. Decentralised controls are optimal controls at subsystem level and are generated from the solution of algebraic Riccati equations for decoupled subsystems resulting from a new aggregation-decomposition technique. The method has been illustrated through a numerical example of a large-scale linear system consisting of three subsystems each of the fourth order.

  19. Solution of the Linear and Non-linear Partial Differential Equations Using Homotopy Perturbation Method

    Directory of Open Access Journals (Sweden)

    Abaker. A. Hassaballa.

    2015-10-01

    Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.

  20. THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION BTXB=D ON LINEAR MANIFOLDS

    Institute of Scientific and Technical Information of China (English)

    邓远北; 胡锡炎; 张磊

    2003-01-01

    This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.

  1. SOLUTION OF A KIND OF LINEAR INTERNAL WAVE EQUATION

    Institute of Scientific and Technical Information of China (English)

    WANG Gang; HOU Yi-jun; ZHENG Quan-an

    2005-01-01

    Considering the effect of horizontal Coriolis parameter and the density compactness of seawater, which were often neglected in internal waves discussion, the governing equation of linear internal waves presented by vertical velocity only will be proposed. Under the assumption that the Brunt-Visl frequency is exponential, an accurate analytic solution of it is obtained. Finally, the expressions of wave functions are also given.

  2. PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    马世旺; 王志成; 许强

    2004-01-01

    Consider the linear neutral FDEd/dt[x(t)+ Ax(t -7)] =∫R[dL(8)]x(t+s)+f(t)where x and f are n-dimensional vectors;A is an n×n constant matrix and L(s) is an n×n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.

  3. Good Linear Operators and Meromorphic Solutions of Functional Equations

    Directory of Open Access Journals (Sweden)

    Nan Li

    2015-01-01

    Full Text Available Nevanlinna theory provides us with many tools applicable to the study of value distribution of meromorphic solutions of differential equations. Analogues of some of these tools have been recently developed for difference, q-difference, and ultradiscrete equations. In many cases, the methodologies used in the study of meromorphic solutions of differential, difference, and q-difference equations are largely similar. The purpose of this paper is to collect some of these tools in a common toolbox for the study of general classes of functional equations by introducing notion of a good linear operator, which satisfies certain regularity conditions in terms of value distribution theory. As an example case, we apply our methods to study the growth of meromorphic solutions of the functional equation M(z,f+P(z,f=h(z, where M(z,f is a linear polynomial in f and L(f, where L is good linear operator, P(z,f is a polynomial in f with degree deg P≥2, both with small meromorphic coefficients, and h(z is a meromorphic function.

  4. Hopewell Furnace NHS Small Scale Features (Linear Features)

    Data.gov (United States)

    National Park Service, Department of the Interior — This shapefile represents the linear small scale features found at Hopewell Furnace National Historic Site based on the Cultural Landscape Report completed in...

  5. Analysis of linear trade models and relation to scale economies.

    Science.gov (United States)

    Gomory, R E; Baumol, W J

    1997-09-01

    We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

  6. Non-linear Frequency Scaling Algorithm for FMCW SAR Data

    NARCIS (Netherlands)

    Meta, A.; Hoogeboom, P.; Ligthart, L.P.

    2006-01-01

    This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran

  7. An Efficient Parallel Solution Framework for the Linear Solution of Large Systems on PC Clusters

    Institute of Scientific and Technical Information of China (English)

    Ozgur Kurc; Semih Ozmen

    2008-01-01

    In this paper,a parallel solution framework for the linear static analysis of large structures on PC clusters is presented.The framework consists of two main steps:data preparation and parallel solution.The parallel solution is performed by a substructure based method with direct solvers.The aim of the data prepa-ration step is to create the best possible substructures so that the parallel solution time is minimized.An ac-tual structural model was solved utilizing both homogeneous and heterogeneous PC clusters to illustrate the performance and applicability of the presented framework.

  8. Mathematical models of non-linear phenomena, processes and systems: from molecular scale to planetary atmosphere

    CERN Document Server

    2013-01-01

    This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.

  9. The linear stability of the Schwarzschild solution to gravitational perturbations

    CERN Document Server

    Dafermos, Mihalis; Rodnianski, Igor

    2016-01-01

    We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to a linearised Kerr metric. We express the equations in a suitable double null gauge. To obtain decay, one must in fact add a residual pure gauge solution which we prove to be itself quantitatively controlled from initial data. Our result a fortiori includes decay statements for general solutions of the Teukolsky equation (satisfied by gauge-invariant null-decomposed curvature components). These latter statements are in fact deduced in the course of the proof by exploiting associated quantities shown to satisfy the Regge--Wheeler equation, for which appropriate decay can be obtained easily by adapting previous work on the linear scalar wave equation. The bounds on the rate of decay to linearised ...

  10. Error estimates for asymptotic solutions of dynamic equations on time scales

    Directory of Open Access Journals (Sweden)

    Gro Hovhannisyan

    2007-02-01

    Full Text Available We establish error estimates for first-order linear systems of equations and linear second-order dynamic equations on time scales by using calculus on a time scales [1,4,5] and Birkhoff-Levinson's method of asymptotic solutions [3,6,8,9].

  11. Diffusive Motion of Linear Microgel Assemblies in Solution

    Directory of Open Access Journals (Sweden)

    Marco-Philipp Schürings

    2016-11-01

    Full Text Available Due to the ability of microgels to rapidly contract and expand in response to external stimuli, assemblies of interconnected microgels are promising for actuation applications, e.g., as contracting fibers for artificial muscles. Among the properties determining the suitability of microgel assemblies for actuation are mechanical parameters such as bending stiffness and mobility. Here, we study the properties of linear, one-dimensional chains of poly(N-vinylcaprolactam microgels dispersed in water. They were fabricated by utilizing wrinkled surfaces as templates and UV-cross-linking the microgels. We image the shapes of the chains on surfaces and in solution using atomic force microscopy (AFM and fluorescence microscopy, respectively. In solution, the chains are observed to execute translational and rotational diffusive motions. Evaluation of the motions yields translational and rotational diffusion coefficients and, from the translational diffusion coefficient, the chain mobility. The microgel chains show no perceptible bending, which yields a lower limit on their bending stiffness.

  12. QUALITATIVE BEHAVIORS OF LINEAR TIME-INVARIANT DYNAMIC EQUATIONS ON TIME SCALES

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We investigate the type of singularity and qualitative structure of solutions to a time-invariant linear dynamic system on time scales. The results truly unify the qualitative behaviors of the system on the continuous and discrete times with any step size.

  13. Linear Scaling Real Time TDDFT in the CONQUEST Code

    CERN Document Server

    O'Rourke, Conn

    2014-01-01

    The real time formulation of Time Dependent Density Functional Theory (RT-TDDFT) is implemented in the linear scaling density functional theory code CONQEST. Proceeding through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals, it is possible to reduced the computational workload. Imposing a cut-off on the density matrix the effort can be made to scale linearly with the size of the system under study. Propagation of the reduced density matrix in this manner provides direct access to the optical response of very large systems, which would be otherwise impractical to obtain using the standard formulations of TDDFT. We discuss our implementation and present several benchmark tests illustrating the validity of the method, and the factors affecting its accuracy. Finally we illustrate the effect of density matrix truncation on the optical response, and illustrate that computational load scales linearly with the system size.

  14. Augmented Arnoldi-Tikhonov Regularization Methods for Solving Large-Scale Linear Ill-Posed Systems

    Directory of Open Access Journals (Sweden)

    Yiqin Lin

    2013-01-01

    Full Text Available We propose an augmented Arnoldi-Tikhonov regularization method for the solution of large-scale linear ill-posed systems. This method augments the Krylov subspace by a user-supplied low-dimensional subspace, which contains a rough approximation of the desired solution. The augmentation is implemented by a modified Arnoldi process. Some useful results are also presented. Numerical experiments illustrate that the augmented method outperforms the corresponding method without augmentation on some real-world examples.

  15. Scaling and linear response in the GOY model

    NARCIS (Netherlands)

    Kadanoff, Leo; Lohse, Detlef; Schörghofer, Norbert

    1997-01-01

    The GOY model is a model for turbulence in which two conserved quantities cascade up and down a linear array of shells. When the viscosity parameter, small nu, Greek, is small the model has a qualitative behavior which is similar to the Kolmogorov theories of turbulence. Here a static solution to th

  16. Bringing nature-based solutions to scale

    Science.gov (United States)

    Jongman, Brenden; Lange, Glenn-Marie; Balog, Simone; van Wesenbeeck, Bregje

    2017-04-01

    Coastal communities in developing countries are highly exposed and vulnerable to coastal flood risk, and are likely to suffer from climate change induced changes in risk. Over the last decade, strong evidence has surfaced that nature-based solutions or ecosystem-based approaches are efficient and effective alternatives for flood risk reduction and climate change adaptation. In developing countries, numerous projects have therefore been implemented, often driven by international donors and NGOs. Some of these projects have been successful in reducing risk while improving environmental and socioeconomic conditions. However, the feasibility assessment, design and implementation of nature-based solutions is a multifaceted process, which needs to be well-understood before such solutions can be effectively implemented as an addition or alternative to grey infrastructure. This process has not always been followed. As a result, many projects have failed to deliver positive outcomes. The international community therefore has a challenge in bringing nature-based solutions to scale in an effective way. In this presentation, we will present best practice guidelines on nature-based solution implementation that are currently being discussed by the international community. Furthermore, we will present the alpha version of a new web platform being developed by the World Bank that will serve as a much-needed central repository for project information on nature-based solutions, and that will host actionable implementation guidelines. The presentation will also serve as an invitation to the scientific community to share their experience and lessons learned, and contribute to the outlining of best practice guidance.

  17. Polarization properties of linearly polarized parabolic scaling Bessel beams

    Science.gov (United States)

    Guo, Mengwen; Zhao, Daomu

    2016-10-01

    The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge.

  18. Thermodynamic Properties of Linear Protein Solutions: an Application to Type Ⅰ Antifreeze Protein Solutions

    Institute of Scientific and Technical Information of China (English)

    LI Li-fen; LIANG Xi-xia; LI Qian-zhong

    2012-01-01

    A statistical thermodynamic theory of linear protein solutions was proposed with the aid of a lattice model and applied to type Ⅰ antifreeze protein(AFPI) solutions.The numerical results for several AFPI solutions show that the Gibbs function of the solution has a minimum at a certain protein concentration,but the protein chemical potential increases with increasing the concentration.The influences of temperature and protein chain length on the AFPI chemical potential were also discussed.The evaluation for the colligative depression of the freezing point confirms that the antifreeze action should be recognized as non-colligative.The theoretical deduction for the concentration dependence of the thermal hysteresis activity coincides qualitatively with the previous experimental and theoretical results.

  19. Linear homotopy solution of nonlinear systems of equations in geodesy

    Science.gov (United States)

    Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.

    2010-01-01

    A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.

  20. General Explicit Solution of Planar Weakly Delayed Linear Discrete Systems and Pasting Its Solutions

    Directory of Open Access Journals (Sweden)

    Josef Diblík

    2014-01-01

    Full Text Available Planar linear discrete systems with constant coefficients and delays x(k+1=Ax(k+∑l=1n‍Blxl(k-ml are considered where k∈ℤ0∞:={0,1,…,∞}, m1,m2,…,mn are constant integer delays, 0solutions with a given starting dimension 2(mn+1 is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.

  1. Suppressing Linear Power on Dwarf Galaxy Halo Scales

    CERN Document Server

    White, M; White, Martin; Croft, Rupert A.C.

    2000-01-01

    Recently is has been suggested that the dearth of small halos around the Milky Way arises due to a modification of the primordial power spectrum of fluctuations from inflation. Such modifications would be expected to alter the formation of structure from bottom-up to top-down on scales near where the short-scale power has been suppressed. Using cosmological simulations we study the effects of such a modification of the initial power spectrum. While the halo multiplicity function depends primarily on the linear theory power spectrum, most other probes of power are more sensitive to the non-linear power spectrum. Collapse of large-scale structures as they go non-linear regenerates a ``tail'' in the power spectrum, masking small-scale modifications to the primordial power spectrum except at very high-z. Even the small-scale (k>2h/Mpc) clustering of the Ly-alpha forest is affected by this process, so that CDM models with sufficient power suppression to reduce the number of 10^10 Msun halos by a factor of about 5 ...

  2. Solutions of Multi Objective Fuzzy Transportation Problems with Non-Linear Membership Functions

    Directory of Open Access Journals (Sweden)

    Dr. M. S. Annie Christi

    2016-11-01

    Full Text Available Multi-objective transportation problem with fuzzy interval numbers are considered. The solution of linear MOTP is obtained by using non-linear membership functions. The optimal compromise solution obtained is compared with the solution got by using a linear membership function. Some numerical examples are presented to illustrate this.

  3. Estimating WISC-IV indexes: proration versus linear scaling.

    Science.gov (United States)

    Glass, Laura A; Ryan, Joseph J; Bartels, Jared M; Morris, Jeri

    2008-10-01

    This investigation compared proration and linear scaling for estimating Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) verbal comprehension (VCI) and perceptual reasoning (PRI) composites from all relevant two subtest combinations. Using 57 primary school students and 41 clinical referrals, actual VCI and PRI scores were highly correlated with estimated index scores based on proration and linear scaling (all rs> or =.90). In the school sample, significant mean score differences between the actual and estimated composites were found in two comparisons; however, differences between mean scores were less than three points. No significant differences emerged in the clinical sample. Results indicate that any of the two subtest combinations produced reasonably accurate estimates of actual indexes. There was no advantage of one computational method over the other. Copyright 2008 Wiley Periodicals, Inc.

  4. Scaling Linear Algebra Kernels using Remote Memory Access

    Energy Technology Data Exchange (ETDEWEB)

    Krishnan, Manoj Kumar; Lewis, Robert R.; Vishnu, Abhinav

    2010-09-13

    This paper describes the scalability of linear algebra kernels based on remote memory access approach. The current approach differs from the other linear algebra algorithms by the explicit use of shared memory and remote memory access (RMA) communication rather than message passing. It is suitable for clusters and scalable shared memory systems. The experimental results on large scale systems (Linux-Infiniband cluster, Cray XT) demonstrate consistent performance advantages over ScaLAPACK suite, the leading implementation of parallel linear algebra algorithms used today. For example, on a Cray XT4 for a matrix size of 102400, our RMA-based matrix multiplication achieved over 55 teraflops while ScaLAPACK’s pdgemm measured close to 42 teraflops on 10000 processes.

  5. Digital deblurring based on linear-scale differential analysis

    Science.gov (United States)

    Bezzubik, Vitali; Belashenkov, Nikolai; Vdovin, Gleb V.

    2014-09-01

    A novel method of sharpness improvement is proposed for digital images. This method is realized via linear multi-scale analysis of source image and sequent synthesis of restored image. The analysis comprises the procedure of computation of intensity gradient values using the special filters providing simultaneous edge detection and noise filtering. Restoration of image sharpness is achieved by simple subtraction of some discrete recovery function from blurred image. Said recovery function is calculated as a sum of several normalized gradient responses found by linear multi-scale analysis using the operation of spatial transposition of those gradient response values relative the points of zero-crossing of first derivatives of gradients. The proposed method provides the restoration of sharpness of edges in digital image without additional operation of spatial noise filtering and a priori knowledge of blur kernel.

  6. Polarization properties of linearly polarized parabolic scaling Bessel beams

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com

    2016-10-07

    The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.

  7. Linear Scaling Density Functional Calculations with Gaussian Orbitals

    Science.gov (United States)

    Scuseria, Gustavo E.

    1999-01-01

    Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.

  8. Graph-based linear scaling electronic structure theory

    CERN Document Server

    Niklasson, Anders M N; Negre, Christian F A; Cawkwell, Marc J; Swart, Pieter J; Mohd-Yusof, Jamal; Germann, Timothy C; Wall, Michael E; Bock, Nicolas; Djidjev, Hristo

    2016-01-01

    We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

  9. THE REGULAR SOLUTIONS OF THE ISENTROPIC EULER EQUATIONS WITH DEGENERATE LINEAR DAMPING

    Institute of Scientific and Technical Information of China (English)

    ZHU XUSHENG; WANG WEIKE

    2005-01-01

    The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then undersome hypotheses on the initial data, the regular solution exists globally.

  10. Orbits for Nine Binaries and One Linear Solution

    Science.gov (United States)

    Cvetković, Z.; Pavlović, R.; Ninković, S.

    2016-03-01

    The subject of the present paper is the analysis of the orbital elements for nine binaries: WDS 00463-0634 = HDS 101, WDS 03264+3520 = HDS 430, WDS 03307-1926 = HDS 441, WDS 04025+0638 = HDS 510, WDS 09252+4606 = HDS 1353, WDS 09446+6459 = CHR 176, WDS 10294+1211 = HDS 1507, WDS 10596+1800 = HDS 1568, and WDS 14562+1745 = HDS 2108. The orbital elements are calculated for the first time for all of them. The eight binaries, denoted as HDS, were discovered during the Hipparcos mission. One binary, denoted as CHR, was discovered in the Center for High Angular Resolution Astronomy, CHARA, in 1988. These studied pairs have measured separations of less than 0.41 arcsec. For the eight pairs that have measured separations less than 0.3 arcsec, the resulting orbital periods fall within 16 and 55 years, and for the remaining one pair the orbital period is 94 years. In addition to the orbital elements, we also give (O - C) residuals in θ and ρ, masses, dynamical parallaxes, absolute magnitudes, spectral types, and ephemerides for the next five years. We also present one linear solution for the double star WDS 19218+7708 = HDS 2740 that has also been calculated for the first time. For this system we give (O - C) residuals in θ and ρ as well, along with ephemerides for the next five years.

  11. Generation of primordial magnetic fields on linear overdensity scales.

    Science.gov (United States)

    Naoz, Smadar; Narayan, Ramesh

    2013-08-02

    Magnetic fields appear to be present in all galaxies and galaxy clusters. Recent measurements indicate that a weak magnetic field may be present even in the smooth low density intergalactic medium. One explanation for these observations is that a seed magnetic field was generated by some unknown mechanism early in the life of the Universe, and was later amplified by various dynamos in nonlinear objects like galaxies and clusters. We show that a primordial magnetic field is expected to be generated in the early Universe on purely linear scales through vorticity induced by scale-dependent temperature fluctuations, or equivalently, a spatially varying speed of sound of the gas. Residual free electrons left over after recombination tap into this vorticity to generate magnetic field via the Biermann battery process. Although the battery operates even in the absence of any relative velocity between dark matter and gas at the time of recombination, the presence of such a relative velocity modifies the predicted spatial power spectrum of the magnetic field. At redshifts of order a few tens, we estimate a root mean square field strength of order 10(-25)-10(-24) G on comoving scales ~10 kpc. This field, which is generated purely from linear perturbations, is expected to be amplified significantly after reionization, and to be further boosted by dynamo processes during nonlinear structure formation.

  12. Linear scaling coupled cluster and perturbation theories in the atomic orbital basis

    Science.gov (United States)

    Scuseria, Gustavo E.; Ayala, Philippe Y.

    1999-11-01

    We present a reformulation of the coupled cluster equations in the atomic orbital (AO) basis that leads to a linear scaling algorithm for large molecules. Neglecting excitation amplitudes in a screening process designed to achieve a target energy accuracy, we obtain an AO coupled cluster method which is competitive in terms of number of amplitudes with the traditional molecular orbital (MO) solution, even for small molecules. For large molecules, the decay properties of integrals and excitation amplitudes becomes evident and our AO method yields a linear scaling algorithm with respect to molecular size. We present benchmark calculations to demonstrate that our AO reformulation of the many-body electron correlation problem defeats the "exponential scaling wall" that has characterized high-level MO quantum chemistry calculations for many years.

  13. Design techniques for large scale linear measurement systems

    Energy Technology Data Exchange (ETDEWEB)

    Candy, J.V.

    1979-03-01

    Techniques to design measurement schemes for systems modeled by large scale linear time invariant systems, i.e., physical systems modeled by a large number (> 5) of ordinary differential equations, are described. The techniques are based on transforming the physical system model to a coordinate system facilitating the design and then transforming back to the original coordinates. An example of a three-stage, four-species, extraction column used in the reprocessing of spent nuclear fuel elements is presented. The basic ideas are briefly discussed in the case of noisy measurements. An example using a plutonium nitrate storage vessel (reprocessing) with measurement uncertainty is also presented.

  14. Approximate Solution Methods for Linear Stochastic Difference Equations. I. Moments

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.

    1983-01-01

    The cumulant expansion for linear stochastic differential equations is extended to the case of linear stochastic difference equations. We consider a vector difference equation, which contains a deterministic matrix A0 and a random perturbation matrix A1(t). The expansion proceeds in powers of ατc, w

  15. Epitaxial engineered solutions for ITRS scaling roadblocks

    Energy Technology Data Exchange (ETDEWEB)

    Harper, Robert [IQE Silicon Ltd., Beech House, Cardiff CF3 OLW (United Kingdom)]. E-mail: rharper@iqesilicon.com

    2006-10-15

    This paper reviews the current and future roles of epitaxy in providing both process and materials solutions to the scaling roadblocks identified by ITRS2005. It is now widely accepted that we are in an 'era of materials enabled device scaling' [International Technology Roadmap for Semiconductors, 2005 Edition, Front End Processing.] and that in addition to new materials for the gate stack, advanced substrates will also become increasingly important in the 21st Century. The Emerging Materials Committee has identified a range of issues such as mobility enhancement and thermal management [M. Bulsara, G. Celler, H. Huff, R. Standly, E. White, Solid State Technol. (2006).] which can be addressed by new 'engineered' substrates that are now manufacturable thanks to combinations of advanced layer transfer and epitaxy processes. Strained silicon has proved to be an invaluable performance booster due to the enhanced mobilities resulting from different forms of uniaxial and biaxial strain. SiGe epitaxy is the key process enabling technology for both process induced (local) strain and bulk (global) strain. Hybrid orientation technology (HOT), where (1 0 0) and (1 1 0) surfaces coexist on the same silicon substrate, is also an exciting development for boosting pMOS mobility. Several embodiments of this approach also exist and all require forms of epitaxial processing. Advanced layer transfer processes make it possible to engineer substrates in a variety of ways which were, until recently, unimaginable. Layer transfer is essential to hybrid orientation technology and also makes strained silicon extendable onto SOI to produce ultra thin body (UTB) strained SOI substrates suitable for fully depleted CMOS devices. In addition to its role in strain processes and engineered substrates, the number of 'in-process' epitaxy stages is also increasing. BiCMOS and HBT epitaxy are established technologies, however, the requirement to reduce source/drain series

  16. Scaling effects in a non-linear electromagnetic energy harvester for wearable sensors

    Science.gov (United States)

    Geisler, M.; Boisseau, S.; Perez, M.; Ait-Ali, I.; Perraud, S.

    2016-11-01

    In the field of inertial energy harvesters targeting human mechanical energy, the ergonomics of the solutions impose to find the best compromise between dimensions reduction and electrical performance. In this paper, we study the properties of a non-linear electromagnetic generator at different scales, by performing simulations based on an experimentally validated model and real human acceleration recordings. The results display that the output power of the structure is roughly proportional to its scaling factor raised to the power of five, which indicates that this system is more relevant at lengths over a few centimetres.

  17. On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients

    Directory of Open Access Journals (Sweden)

    Rontó András

    2008-01-01

    Full Text Available Abstract The problem on solutions with specified growth for linear functional differential equations with negative coefficients is treated by using two-sided monotone iterations. New theorems on the existence and localisation of such solutions are established.

  18. On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients

    Directory of Open Access Journals (Sweden)

    András Rontó

    2008-10-01

    Full Text Available The problem on solutions with specified growth for linear functional differential equations with negative coefficients is treated by using two-sided monotone iterations. New theorems on the existence and localisation of such solutions are established.

  19. Uniqueness of solution of a quasi-linear Reaction-diffusion system

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, we consider nonnegative classical solutions of a Quasi-linear reactiondiffusion system with nonlinear boundary conditions. We prove the uniqueness of a nonnegative classical solution to this problem.

  20. A Way to Find All the Optimal Solutions in Linear Programming

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    With the expression theorem of convex polyhedron, this paper gives the general expres sion for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.

  1. ON GLOBAL MEROMORPHIC SOLUTIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Yinying KONG; Daochun SUN

    2013-01-01

    The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients,which perfect the solution theory of such equations.

  2. EXTENDABILITY OF SOLUTIONS FOR THE LINEAR SYSTEM OF ELLIPTIC TYPE EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    马忠泰

    2004-01-01

    The solutions of linear system of elliptic type equations with first order is discussed by using the method of several complex analysis and, a series of newe xtended results of the solutions for the system of elliptic type are obtained.

  3. Non linear evolution: revisiting the solution in the saturation region

    CERN Document Server

    Contreras, Carlos; Meneses, Rodrigo

    2014-01-01

    In this paper we revisit the problem of the solution to Balitsky-Kovchegov equation deeply in the saturation domain. We find that solution has the form of Levin-Tuchin solution but it depends on variable $\\bar{z} = \\ln(r^2 Q^2_s) + \\mbox{Const}$ and the value of $\\mbox{Const}$ is calculated in this paper. We propose the solution for full BFKL kernel at large $z$ in the entire kinematic region that satisfies the McLerram-Venugopalan initial condition

  4. Computational alanine scanning with linear scaling semiempirical quantum mechanical methods.

    Science.gov (United States)

    Diller, David J; Humblet, Christine; Zhang, Xiaohua; Westerhoff, Lance M

    2010-08-01

    Alanine scanning is a powerful experimental tool for understanding the key interactions in protein-protein interfaces. Linear scaling semiempirical quantum mechanical calculations are now sufficiently fast and robust to allow meaningful calculations on large systems such as proteins, RNA and DNA. In particular, they have proven useful in understanding protein-ligand interactions. Here we ask the question: can these linear scaling quantum mechanical methods developed for protein-ligand scoring be useful for computational alanine scanning? To answer this question, we assembled 15 protein-protein complexes with available crystal structures and sufficient alanine scanning data. In all, the data set contains Delta Delta Gs for 400 single point alanine mutations of these 15 complexes. We show that with only one adjusted parameter the quantum mechanics-based methods outperform both buried accessible surface area and a potential of mean force and compare favorably to a variety of published empirical methods. Finally, we closely examined the outliers in the data set and discuss some of the challenges that arise from this examination.

  5. Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez-Estrada, R.F.

    1979-08-01

    A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.

  6. Linear delta expansion technique for the solution of anharmonic oscillations

    Indian Academy of Sciences (India)

    P K Bera; J Datta

    2007-01-01

    The linear delta expansion technique has been developed for solving the differential equation of motion for symmetric and asymmetric anharmonic oscillators. We have also demonstrated the sophistication and simplicity of this new perturbation technique.

  7. Superlinear Convergence of Affine Scaling Interior Point Newton Method for Linear Inequality Constrained Minimization without Strict Complementarity

    Institute of Scientific and Technical Information of China (English)

    De-tong Zhu

    2009-01-01

    In this paper we extend and improve the classical affine scaling interior-point Newton method for solving nonlinear optimization subject to linear inequality constraints in the absence of the strict complementar-ity assumption. Introducing a computationally efficient technique and employing an identification function for the definition of the new affine scaling matrix, we propose and analyze a new affine scaling interior-point Newton method which improves the Coleman and Li affine scaling matrix in [2] for solving the linear inequality con-strained optimization. Local superlinear and quadratical convergence of the proposed algorithm is established under the strong second order sufficiency condition without assuming strict complementarity of the solution.

  8. ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Cheng Ouyang

    2005-01-01

    A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.

  9. The clustering of dark matter haloes: scale-dependent bias on quasi-linear scales

    Science.gov (United States)

    Jose, Charles; Lacey, Cedric G.; Baugh, Carlton M.

    2016-11-01

    We investigate the spatial clustering of dark matter haloes, collapsing from 1σ-4σ fluctuations, in the redshift range 0-5 using N-body simulations. The halo bias of high redshift haloes (z ≥ 2) is found to be strongly nonlinear and scale dependent on quasi-linear scales that are larger than their virial radii (0.5-10 Mpc h-1). However, at lower redshifts, the scale dependence of nonlinear bias is weaker and is of the order of a few per cent on quasi-linear scales at z ˜ 0. We find that the redshift evolution of the scale-dependent bias of dark matter haloes can be expressed as a function of four physical parameters: the peak height of haloes, the nonlinear matter correlation function at the scale of interest, an effective power-law index of the rms linear density fluctuations and the matter density of the universe at the given redshift. This suggests that the scale dependence of halo bias is not a universal function of the dark matter power spectrum, which is commonly assumed. We provide a fitting function for the scale-dependent halo bias as a function of these four parameters. Our fit reproduces the simulation results to an accuracy of better than 4 per cent over the redshift range 0 ≤ z ≤ 5. We also extend our model by expressing the nonlinear bias as a function of the linear matter correlation function. It is important to incorporate our results into the clustering models of dark matter haloes at any redshift, including those hosting early generations of stars and galaxies before reionization.

  10. Linear Estimation of Location and Scale Parameters Using Partial Maxima

    CERN Document Server

    Papadatos, Nickos

    2010-01-01

    Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where X^*_{j:j}=max{X^*_1,...,X^*_j}. This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (1952, Least-squares estimation of location and scale parameters using order statistics, Biometrika, vol. 39, pp. 88-95) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/log n), for a wide class of distributions.

  11. Machine Protection Issues and Solutions for Linear Accelerator Complexes

    CERN Document Server

    Jonker, M; Schmidt, R; Schulte, D; Ross, M

    2013-01-01

    The workshop “Machine Protection focusing on Linear Accelerator Complexes” was held from 6-8 June 2012 at CERN. This workshop brought together experts working on machine protection systems for accelerator facilities with high brilliance or large stored beam energies, with the main focus on linear accelerators and their injectors. An overview of the machine protection systems for several accelerators was given. Beam loss mechanisms and their detection were discussed. Mitigation of failures and protection systems were presented. This paper summarises the workshop and reviews the current state of the art in machine protection systems.

  12. Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

    Science.gov (United States)

    Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

    2003-01-01

    An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

  13. POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

  14. Nonlinear Alignment and Its Local Linear Iterative Solution

    Directory of Open Access Journals (Sweden)

    Sumin Zhang

    2016-01-01

    Full Text Available In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.

  15. Head movement as an artefact of optimal solutions to linearization ...

    African Journals Online (AJOL)

    IT

    or a child acquiring the language to infer the original syntactic information from the signal and ... explore it, will turn out to require head movement as an inalienable property. The effect of head movement will follow from a general linearization algorithm which, in turn, is motivated by ...... In colloquial usage the negative.

  16. Order reduction of large-scale linear oscillatory system models

    Energy Technology Data Exchange (ETDEWEB)

    Trudnowksi, D.J. (Pacific Northwest Lab., Richland, WA (United States))

    1994-02-01

    Eigen analysis and signal analysis techniques of deriving representations of power system oscillatory dynamics result in very high-order linear models. In order to apply many modern control design methods, the models must be reduced to a more manageable order while preserving essential characteristics. Presented in this paper is a model reduction method well suited for large-scale power systems. The method searches for the optimal subset of the high-order model that best represents the system. An Akaike information criterion is used to define the optimal reduced model. The method is first presented, and then examples of applying it to Prony analysis and eigenanalysis models of power systems are given.

  17. Linear scaling calculation of band edge states and doped semiconductors.

    Science.gov (United States)

    Xiang, H J; Yang, Jinlong; Hou, J G; Zhu, Qingshi

    2007-06-28

    Linear scaling methods provide total energy, but no energy levels and canonical wave functions. From the density matrix computed through the density matrix purification methods, we propose an order-N [O(N)] method for calculating both the energies and wave functions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematically and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory.

  18. Scaling laws for e sup + /e sup - linear colliders

    CERN Document Server

    Delahaye, J P; Raubenheimer, T O; Wilson, Ian H

    1999-01-01

    Design studies of a future TeV e sup + e sup - Linear Collider (TLC) are presently being made by five major laboratories within the framework of a world-wide collaboration. A figure of merit is defined which enables an objective comparison of these different designs. This figure of merit is shown to depend only on a small number of parameters. General scaling laws for the main beam parameters and linac parameters are derived and prove to be very effective when used as guidelines to optimize the linear collider design. By adopting appropriate parameters for beam stability, the figure of merit becomes nearly independent of accelerating gradient and RF frequency of the accelerating structures. In spite of the strong dependence of the wake fields with frequency, the single-bunch emittance blow-up during acceleration along the linac is also shown to be independent of the RF frequency when using equivalent trajectory correction schemes. In this situation, beam acceleration using high-frequency structures becomes ve...

  19. Scaling Laws for Normal Conducting $e^{\\pm}$ Linear Colliders

    CERN Document Server

    Delahaye, J P; Raubenheimer, T O; Wilson, Ian H

    1998-01-01

    Design studies of a future TeV e± Linear Collider (TLC) are presently being made by five major laboratories within the framework of a world-wide collaboration. A figure of merit is defined which enabl es an objective comparison of these different designs. This figure of merit is shown to depend only on a small number of parameters. General scaling laws for the main beam parameters and linac paramet ers are derived and prove to be very effective when used as guidelines to optimize the linear collider design. By adopting appropriate parameters for beam stability, the figure of merit becomes nearly independent of accelerating gradient and RF frequency of the accelerating structures. In spite of the strong dependence of the wake-fields with frequency, the single bunch emittance preservation durin g acceleration along the linac is also shown to be independent of the RF frequency when using equivalent trajectory correction schemes. In this situation, beam acceleration using high frequency struct ures becomes very ...

  20. Parameter Scaling in Non-Linear Microwave Tomography

    DEFF Research Database (Denmark)

    Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar;

    2012-01-01

    Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....

  1. Parameter Scaling in Non-Linear Microwave Tomography

    DEFF Research Database (Denmark)

    Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar

    2012-01-01

    Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....

  2. Robust Stability and H∞ Control of Uncertain Piecewise Linear Switched Systems with Filippov Solutions

    DEFF Research Database (Denmark)

    Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal

    2012-01-01

    This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in finite...... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...

  3. Solute transport scales in an unsaturated stony soil

    Science.gov (United States)

    Coppola, Antonio; Comegna, Alessandro; Dragonetti, Giovanna; Dyck, Miles; Basile, Angelo; Lamaddalena, Nicola; Kassab, Mohamed; Comegna, Vincenzo

    2011-06-01

    Solute transport parameters are known to be scale-dependent due mainly to the increasing scale of heterogeneities with transport distance and with the lateral extent of the transport field examined. Based on a transect solute transport experiment, in this paper we studied this scale dependence by distinguishing three different scales with different homogeneity degrees of the porous medium: the observation scale, transport scale and transect scale. The main objective was to extend the approach proposed by van Wesenbeeck and Kachanoski to evaluating the role of textural heterogeneities on the transition from the observation scale to the transport scale. The approach is based on the scale dependence of transport moments estimated from solute concentrations distributions. In our study, these moments were calculated starting from time normalized resident concentrations measured by time domain reflectometry (TDR) probes at three depths in 37 soil sites 1 m apart along a transect during a steady state transport experiment. The Generalized Transfer Function (GTF) was used to describe the evolution of apparent solute spreading along the soil profile at each observation site by analyzing the propagation of the moments of the concentration distributions. Spectral analysis was used to quantify the relationship between the solid phase heterogeneities (namely, texture and stones) and the scale dependence of the solute transport parameters. Coupling the two approaches allowed us to identify two different transport scales (around 4-5 m and 20 m, respectively) mainly induced by the spatial pattern of soil textural properties. The analysis showed that the larger transport scale is mainly determined by the skeleton pattern of variability. Our analysis showed that the organization in hierarchical levels of soil variability may have major effects on the differences between solute transport behavior at transport scale and transect scale, as the transect scale parameters will include

  4. A linear regression solution to the spatial autocorrelation problem

    Science.gov (United States)

    Griffith, Daniel A.

    The Moran Coefficient spatial autocorrelation index can be decomposed into orthogonal map pattern components. This decomposition relates it directly to standard linear regression, in which corresponding eigenvectors can be used as predictors. This paper reports comparative results between these linear regressions and their auto-Gaussian counterparts for the following georeferenced data sets: Columbus (Ohio) crime, Ottawa-Hull median family income, Toronto population density, southwest Ohio unemployment, Syracuse pediatric lead poisoning, and Glasgow standard mortality rates, and a small remotely sensed image of the High Peak district. This methodology is extended to auto-logistic and auto-Poisson situations, with selected data analyses including percentage of urban population across Puerto Rico, and the frequency of SIDs cases across North Carolina. These data analytic results suggest that this approach to georeferenced data analysis offers considerable promise.

  5. From linear to non-linear scales: analytical and numerical predictions for the weak lensing convergence

    CERN Document Server

    Barber, A J; Valageas, P; Barber, Andrew J.; Munshi, Dipak; Valageas, Patrick

    2004-01-01

    Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the many-body density correlations. We describe two model-independent approximations which provide two simple methods to compute the probability distribution function, pdf, of the convergence. We apply one of these to the case where the density field can be described by a log-normal pdf. Next, we discuss two hierarchical models for the high-order correlations which allow one to perform exact calculations and evaluate the previous approximations in such specific cases. Finally, we apply these methods to a very simple model for the evolution of the density field from linear to highly non-linear scales. Comparisons with the results obtained from numerical simulations, obtained from a number of different realizations, show excellent agreement w...

  6. Existence of solutions for a Schrödinger system with linear and nonlinear couplings

    Science.gov (United States)

    Li, Kui; Zhang, Zhitao

    2016-08-01

    We study an important system of Schrödinger equations with linear and nonlinear couplings arising from Bose-Einstein condensates. We use the Nehari manifold to prove the existence of a ground state solution; moreover, we give the sign of the solutions depending on linear coupling; by using index theory and Nehari manifold, we prove that there exist infinitely many positive bound state solutions.

  7. Taylor polynomial solution of difference equation with constant coefficients via time scales calculus

    Directory of Open Access Journals (Sweden)

    Veysel Hatipoglu

    2015-09-01

    Full Text Available In this study, we present a practical matrix method to find an approximate solution of higher order linear difference equation with constant coefficients under the initial-boundary conditions in terms of Taylor polynomials. To obtain this goal, we first present time scale extension of previous polynomial approach, then restrict the formula to the Integers with h step. This method converts the difference equation to a matrix equation, which may be considered as a system of linear algebraic equations.

  8. Max-plus-linear model-based predictive control for constrained hybrid systems:linear programming solution

    Institute of Scientific and Technical Information of China (English)

    Yuanyuan ZOU; Shaoyuan LI

    2007-01-01

    In this paper,a linear programming method is proposed to solve model predictive control for a class of hybrid systems.Firstly,using the(max,+)algebra,a typical subclass of hybrid systems called max-plus-linear(MPL)systems is obtained.And then,model predictive control(MPC)framework is extended to MPL systems.In general,the nonlinear optimization approach or extended linear complementarity problem(ELCP)were applied to solve the MPL-MPC optimization problem.A new optimization method based on canonical forms for max-min-plus-scaling(MMPS)functions (using the operations maximization,minimization,addition and scalar multiplication)with linear constraints on the inputs is presented.The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization.The validity of the algorithm is illustrated by an example.

  9. Oscillation and wandering characteristics of solutions of a linear differential system

    Energy Technology Data Exchange (ETDEWEB)

    Sergeev, Igor N [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

    2012-02-28

    We introduce new Lyapunov characteristics for the oscillation and wandering of solutions of linear differential equations or systems, namely, the frequency of a solution (the mean number of zeros on the time axis), of some coordinate of the solution, or of all possible linear combinations of these coordinates, and also the mean angular velocity of the rotation of a solution (about the origin in the phase space) and various wandering exponents (derived from the mean angular velocity). We shall show that the sets of values of all these quantities on the solutions of a linear autonomous system coincide with the set of absolute values of the imaginary parts of eigenvalues of the matrix of the system. We shall see that the frequencies of solutions are bounded above by their wandering exponents, and the frequencies and wandering exponents of all solutions of an arbitrary second-order equation coincide.

  10. Biological Scaling Problems and Solutions in Amphibians.

    Science.gov (United States)

    Levy, Daniel L; Heald, Rebecca

    2015-08-10

    Size is a primary feature of biological systems that varies at many levels, from the organism to its constituent cells and subcellular structures. Amphibians populate some of the extremes in biological size and have provided insight into scaling mechanisms, upper and lower size limits, and their physiological significance. Body size variation is a widespread evolutionary tactic among amphibians, with miniaturization frequently correlating with direct development that occurs without a tadpole stage. The large genomes of salamanders lead to large cell sizes that necessitate developmental modification and morphological simplification. Amphibian extremes at the cellular level have provided insight into mechanisms that accommodate cell-size differences. Finally, how organelles scale to cell size between species and during development has been investigated at the molecular level, because subcellular scaling can be recapitulated using Xenopus in vitro systems.

  11. THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Zhen-yun Peng; Xi-yan Hu; Lei Zhang

    2004-01-01

    The necessary and sufficient conditions for the existence of and the expressions for bismmetric soutions of the matrix equation(Ⅰ)A1X1B1+A2X2B2+…AkXkBk=D,(Ⅱ)A1XB1+A2XB2+…+AkXBk=D and (Ⅲ)(A1XB1,A2XB2,…,AkXBK)=(D1,D2,…,Dk) are derived by using kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given.Numerical methods and numerical experiments of finding the nearest solutions are also provided.

  12. Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Yongkun Li

    2011-01-01

    Full Text Available Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale T=ℝ or ℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.

  13. Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

    Science.gov (United States)

    Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.; Thiele, Ines; Palsson, Bernhard O.; Saunders, Michael A.

    2017-01-01

    Constraint-Based Reconstruction and Analysis (COBRA) is currently the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We have developed a quadruple-precision version of our linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.

  14. Scaling Behaviour of Diffusion Limited Aggregation with Linear Seed

    Institute of Scientific and Technical Information of China (English)

    TANG Qiang; TIAN Ju-Ping; YAO Kai-Lun

    2006-01-01

    @@ We present a computer model of diffusion limited aggregation with linear seed. The clusters with varying linear seed lengths are simulated, and their pattern structure, fractal dimension and multifractal spectrum are obtained.The simulation results show that the linear seed length has little effect on the pattern structure of the aggregation clusters if its length is comparatively shorter. With its increasing, the linear seed length has stronger effects on the pattern structure, while the dimension Df decreases. When the linear seed length is larger, the corresponding pattern structure is cross alike. The larger the linear seed length is, the more obvious the cross-like structure with more particles clustering at the two ends of the linear seed and along the vertical direction to the centre of the linear seed. Furthermore, the multifractal spectra curve becomes lower and the range of singularity narrower.The longer the length of a linear seed is, the less irregular and nonuniform the pattern becomes.

  15. Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

    DEFF Research Database (Denmark)

    Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.

    2017-01-01

    Constraint-Based Reconstruction and Analysis (COBRA) is currently the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many...

  16. Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials

    CERN Document Server

    Santoprete, Manuele

    2009-01-01

    In this paper we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. Firstly, in the case the potential is a homogeneous function of degree $-a$, we find that any relative equilibrium of the $n$-body problem with $a>2$ is spectrally unstable. We also find a similar condition in the quasihomogeneous case. Then we consider the case of three bodies and we study the stability of the equilateral triangle relative equilibria. In the case of homogeneous potentials we recover the classical result obtained by Routh in a simpler way. In the case of quasihomogeneous potentials we find a generalization of Routh inequality and we show that, for certain values of the masses, the stability of the relative equilibria depends on the size of the configuration.

  17. Employment of Gibbs-Donnan-based concepts for interpretation of the properties of linear polyelectrolyte solutions

    Science.gov (United States)

    Marinsky, J.A.; Reddy, M.M.

    1991-01-01

    Earlier research has shown that the acid dissociation and metal ion complexation equilibria of linear, weak-acid polyelectrolytes and their cross-linked gel analogues are similarly sensitive to the counterion concentration levels of their solutions. Gibbs-Donnan-based concepts, applicable to the gel, are equally applicable to the linear polyelectrolyte for the accommodation of this sensitivity to ionic strength. This result is presumed to indicate that the linear polyelectrolyte in solution develops counterion-concentrating regions that closely resemble the gel phase of their analogues. Advantage has been taken of this description of linear polyelectrolytes to estimate the solvent uptake by these regions. ?? 1991 American Chemical Society.

  18. Daubechies wavelets for linear scaling density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Mohr, Stephan [Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland); Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Ratcliff, Laura E.; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry [Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Boulanger, Paul [Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09 (France); Goedecker, Stefan [Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland)

    2014-05-28

    We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

  19. Linearly Scaling 3D Fragment Method for Large-Scale Electronic Structure Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Lin-Wang; Lee, Byounghak; Shan, Hongzhang; Zhao, Zhengji; Meza, Juan; Strohmaier, Erich; Bailey, David H.

    2008-07-01

    We present a new linearly scaling three-dimensional fragment (LS3DF) method for large scale ab initio electronic structure calculations. LS3DF is based on a divide-and-conquer approach, which incorporates a novel patching scheme that effectively cancels out the artificial boundary effects due to the subdivision of the system. As a consequence, the LS3DF program yields essentially the same results as direct density functional theory (DFT) calculations. The fragments of the LS3DF algorithm can be calculated separately with different groups of processors. This leads to almost perfect parallelization on tens of thousands of processors. After code optimization, we were able to achieve 35.1 Tflop/s, which is 39percent of the theoretical speed on 17,280 Cray XT4 processor cores. Our 13,824-atom ZnTeO alloy calculation runs 400 times faster than a direct DFTcalculation, even presuming that the direct DFT calculation can scale well up to 17,280 processor cores. These results demonstrate the applicability of the LS3DF method to material simulations, the advantage of using linearly scaling algorithms over conventional O(N3) methods, and the potential for petascale computation using the LS3DF method.

  20. Linear scaling 3D fragment method for large-scale electronic structure calculations

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Lin-Wang; Wang, Lin-Wang; Lee, Byounghak; Shan, HongZhang; Zhao, Zhengji; Meza, Juan; Strohmaier, Erich; Bailey, David

    2008-07-11

    We present a new linearly scaling three-dimensional fragment (LS3DF) method for large scale ab initio electronic structure calculations. LS3DF is based on a divide-and-conquer approach, which incorporates a novel patching scheme that effectively cancels out the artificial boundary effects due to the subdivision of the system. As a consequence, the LS3DF program yields essentially the same results as direct density functional theory (DFT) calculations. The fragments of the LS3DF algorithm can be calculated separately with different groups of processors. This leads to almost perfect parallelization on tens of thousands of processors. After code optimization, we were able to achieve 35.1 Tflop/s, which is 39% of the theoretical speed on 17,280 Cray XT4 processor cores. Our 13,824-atom ZnTeO alloy calculation runs 400 times faster than a direct DFT calculation, even presuming that the direct DFT calculation can scale well up to 17,280 processor cores. These results demonstrate the applicability of the LS3DF method to material simulations, the advantage of using linearly scaling algorithms over conventional O(N{sup 3}) methods, and the potential for petascale computation using the LS3DF method.

  1. Propagation of sound waves through a linear shear layer - A closed form solution

    Science.gov (United States)

    Scott, J. N.

    1978-01-01

    Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis is exact for all frequencies and is developed assuming a linear velocity profile in the shear layer. This assumption allows the solution to be expressed in terms of parabolic cylinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number give expressions which correspond to solutions previously obtained for these limiting cases.

  2. Propagation of sound waves through a linear shear layer: A closed form solution

    Science.gov (United States)

    Scott, J. N.

    1978-01-01

    Closed form solutions are presented for sound propagation from a line source in or near a shear layer. The analysis was exact for all frequencies and was developed assuming a linear velocity profile in the shear layer. This assumption allowed the solution to be expressed in terms of parabolic cyclinder functions. The solution is presented for a line monopole source first embedded in the uniform flow and then in the shear layer. Solutions are also discussed for certain types of dipole and quadrupole sources. Asymptotic expansions of the exact solutions for small and large values of Strouhal number gave expressions which correspond to solutions previously obtained for these limiting cases.

  3. Linear and Nonlinear Optical Properties of Micrometer-Scale Gold Nanoplates

    Institute of Scientific and Technical Information of China (English)

    LIU Xiao-Lan; PENG Xiao-Niu; YANG Zhong-Jian; LI Min; ZHOU Li

    2011-01-01

    Micrometer-scale gold nanoplates have been synthesized in high yield through a polyol process.The morphology, crystal structure and linear optical extinction of the gold nanoplates have been characterized.These gold nanoplates are single-crystalline with triangular, truncated triangular and hexagonal shapes, exhibiting strong surface plasmon resonance (SPR) extinction in the visible and near-infrared (NIR) region.The linear optical properties of gold nanoplates are also investigated by theoretical calculations.We further investigate the nonlinear opticai properties of the gold nanoplates in solution by Z-scan technique.The nonlinear absorption (NLA )coefficient and nonlinear refraction (NLR) index are measured to be 1.18 × 102 cm/GW and - 1.04 × 10-3 cm2/GW,respectively.%@@ Micrometer-scale gold nanoplates have been synthesized in high yield through a polyol process.The morphology,crystal structure and linear optical extinction of the gold nanoplates have been characterized.These gold nanoplates are single-crystalline with triangular,truncated triangular and hexagonal shapes,exhibiting strong surface plasmon resonance(SPR) extinction in the visible and near-infrared(NIR) region.The linear optical properties of gold nanoplates are also investigated by theoretical calculations.We further investigate the nonlinear optical properties of the gold nanoplates in solution by Z-scan technique.The nonlinear absorption(NLA)coefficient and nonlinear refraction(NLR) index are measured to be 1.18 × 102 cm/GW and - 1.04 × 10-3 cm2/GW,respectively.

  4. ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    CaoTingbin; ChenZongxuan; ZhengXiumin; TuJin

    2005-01-01

    In this paper, we investigate complexhigher order linear differential equationshomogeneous and non-homogeneous with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutionsand the iterated convergence exponent of the zeros of meromorphic solutions.

  5. Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

    DEFF Research Database (Denmark)

    Mejlbro, Leif

    1997-01-01

    An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

  6. Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method

    Directory of Open Access Journals (Sweden)

    Jin-Fa Cheng

    2011-01-01

    Full Text Available We obtain the analytical general solution of the linear fractional differential equations with constant coefficients by Adomian decomposition method under nonhomogeneous initial value condition, which is in the sense of the Caputo fractional derivative.

  7. ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES

    Institute of Scientific and Technical Information of China (English)

    陈化; 罗壮初

    2002-01-01

    In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct × Cnx. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct × Cnx.

  8. On Improving the Convergence of the Solution of a System of Linear Equations

    Science.gov (United States)

    2005-08-01

    vector acceleration technique to enhance the convergence. One significant advantage of using the bcg estimates is that the moment matrix , A, does not need...requires the solution of a system of linear equations of the form, Ax = b, where the dimension of the matrix A increases with the nunber of unknowns...appendix to the report. The solution of a system of linear equations can be obtained from direct methods, such as matrix inversion, and indirect methods

  9. Dual mean field search for large scale linear and quadratic knapsack problems

    Science.gov (United States)

    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.

  10. Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates

    Science.gov (United States)

    Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier

    2016-07-01

    A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.

  11. Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates

    Science.gov (United States)

    Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier

    2017-01-01

    A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.

  12. A note on the time decay of solutions for the linearized Wigner-Poisson system

    KAUST Repository

    Gamba, Irene

    2009-01-01

    We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.

  13. Linear-scaling computation of excited states in time-domain

    Institute of Scientific and Technical Information of China (English)

    YAM ChiYung; CHEN GuanHua

    2014-01-01

    The applicability of quantum mechanical methods is severely limited by their poor scaling.To circumvent the problem,linearscaling methods for quantum mechanical calculations had been developed.The physical basis of linear-scaling methods is the locality in quantum mechanics where the properties or observables of a system are weakly influenced by factors spatially far apart.Besides the substantial efforts spent on devising linear-scaling methods for ground state,there is also a growing interest in the development of linear-scaling methods for excited states.This review gives an overview of linear-scaling approaches for excited states solved in real time-domain.

  14. Scaled-particle theory analysis of cylindrical cavities in solution.

    Science.gov (United States)

    Ashbaugh, Henry S

    2015-04-01

    The solvation of hard spherocylindrical solutes is analyzed within the context of scaled-particle theory, which takes the view that the free energy of solvating an empty cavitylike solute is equal to the pressure-volume work required to inflate a solute from nothing to the desired size and shape within the solvent. Based on our analysis, an end cap approximation is proposed to predict the solvation free energy as a function of the spherocylinder length from knowledge regarding only the solvent density in contact with a spherical solute. The framework developed is applied to extend Reiss's classic implementation of scaled-particle theory and a previously developed revised scaled-particle theory to spherocylindrical solutes. To test the theoretical descriptions developed, molecular simulations of the solvation of infinitely long cylindrical solutes are performed. In hard-sphere solvents classic scaled-particle theory is shown to provide a reasonably accurate description of the solvent contact correlation and resulting solvation free energy per unit length of cylinders, while the revised scaled-particle theory fitted to measured values of the contact correlation provides a quantitative free energy. Applied to the Lennard-Jones solvent at a state-point along the liquid-vapor coexistence curve, however, classic scaled-particle theory fails to correctly capture the dependence of the contact correlation. Revised scaled-particle theory, on the other hand, provides a quantitative description of cylinder solvation in the Lennard-Jones solvent with a fitted interfacial free energy in good agreement with that determined for purely spherical solutes. The breakdown of classical scaled-particle theory does not result from the failure of the end cap approximation, however, but is indicative of neglected higher-order curvature dependences on the solvation free energy.

  15. Analytical solution of the linearized hillslope-storage Boussinesq equation for exponential hillslope width functions

    NARCIS (Netherlands)

    Troch, P.A.A.; Loon, van A.H.; Hilberts, A.G.J.

    2004-01-01

    This technical note presents an analytical solution to the linearized hillslope-storage Boussinesq equation for subsurface flow along complex hillslopes with exponential width functions and discusses the application of analytical solutions to storage-based subsurface flow equations in catchment stud

  16. Global behavior of the solutions to Boussinesq type equation with linear restoring force

    Science.gov (United States)

    Kutev, N.; Kolkovska, N.; Dimova, M.

    2014-11-01

    Global existence or finite time blow up of the weak solutions to Boussinesq type equation with linear restoring force is proved. For subcritical initial energy the potential well method is applied. Finite time blow up of the solutions with arbitrary high positive initial energy is proved under general structural conditions for the initial data. Numerical experiments illustrating the theoretical results are presented.

  17. A practical localization solution for wireless sensor networks deployed in linear topography

    NARCIS (Netherlands)

    Zhang, Kui; Guo, Peng; Meratnia, Nirvana; Havinga, Paul J.M.

    2010-01-01

    In this paper, we propose a practical range-free localization solution for wireless sensor networks (WSNs). Different from existing localization approaches, the proposed solution is specially designed for an ultra sparse mobile WSNs deployed in coal mine tunnels with linear topography. To obtain mor

  18. Some examples of non-linear systems and characteristics of their solutions

    CSIR Research Space (South Africa)

    Greben, JM

    2006-07-01

    Full Text Available . In contrast to certain other applications in complexity theory, these non-linear solutions are characterized by great stability. To go beyond the dominant non-perturbative solution one has to consider the source term as well. The parameter freedom...

  19. A NUMERICAL SOLUTION OF A SYSTEM OF LINEAR INTEGRO-PARTIAL DIFFERENTIAL EQUATIONS,

    Science.gov (United States)

    The numerical solution to a system of linear integro- partial differential equations is treated. A numerical solution to the system was obtained by...using difference approximations to the partial differential equations . To assure convergence, a stability condition derived from the related plate

  20. On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

    Directory of Open Access Journals (Sweden)

    M. De la Sen

    2014-01-01

    Full Text Available This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

  1. A discrete solvent reaction field model for calculating molecular linear response properties in solution

    NARCIS (Netherlands)

    Jensen, L; van Duijnen, PT; Snijders, JG

    2003-01-01

    A discrete solvent reaction field model for calculating frequency-dependent molecular linear response properties of molecules in solution is presented. The model combines a time-dependent density functional theory (QM) description of the solute molecule with a classical (MM) description of the discr

  2. A Linear Scaling Three Dimensional Fragment Method for Large ScaleElectronic Structure Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Lin-Wang; Zhao, Zhengji; Meza, Juan

    2007-07-26

    We present a novel linear scaling ab initio total energyelectronic structure calculation method, which is simple to implement,easily to parallelize, and produces essentially thesame results as thedirect ab initio method, while it could be thousands of times faster.Using this method, we have studied the dipole moments of CdSe quantumdots, and found both significant bulk and surface contributions. The bulkdipole contribution cannot simply be estimated from the bulk spontaneouspolarization value by a proportional volume factor. Instead it has ageometry dependent screening effect. The dipole moment also produces astrong internal electric field which induces a strong electron holeseparation.

  3. The origin of linear scaling Fock matrix calculation with density prescreening

    Energy Technology Data Exchange (ETDEWEB)

    Mitin, Alexander V., E-mail: mitin@phys.chem.msu.ru [Chemistry Department, Moscow State University, Moscow, 119991 (Russian Federation)

    2015-12-31

    A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.

  4. Analytical solutions in rotating linear dilaton black holes: Hawking radiation of charged massive scalar particles

    CERN Document Server

    Sakalli, I

    2016-01-01

    Hawking radiation of charged massive spin-0 particles are studied in the gravitational, electromagnetic, dilaton, and axion fields of rotating linear dilaton black holes. In this geometry, we separate the covariant Klein--Gordon equation into radial and angular parts and obtain the exact solutions of both the equations in terms of the confluent Heun functions. Using the radial solution, we analyze the behavior of the wave solutions near the event horizon of the rotating linear dilaton black hole and derive its Hawking radiation spectrum via the Damour--Ruffini--Sannan method.

  5. Analytical solutions in rotating linear dilaton black holes: Resonant frequencies, quantization, greybody factor, and Hawking radiation

    Science.gov (United States)

    Sakalli, I.

    2016-10-01

    Charged massive scalar field perturbations are studied in the gravitational, electromagnetic, dilaton, and axion fields of rotating linear dilaton black holes. In this geometry, we separate the covariant Klein-Gordon equation into radial and angular parts and obtain the exact solutions of both the equations in terms of the confluent Heun functions. Using the radial solution, we study the problems of resonant frequencies, entropy/area quantization, and greybody factor. We also analyze the behavior of the wave solutions near the event horizon of the rotating linear dilaton black hole and derive its Hawking temperature via the Damour-Ruffini-Sannan method.

  6. Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Batt, J.; Rein, G. (Muenchen Univ. (Germany). Mathematisches Inst.); Morrison, P.J. (Texas Univ., Austin, TX (United States))

    1993-03-01

    Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e. particle, energy. The main tool in the analysis is the free energy of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.

  7. Global search of non-linear systems periodic solutions: A rotordynamics application

    OpenAIRE

    Sarrouy, Emmanuelle; Thouverez, Fabrice

    2010-01-01

    International audience; Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear d...

  8. Linear and Non-linear Numerical Sea-keeping Evaluation of a Fast Monohull Ferry Compared to Full Scale Measurements

    DEFF Research Database (Denmark)

    Wang, Zhaohui; Folsø, Rasmus; Bondini, Francesca;

    1999-01-01

    presents the results from the performed full scale measurements, and compares these to results from calculations performed with 3 different software systems: I-SHIP, SGN80 and SHIPSTAR.SGN80 is a linear strip theory software system in frequency domain, I-SHIP is a more advanced system, which allows...... the user to compare several linear and nonlinear strip theories, and SHIPSTAR is an advanced non-linear time-domain strip theory sea-keeping code.The calculations agree well with the measurements at Fn=0.32, whereas the agreement is less satisfying at Fn=0.55. Various reasons for this disagreement......, full-scale measurements have been performed on board a 128 m monohull fast ferry. This paper deals with the results from these full-scale measurements. The primary results considered are pitch motion, midship vertical bending moment and vertical acceleration at the bow. Previous comparisons between...

  9. Analyticity of solutions of analytic non-linear general elliptic boundary value problems,and some results about linear problems

    Institute of Scientific and Technical Information of China (English)

    WANG Rouhuai

    2006-01-01

    The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.

  10. A new mobile-immobile model for reactive solute transport with scale-dependent dispersion

    Science.gov (United States)

    Gao, Guangyao; Zhan, Hongbin; Feng, Shaoyuan; Fu, Bojie; Ma, Ying; Huang, Guanhua

    2010-08-01

    This study proposed a new mobile-immobile model (MIM) to describe reactive solute transport with scale-dependent dispersion in heterogeneous porous media. The model was derived from the conventional MIM but assumed the dispersivity to be a linear or exponential function of travel distance. The linear adsorption and the first-order degradation of solute were also considered in the model. The Laplace transform technique and the de Hoog numerical Laplace inversion method were applied to solve the developed model. Solute breakthrough curves (BTCs) obtained from MIM with scale-dependent and constant dispersions were compared, and a constant effective dispersivity was provided to reflect the lumped scale-dependent dispersion effect. The effective dispersivity was calculated by arithmetically averaging the distance-dependent dispersivity. With this effective dispersivity, MIM could produce similar BTC as that from MIM with scale-dependent dispersion in porous media with moderate heterogeneity. The applicability of the proposed new model was tested with concentration data from a 1,250-cm long and highly heterogeneous soil column. The simulation results indicated that MIM with constant and linear distance-dependent dispersivities were unable to adequately describe the measured BTCs in the column, while MIM with exponential distance-dependent dispersivity satisfactorily captured the evolution of BTCs.

  11. CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

    Science.gov (United States)

    Jamison, J. W.

    1994-01-01

    CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

  12. An {Mathematical expression} iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming

    NARCIS (Netherlands)

    J.F. Sturm; J. Zhang (Shuzhong)

    1996-01-01

    textabstractIn this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Mon

  13. Approximation of the solution of certain nonlinear ODEs with linear complexity

    Science.gov (United States)

    Dratman, Ezequiel

    2010-03-01

    We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an [epsilon]-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.

  14. Large space-time scale behavior of linearly interacting diffusions

    NARCIS (Netherlands)

    Swart, J.M.

    1999-01-01

    This dissertation in mathematics is devoted to systems consisting of a countably infinite collection of diffusion processes with a linear attractive interaction. Such systems have been used in population biology as a stochastic model for the distribution of genes over a population, or for the size o

  15. Robust linear equation dwell time model compatible with large scale discrete surface error matrix.

    Science.gov (United States)

    Dong, Zhichao; Cheng, Haobo; Tam, Hon-Yuen

    2015-04-01

    The linear equation dwell time model can translate the 2D convolution process of material removal during subaperture polishing into a more intuitional expression, and may provide relatively fast and reliable results. However, the accurate solution of this ill-posed equation is not so easy, and its practicability for a large scale surface error matrix is still limited. This study first solves this ill-posed equation by Tikhonov regularization and the least square QR decomposition (LSQR) method, and automatically determines an optional interval and a typical value for the damped factor of regularization, which are dependent on the peak removal rate of tool influence functions. Then, a constrained LSQR method is presented to increase the robustness of the damped factor, which can provide more consistent dwell time maps than traditional LSQR. Finally, a matrix segmentation and stitching method is used to cope with large scale surface error matrices. Using these proposed methods, the linear equation model becomes more reliable and efficient in practical engineering.

  16. Input-output description of linear systems with multiple time-scales

    Science.gov (United States)

    Madriz, R. S.; Sastry, S. S.

    1984-01-01

    It is pointed out that the study of systems evolving at multiple time-scales is simplified by studying reduced-order models of these systems valid at specific time-scales. The present investigation is concerned with an extension of results on the time-scale decomposition of autonomous systems to that of input-output systems. The results are employed to study conditions under which positive realness of a transfer function is preserved under singular perturbation. Attention is given to the perturbation theory for linear operators, the multiple time-scale structure of autonomous linear systems, the input-output description of two time-scale linear systems, the positive realness of two time-scale systems, and multiple time-scale linear systems.

  17. A solution to the non-linear equations of D=10 super Yang-Mills theory

    CERN Document Server

    Mafra, Carlos R

    2015-01-01

    In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.

  18. The Solution Structure and Error Estimation for The Generalized Linear Complementarity Problem

    Directory of Open Access Journals (Sweden)

    Tingfa Yan

    2014-07-01

    Full Text Available In this paper, we consider the generalized linear complementarity problem (GLCP. Firstly, we develop some equivalent reformulations of the problem under milder conditions, and then characterize the solution of the GLCP. Secondly, we also establish the global error estimation for the GLCP by weakening the assumption. These results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

  19. On the non-linear scale of cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)

    2013-09-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  20. On the non-linear scale of cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-04-15

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  1. Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

    Science.gov (United States)

    Sen, Symal K.; Shaykhian, Gholam Ali

    2011-01-01

    Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

  2. Inversion of the linearized Korteweg-de Vries equation at the multi-soliton solutions

    CERN Document Server

    Haragus-Courcelle, M

    1998-01-01

    Uniform estimates for the decay structure of the $n$-soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the $n$-soliton solution is investigated in a class $\\WW$ consisting of sums of travelling waves plus an exponentially decaying residual term. An analog of the kernel of the time-independent equation is proposed, leading to solvability conditions on the inhomogeneous term. Estimates on the inversion of the linearized KdV equation at the $n$-soliton are obtained.

  3. Non-local investigation of bifurcations of solutions of non-linear elliptic equations

    Energy Technology Data Exchange (ETDEWEB)

    Il' yasov, Ya Sh

    2002-12-31

    We justify the projective fibration procedure for functionals defined on Banach spaces. Using this procedure and a dynamical approach to the study with respect to parameters, we prove that there are branches of positive solutions of non-linear elliptic equations with indefinite non-linearities. We investigate the asymptotic behaviour of these branches at bifurcation points. In the general case of equations with p-Laplacian we prove that there are upper bounds of branches of positive solutions with respect to the parameter.

  4. Analytical solution of linear ordinary differential equations by differential transfer matrix method

    Directory of Open Access Journals (Sweden)

    Sina Khorasani

    2003-08-01

    Full Text Available We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the $n$th-order differential equation to a system of $n$ linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method.

  5. The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In general normed spaces,we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior.We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function.Moreover,we provide necessary and suffcient conditions about the existence of weak(sharp) Pareto solutions.

  6. Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions

    Science.gov (United States)

    Feng, Lili; Yu, Fajun; Li, Li

    2017-01-01

    Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.

  7. Exact Solutions of Discrete Complex Cubic Ginzburg-Landau Equation and Their Linear Stability

    Institute of Scientific and Technical Information of China (English)

    张金良; 刘治国

    2011-01-01

    The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.

  8. Non-linear variability in geophysics scaling and fractals

    CERN Document Server

    Lovejoy, S

    1991-01-01

    consequences of broken symmetry -here parity-is studied. In this model, turbulence is dominated by a hierarchy of helical (corkscrew) structures. The authors stress the unique features of such pseudo-scalar cascades as well as the extreme nature of the resulting (intermittent) fluctuations. Intermittent turbulent cascades was also the theme of a paper by us in which we show that universality classes exist for continuous cascades (in which an infinite number of cascade steps occur over a finite range of scales). This result is the multiplicative analogue of the familiar central limit theorem for the addition of random variables. Finally, an interesting paper by Pasmanter investigates the scaling associated with anomolous diffusion in a chaotic tidal basin model involving a small number of degrees of freedom. Although the statistical literature is replete with techniques for dealing with those random processes characterized by both exponentially decaying (non-scaling) autocorrelations and exponentially decaying...

  9. AN ACCURATE SOLUTION OF THE LINEAR THEORY OF THE WIND-DRIVEN OCEAN CIRCULATION-I. THE GENERALIZED SOLUTION

    Institute of Scientific and Technical Information of China (English)

    Zhang Qing-hua; Qu Yuan-yuan; Xia Chang-shui

    2003-01-01

    To model the wind-driven ocean circulation of the isobath rectangular basin, the linear vorticity equation with the meridional friction term was used compared to the Munk's theory on the ocean circulation. The generalized solution of the vorticity equation was thus worked out in the sense of Fourier averaging by using the corrected Fourier expansion. The method to obtain the undetermined coefficients was presented using the viscous boundary conditions.

  10. Silica scaling in forward osmosis: From solution to membrane interface.

    Science.gov (United States)

    Xie, Ming; Gray, Stephen R

    2017-01-01

    Membrane silica scaling hinders sustainable water production. Understanding silica scaling mechanisms provides options for better membrane process management. In this study, we elucidated silica scaling mechanisms on an asymmetric cellulose triacetate (CTA) membrane and polyamide thin-film composite (TFC) membrane. Scaling filtration showed that TFC membrane was subjected to more severe water flux decline in comparison with the CTA membrane, together with different scaling layer morphology. To elucidate the silica scaling mechanisms, silica species in the aqueous solution were characterised by mass spectrometry as well as light scattering. Key thermodynamic parameters of silica surface nucleation on the CTA and TFC membranes were estimated to compare the surface nucleation energy barrier. In addition, high resolution X-ray photoelectron spectroscopy resolved the chemical origin of the silica-membrane interaction via identifying the specific silicon bonds. These results strongly support that silica scaling in the CTA membrane was driven by the aggregation of mono-silicic acid into large silica aggregates, followed by the deposition from bulk solution onto the membrane surface; by contrast, silica polymerised on the TFC membrane surface where mono-silicic acid interacted with TFC membrane surface, which was followed by silica surface polymerisation.

  11. Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions.

    Science.gov (United States)

    Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul

    2015-11-14

    Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved-up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

  12. Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

    Energy Technology Data Exchange (ETDEWEB)

    Lorenzen, Konstantin; Mathias, Gerald; Tavan, Paul, E-mail: tavan@physik.uni-muenchen.de [Lehrstuhl für BioMolekulare Optik, Ludig–Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

    2015-11-14

    Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

  13. Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.

    Science.gov (United States)

    Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J

    2016-10-03

    Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods.

  14. Critical scaling in hidden state inference for linear Langevin dynamics

    OpenAIRE

    Bravi, Barbara; Sollich, Peter

    2016-01-01

    We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and we study analytically the average prediction error given by the Extended Plefka Expansion applied to it, as presented in [1]. We focus on a stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings in the infinite network size limit. The expected error on the hidden time courses can be found as the equal-time hidden-to-hidden cova...

  15. Prediction of scale potential in ethylene glycol containing solutions

    Energy Technology Data Exchange (ETDEWEB)

    Sandengen, Kristian; Oestvold, Terje

    2006-03-15

    This work presents a method for scale prediction in MEG (Mono Ethylene Glycol / 1,2-ethane-diol) containing solutions. It is based on an existing PVT scale model using a Pitzer ion interaction model for the aqueous phase. The model is well suited for scale prediction in saline solutions, where the PVT part is necessary for calculating CO{sub 2} phase equilibria being critical for carbonate scale. MEG influences the equilibria contained in the model, and its effect has been added empirically. Thus the accuracy of the model is limited by the amount of available experimental data. The model is applicable in the range 0-99wt% MEG and includes a wide variety of salts. In addition to the aspects of scale modelling in MEG+water solutions, this work presents new experimental data on CaSO4 solubility (0-95wt% MEG and 22-80 deg.C). CaSO4 solubility is greatly reduced by MEG to an extent that ''Salting-out'' is possible. (author) (tk)

  16. Linear polymer aqueous solutions in soft lubrication:From boundary to mixed lubrication

    Institute of Scientific and Technical Information of China (English)

    LIU; ShuHai; TAN; GuiBin; WANG; DeGuo

    2013-01-01

    In order to better understand linear polymer aqueous solutions in soft lubrication from boundary to mixed lubrication,poly(ethylene glycol) and sodium hyaluronateare used as model polymers were investigated by using UMT-2 tribometer with the ball-on-disk mode. The relationship between the master Stribeck curves of the polymer aqueous solutions and the influence factors were investigated. Experimental results indicated that soft lubrication is determined by lubricant rheological properties and surface-lubricant interactions, e.g., wetting behavior of polymer aqueous solution on tribological surfaces.

  17. Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

    Directory of Open Access Journals (Sweden)

    Olumuyiwa A. Agbolade

    2017-01-01

    Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

  18. Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems with One Weakly Linearly Degenerate Characteristic

    Institute of Scientific and Technical Information of China (English)

    Peng QU; Cunming LIU

    2012-01-01

    For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H2 classical solution to the Cauchy problem with small initial data is obtained.

  19. Linear viscoelastic behavior of enzymatically modified guar gum solutions: structure, relaxations and gel formation

    NARCIS (Netherlands)

    Wientjes, R.H.W.; Duits, M.H.G.; Bakker, J.W.P.; Jongschaap, R.J.J.; Mellema, J.

    2001-01-01

    To gain more insight into the mechanisms of stress relaxation in aqueous guar gum solutions, we investigated the effect of chemical modifications of the polymer and of the solvent on the linear viscoelastic behavior in different regions of the frequency domain. Interchain bonding could be ruled out

  20. A comparative study of iterative solutions to linear systems arising in quantum mechanics

    NARCIS (Netherlands)

    Jing, Yan-Fei; Huang, Ting-Zhu; Duan, Yong; Carpentieri, Bruno

    2010-01-01

    This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods

  1. Centered Solutions for Uncertain Linear Equations (revision of CentER DP 2015-044)

    NARCIS (Netherlands)

    Zhen, Jianzhe; den Hertog, Dick

    2016-01-01

    Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex.We derive a convex representation of this intersection.

  2. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations

    Science.gov (United States)

    Rasmussen, Chris; Keynes, Michael

    2003-01-01

    The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant coefficients. The significance of this paper is two-fold. First, it represents an innovative alternative…

  3. Acceleration of multiple solution of a boundary value problem involving a linear algebraic system

    Science.gov (United States)

    Gazizov, Talgat R.; Kuksenko, Sergey P.; Surovtsev, Roman S.

    2016-06-01

    Multiple solution of a boundary value problem that involves a linear algebraic system is considered. New approach to acceleration of the solution is proposed. The approach uses the structure of the linear system matrix. Particularly, location of entries in the right columns and low rows of the matrix, which undergo variation due to the computing in the range of parameters, is used to apply block LU decomposition. Application of the approach is considered on the example of multiple computing of the capacitance matrix by method of moments used in numerical electromagnetics. Expressions for analytic estimation of the acceleration are presented. Results of the numerical experiments for solution of 100 linear systems with matrix orders of 1000, 2000, 3000 and different relations of variated and constant entries of the matrix show that block LU decomposition can be effective for multiple solution of linear systems. The speed up compared to pointwise LU factorization increases (up to 15) for larger number and order of considered systems with lower number of variated entries.

  4. ESTIMATION METHOD FOR SOLUTIONS TO GENERAL LINEAR SYSTEM OF VOLTERRAINTEGRAL INEQUALITIES INVOLVING ITERATED INTEGRAL FUNCTIONALS

    Institute of Scientific and Technical Information of China (English)

    MA Qinghua; YANG Enhao

    2000-01-01

    An estimation method for solutions to the general linear system of Volterratype integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the present second author in Journ. Math. Anal. Appl.(1984). A certain two-dimensional system of nonlinear ordinary differential equations is also discussed to demonstrate the usefulness of our method.

  5. On Global Smooth Solution of A Semi-Linear System of Wave Equations in R3

    Institute of Scientific and Technical Information of China (English)

    WU Haigen

    2009-01-01

    In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth so-lution of the system for subcritical case by using conservation of energy and Strichartz's estimate. On the basis of Morawetz-Poho2ev identity, we obtain the same result for the critical case.

  6. Thermodynamic and Hydrodynamic Properties of Dilute Solutions of Cyclic and Linear Polystyrenes

    NARCIS (Netherlands)

    Hadziioannou, G.; Cotts, P.M.; Brinke, G. ten; Han, C.C.; Lutz, P.; Strazielle, C.; Rempp, P.

    1987-01-01

    The thermodynamic and hydrodynamic properties of cyclic and linear polystyrenes, ranging from 10000 to 180000 molecular weight, in dilute solutions of cyclohexane have been measured by small-angle neutron scattering (SANS) and dynamic light scattering. The diffusion coefficient D(c) was measured at

  7. Multiple Solutions for a Fourth-order Asymptotically Linear Elliptic Problem

    Institute of Scientific and Technical Information of China (English)

    Ai Xia QIAN; Shu Jie LI

    2006-01-01

    Under simple conditions, we prove the existence of three solutions for a fourth-order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding functional.

  8. Solution of the Schrodinger Equation for a Diatomic Oscillator Using Linear Algebra: An Undergraduate Computational Experiment

    Science.gov (United States)

    Gasyna, Zbigniew L.

    2008-01-01

    Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)

  9. Solutions to quasi-linear differential equations with iterated deviating arguments

    Directory of Open Access Journals (Sweden)

    Rajib Haloi

    2014-12-01

    Full Text Available We establish sufficient conditions for the existence and uniqueness of solutions to quasi-linear differential equations with iterated deviating arguments, complex Banach space. The results are obtained by using the semigroup theory for parabolic equations and fixed point theorems. The main results are illustrated by an example.

  10. A comparative study of iterative solutions to linear systems arising in quantum mechanics

    NARCIS (Netherlands)

    Jing, Yan-Fei; Huang, Ting-Zhu; Duan, Yong; Carpentieri, Bruno

    2010-01-01

    This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods

  11. Localized density matrix minimization and linear scaling algorithms

    CERN Document Server

    Lai, Rongjie

    2015-01-01

    We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\\ell_1$ regularization to the free energy of the quantum system. Based on the fact that the density matrix decays exponential away from the diagonal for insulating system or system at finite temperature, the proposed $\\ell_1$ regularized variational method provides a nice way to approximate the original quantum system. We provide theoretical analysis of the approximation behavior and also design convergence guaranteed numerical algorithms based on Bregman iteration. More importantly, the $\\ell_1$ regularized system naturally leads to localized density matrices with banded structure, which enables us to develop approximating algorithms to find the localized density matrices with computation cost linearly dependent on the problem size.

  12. Exact solution to the Coulomb wave using the linearized phase-amplitude method

    Directory of Open Access Journals (Sweden)

    Shuji Kiyokawa

    2015-08-01

    Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

  13. An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

    Science.gov (United States)

    Bauld, N. R., Jr.; Goree, J. G.

    1983-01-01

    The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

  14. Parallelized preconditioned BiCGStab solution of sparse linear system equations in F-COBRA-TF

    Energy Technology Data Exchange (ETDEWEB)

    Geemert, Rene van; Glück, Markus; Riedmann, Michael; Gabriel, Harry, E-mail: rene.vangeemert@areva.com, E-mail: michael.riedmann@areva.com, E-mail: harry.gabriel@areva.com [AREVA NP GmbH, Erlangen (Germany)

    2011-07-01

    Recently, the in-house development of a preconditioned and parallelized BiCGStab solver has been pursued successfully in AREVA’s advanced sub-channel code F-COBRA-TF. This solver can be run either in a sequential computation mode on a single CPU, or in a parallel computation mode on multiple parallel CPUs. The developed procedure enables the computation of several thousands of successive sparse linear system solutions in F-COBRA-TF with acceptable wall clock run times. The current paper provides general information about F-COBRA-TF in terms of modeling capabilities and application areas, and points out where the relevance arises for the efficient iterative solution of sparse linear systems. Furthermore, the preconditioning and parallelization strategies in the developed BiCGStab iterative solution approach are discussed. The paper is concluded with a number of verification examples. (author)

  15. Global search of non-linear systems periodic solutions: A rotordynamics application

    Science.gov (United States)

    Sarrouy, E.; Thouverez, F.

    2010-08-01

    Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions—where T is known—of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.

  16. Preservation of local linearity by neighborhood subspace scaling for solving the pre-image problem

    Institute of Scientific and Technical Information of China (English)

    Sheng-kai YANG; Jian-yi MENG; Hai-bin SHEN

    2014-01-01

    An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative, and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis (PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.

  17. Linear scaling calculation of maximally localized Wannier functions with atomic basis set.

    Science.gov (United States)

    Xiang, H J; Li, Zhenyu; Liang, W Z; Yang, Jinlong; Hou, J G; Zhu, Qingshi

    2006-06-21

    We have developed a linear scaling algorithm for calculating maximally localized Wannier functions (MLWFs) using atomic orbital basis. An O(N) ground state calculation is carried out to get the density matrix (DM). Through a projection of the DM onto atomic orbitals and a subsequent O(N) orthogonalization, we obtain initial orthogonal localized orbitals. These orbitals can be maximally localized in linear scaling by simple Jacobi sweeps. Our O(N) method is validated by applying it to water molecule and wurtzite ZnO. The linear scaling behavior of the new method is demonstrated by computing the MLWFs of boron nitride nanotubes.

  18. CMB all-scale blackbody distortions induced by linearizing temperature

    Science.gov (United States)

    Notari, Alessio; Quartin, Miguel

    2016-08-01

    Cosmic microwave background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal in the maps in the form of y -type distortions which is degenerate with the thermal Sunyaev Zel'dovich (tSZ) effect. These are small effects that arise at second order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of our peculiar velocity, the tSZ and primordial y -distortions. They can nevertheless be well modeled and accounted for. We show that the distortions arise from a leakage of the CMB dipole into the y -channel which couples to all multipoles, mostly affecting the range ℓ≲400 . This should be visible in Planck's y -maps with an estimated signal-to-noise ratio of about 12. We note however that such frequency-dependent terms carry no new information on the nature of the CMB dipole. This implies that the real significance of Planck's Doppler coupling measurements is actually lower than reported by the collaboration. Finally, we quantify the level of contamination in tSZ and primordial y -type distortions and show that it is above the sensitivity of proposed next-generation CMB experiments.

  19. CMB all-scale blackbody distortions induced by linearizing temperature

    CERN Document Server

    Notari, Alessio

    2016-01-01

    Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a \\emph{linearized} formula for relating them to the temperature blackbody fluctuations. However such a procedure also generates a signal in the maps in the form of y-type distortions, and thus degenerate with the thermal SZ (tSZ) effect. These are small effects that arise at second-order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of: our peculiar velocity, the tSZ and of primordial y-distortions, but they can nevertheless be well-modelled and accounted for. We show that the largest distortions arises at high ell from a leakage of the CMB dipole into the y-channel which couples to all multipoles, but mostly affects the range ell <~ 400. This should be visible in Planck's y-maps with an estimated signal-to-noise ratio of about 9. We note however that such frequency-de...

  20. Linear-scaling and parallelizable algorithms for stochastic quantum chemistry

    CERN Document Server

    Booth, George H; Alavi, Ali

    2013-01-01

    For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimized paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can often achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelization which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the metho...

  1. Multiscale plant wakes, turbulence and non linear scaling flexible effects

    Science.gov (United States)

    Vila, Teresa; Redondo, Jose M.; Velasco, David

    2010-05-01

    We present velocity ADV measurements and flow visualization of the turbulent wakes behind plant arrays, as these are often fractal in nature, we compare the multifractal spectra and the turbulence structure behind the wakes. Both statistical measures allowing to calculate integral lengthscales and their profiles modified by the plant cannopies [1,2] as well as intermittency and spectral behaviour are also measured [3,4]. We distinguish several momentum transfer mechanisms between the cannopy and the flow, an internal one where lateral turbulent tensions are dominant, and another one just above the plant average height dominated by vertical Reynolds stresses. Visualization of flow over individual plant models show the role of coherent vortices triggered by plant elasticity. The deformation rate of the plants and their Youngs modulus may be correlated with overal plant drag and geometry. This is modified strongly in fractal canopies. Large turbulent integral scales are linked to rugosity and the scaling of the waves.[5,6] Pearlescence experiments where local shear is visualized and numerical simulations of Fractal grids are compared following [7]. [1] Nepf,H.M. Drag, turbulence and diffusion in flow through emergent vegetation. Water Resources Res. 35(2)(1999) [2] Ben Mahjoub,O., Redondo J.M. and Babiano A. Jour.Structure functions in complex flows. Flow Turbulence and Combustion 59, 299-313. [3] El-Hakim, O. Salama, M. Velocity distribution inside and above branched flexible roughness. ASCE Journal of Irrigation and Drainage Engineering, Vol. 118, No 6, (November/December 1992) 914-927. [4] Finnigan,J. Turbulence in plant canopies. Annu. Rev. Fluid Mech. 2000 , Vol. 32: 519-571. [5] Ikeda, S., Kanazawa, M. Three- dimensional organized vortices above flexible water plants. ASCE Journal of Hydraulic Engineering, Vol. 122, No 11, (1996) 634-640. [6] Velasco, D.,Bateman A.,Redondo J.M and Medina V. An open channel flow experimental and theorical study of resistance and

  2. A mixed-integer linear programming approach to the reduction of genome-scale metabolic networks.

    Science.gov (United States)

    Röhl, Annika; Bockmayr, Alexander

    2017-01-03

    Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement. Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways. Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.

  3. Iterative solution of large, sparse linear systems on a static data flow architecture - Performance studies

    Science.gov (United States)

    Reed, D. A.; Patrick, M. L.

    1985-01-01

    The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.

  4. Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

    Science.gov (United States)

    Van Benthem, Mark H.; Keenan, Michael R.

    2008-11-11

    A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

  5. Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.

  6. Analytical solution for a class of linear quadratic open-loop Nash game with multiple players

    Institute of Scientific and Technical Information of China (English)

    Xiaohong NIAN; Zhisheng DUAN; Wenyan TANG

    2006-01-01

    In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrixcan be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure.

  7. A High-Quality Preconditioning Technique for Multi-Length-Scale Symmetric Positive Definite Linear Systems

    Institute of Scientific and Technical Information of China (English)

    Ichitaro Yamazaki; Zhaojun Bai; Wenbin Chen; Richard Scalettar

    2009-01-01

    We study preconditioning techniques used in conjunction with the conjugate gradient method for solving multi-length-scale symmetric positive definite linear systems originating from the quantum Monte Carlo simulation of electron interaction of correlated materials. Existing preconditioning techniques are not designed to be adaptive to varying numerical properties of the multi-length-scale systems. In this paper, we propose a hybrid incomplete Cholesky (HIC) preconditioner and demonstrate its adaptivity to the multi-length-scale systems. In addition, we propose an extension of the compressed sparse column with row access (CSCR) sparse matrix storage format to efficiently accommodate the data access pattern to compute the HIC preconditioner. We show that for moderately correlated materials, the HIC preconditioner achieves the optimal linear scaling of the simulation. The development of a linear-scaling preconditioner for strongly correlated materials remains an open topic.

  8. Multiobjective Optimization of Linear Cooperative Spectrum Sensing: Pareto Solutions and Refinement.

    Science.gov (United States)

    Yuan, Wei; You, Xinge; Xu, Jing; Leung, Henry; Zhang, Tianhang; Chen, Chun Lung Philip

    2016-01-01

    In linear cooperative spectrum sensing, the weights of secondary users and detection threshold should be optimally chosen to minimize missed detection probability and to maximize secondary network throughput. Since these two objectives are not completely compatible, we study this problem from the viewpoint of multiple-objective optimization. We aim to obtain a set of evenly distributed Pareto solutions. To this end, here, we introduce the normal constraint (NC) method to transform the problem into a set of single-objective optimization (SOO) problems. Each SOO problem usually results in a Pareto solution. However, NC does not provide any solution method to these SOO problems, nor any indication on the optimal number of Pareto solutions. Furthermore, NC has no preference over all Pareto solutions, while a designer may be only interested in some of them. In this paper, we employ a stochastic global optimization algorithm to solve the SOO problems, and then propose a simple method to determine the optimal number of Pareto solutions under a computational complexity constraint. In addition, we extend NC to refine the Pareto solutions and select the ones of interest. Finally, we verify the effectiveness and efficiency of the proposed methods through computer simulations.

  9. Existence and global exponential stability of periodic solutions for n-dimensional neutral dynamic equations on time scales.

    Science.gov (United States)

    Li, Bing; Li, Yongkun; Zhang, Xuemei

    2016-01-01

    In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).

  10. On the solution of a class of fuzzy system of linear equations

    Indian Academy of Sciences (India)

    Davod Khojasteh Salkuyeh

    2015-04-01

    In this paper, we consider the system of linear equations $A\\widetilde{x}=\\widetilde{b}$, where $A \\in \\mathbb{R}^{n \\times n}$ is a crisp H-matrix and \\widetilde{b} is a fuzzy -vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical results.

  11. Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

    Science.gov (United States)

    Saakian, David B.

    2017-08-01

    We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

  12. Scattering of Light in Defocusing Media upon Linear Substrate Analysis of Formal Solutions

    CERN Document Server

    Ochirbat, G

    2000-01-01

    An analysis of formal solutions to the system of Maxwell equations has been performed for a scattering problem of stationary TM light waves in defocusing matter on a linear substrate. Bruster waves have been observed. A nontrivial plane wave has been found for which relation between a refraction constant and an intensity-dependent dielectric constant has been found. An asymptotic plane TM wave has been obtained, and a procedure of its finding has been elaborated.

  13. Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving

    Institute of Scientific and Technical Information of China (English)

    杨洁; 逯怀新; 赵博; 赵梅生; 张永德

    2003-01-01

    We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1, 1) Lie algebra structure,with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.

  14. Superdiffusions and positive solutions of non-linear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dynkin, E B [Cornell University, New York (United States)

    2004-02-28

    By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.

  15. Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

    Directory of Open Access Journals (Sweden)

    Sankar Prasad Mondal

    2016-06-01

    Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

  16. Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blondel's technique. We give a complete answer to the open problem proposed by Patel et al., which automatically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature.

  17. Series solutions of non-linear Riccati differential equations with fractional order

    Energy Technology Data Exchange (ETDEWEB)

    Cang Jie; Tan Yue; Xu Hang [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China); Liao Shijun [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: sjliao@sjtu.edu.cn

    2009-04-15

    In this paper, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h. Besides, it is proved that well-known Adomian's decomposition method is a special case of the homotopy analysis method when h = -1. This work illustrates the validity and great potential of the homotopy analysis method for the non-linear differential equations with fractional order. The basic ideas of this approach can be widely employed to solve other strongly non-linear problems in fractional calculus.

  18. Energetics of slope flows: linear and weakly nonlinear solutions of the extended Prandtl model

    Science.gov (United States)

    Güttler, Ivan; Marinović, Ivana; Večenaj, Željko; Grisogono, Branko

    2016-07-01

    The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is

  19. On the economical solution method for a system of linear algebraic equations

    Directory of Open Access Journals (Sweden)

    Jan Awrejcewicz

    2004-01-01

    Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

  20. Thresholded Basis Pursuit: Quantizing Linear Programming Solutions for Optimal Support Recovery and Approximation in Compressed Sensing

    CERN Document Server

    Saligrama, V

    2008-01-01

    We consider the classical Compressed Sensing problem. We have a large under-determined set of noisy measurements Y=GX+N, where X is a sparse signal and G is drawn from a random ensemble. In this paper we focus on a quantized linear programming solution for support recovery. Our solution of the problem amounts to solving $\\min \\|Z\\|_1 ~ s.t. ~ Y=G Z$, and quantizing/thresholding the resulting solution $Z$. We show that this scheme is guaranteed to perfectly reconstruct a discrete signal or control the element-wise reconstruction error for a continuous signal for specific values of sparsity. We show that in the linear regime when the sparsity, $k$, increases linearly with signal dimension, $n$, the sign pattern of $X$ can be recovered with $SNR=O(\\log n)$ and $m= O(k)$ measurements. Our proof technique is based on perturbation of the noiseless $\\ell_1$ problem. Consequently, the achievable sparsity level in the noisy problem is comparable to that of the noiseless problem. Our result offers a sharp characterizat...

  1. On the economical solution method for a system of linear algebraic equations

    Directory of Open Access Journals (Sweden)

    Awrejcewicz Jan

    2004-01-01

    Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ 3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O( h x 1 2 + h x 2 2 . The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

  2. Non-linear effects on solute transfer between flowing water and a sediment bed.

    Science.gov (United States)

    Higashino, Makoto; Stefan, Heinz G

    2011-11-15

    A previously developed model of periodic pore water flow in space and time, and associated solute transport in a stream bed of fine sand is extended to coarse sand and fine gravel. The pore water flow immediately below the sediment/water interface becomes intermittently a non-Darcy flow. The periodic pressure and velocity fluctuations considered are induced by near-bed coherent turbulent motions in the stream flow; they penetrate from the sediment/water interface into the sediment pore system and are described by a wave number (χ) and a period (T) that are given as functions of the shear velocity (U(∗)) between the flowing water and the sediment bed. The stream bed has a flat surface without bed forms. The flow field in the sediment pore system is described by the continuity equation and a resistance law that includes both viscous (Darcy) and non-linear (inertial) effects. Simulation results show that non-linear (inertial) effects near the sediment/water interface increase flow resistance and reduce mean flow velocities. Compared to pure Darcy flow, non-linear (inertial) effects reduce solute exchange rates between overlying water and the sediment bed but only by a moderate amount (less than 50%). Turbulent coherent flow structures in the stream flow enhance solute transfer in the pore system of a stream bed compared to pure molecular diffusion, but by much less than standing surface waves or bed forms.

  3. Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

    Energy Technology Data Exchange (ETDEWEB)

    Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

    1996-12-31

    The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

  4. Self-Similar Nonlinear Dynamical Solutions for One-Component Nonneutral Plasma in a Time-Dependent Linear Focusing Field

    Energy Technology Data Exchange (ETDEWEB)

    Hong Qin and Ronald C. Davidson

    2011-07-19

    In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.

  5. On Complex Oscillation Theory of Solutions of Some Higher Order Linear Differential Equations

    Institute of Scientific and Technical Information of China (English)

    Jianren LONG

    2012-01-01

    In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ(A)< 1/2.Suppose that k ≥ 2 and f(k)+ A(z)f =0 has a solution f with λ(f)< ρ(A),and suppose that A1 =A + h,where h ≠ 0 is an entire function with ρ(h)< ρ(A).Then g(k)+ A1(z)g =0 does not have a solution g with λ(g)< ∞.

  6. On Attainability of Optimal Solutions for Linear Elliptic Equations with Unbounded Coefficients

    Directory of Open Access Journals (Sweden)

    P. I. Kogut

    2011-12-01

    Full Text Available We study an optimal boundary control problem (OCP associated to a linear elliptic equation —div (Vj/ + A(xVy = f describing diffusion in a turbulent flow. The characteristic feature of this equation is the fact that, in applications, the stream matrix A(x = [a,ij(x]i,j=i,...,N is skew-symmetric, ац(х = —a,ji(x, measurable, and belongs to L -space (rather than L°°. An optimal solution to such problem can inherit a singular character of the original stream matrix A. We show that optimal solutions can be attainable by solutions of special optimal boundary control problems.

  7. Exact solutions to the geodesic equations of linear dilaton black holes

    CERN Document Server

    Hamo, A H H

    2015-01-01

    In this paper, we analyze the geodesics of the 4-dimensional ($4D$) linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-Dilaton (EMD) theory. LDBHs have non-asymptotically flat (NAF) geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange (EL) equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the WeierstrassP-function ($\\wp$-function), which is an elliptic-type special function.

  8. Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

    KAUST Repository

    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.

  9. A simple model for electrical charge in globular macromolecules and linear polyelectrolytes in solution

    Science.gov (United States)

    Krishnan, M.

    2017-05-01

    We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule's interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an "interaction charge" for the molecule which we demonstrate agrees closely with the "effective charge" discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of pKa shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or

  10. Exact Solutions of a Generalized Weighted Scale Free Network

    Directory of Open Access Journals (Sweden)

    Li Tan

    2013-01-01

    Full Text Available We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.

  11. Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

    Energy Technology Data Exchange (ETDEWEB)

    Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami

    2017-03-27

    Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Results: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.

  12. On the error of estimating the sparsest solution of underdetermined linear systems

    CERN Document Server

    Babaie-Zadeh, Massoud; Mohimani, Hosein

    2011-01-01

    Let A be an n by m matrix with m>n, and suppose that the underdetermined linear system As=x admits a sparse solution s0 for which ||s0||_0 < 1/2 spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now that we have somehow a solution s_hat as an estimation of s0, and suppose that s_hat is only `approximately sparse', that is, many of its components are very small and nearly zero, but not mathematically equal to zero. Is such a solution necessarily close to the true sparsest solution? More generally, is it possible to construct an upper bound on the estimation error ||s_hat-s0||_2 without knowing s0? The answer is positive, and in this paper we construct such a bound based on minimal singular values of submatrices of A. We will also state a tight bound, which is more complicated, but besides being tight, enables us to study the case of random dictionaries and obtain probabilistic upper bounds. We will also study the noisy case, that is, where x=As+n. Moreover, we will s...

  13. Exact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programming

    KAUST Repository

    Li, Yanning

    2013-10-01

    This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.

  14. Multi-scale modelling of uranyl chloride solutions

    Energy Technology Data Exchange (ETDEWEB)

    Nguyen, Thanh-Nghi; Duvail, Magali, E-mail: magali.duvail@icsm.fr; Villard, Arnaud; Dufrêche, Jean-François, E-mail: jean-francois.dufreche@univ-montp2.fr [Institut de Chimie Séparative de Marcoule (ICSM), UMR 5257, CEA-CNRS-Université Montpellier 2-ENSCM, Site de Marcoule, Bâtiment 426, BP 17171, F-30207 Bagnols-sur-Cèze Cedex (France); Molina, John Jairo [Fukui Institute for Fundamental Chemistry, Kyoto University, Takano-Nishihiraki-cho 34-4, Sakyo-ku, Kyoto 606-8103 (Japan); Guilbaud, Philippe [CEA/DEN/DRCP/SMCS/LILA, Marcoule, F-30207 Bagnols-sur-Cèze Cedex (France)

    2015-01-14

    Classical molecular dynamics simulations with explicit polarization have been successfully used to determine the structural and thermodynamic properties of binary aqueous solutions of uranyl chloride (UO{sub 2}Cl{sub 2}). Concentrated aqueous solutions of uranyl chloride have been studied to determine the hydration properties and the ion-ion interactions. The bond distances and the coordination number of the hydrated uranyl are in good agreement with available experimental data. Two stable positions of chloride in the second hydration shell of uranyl have been identified. The UO{sub 2}{sup 2+}-Cl{sup −} association constants have also been calculated using a multi-scale approach. First, the ion-ion potential averaged over the solvent configurations at infinite dilution (McMillan-Mayer potential) was calculated to establish the dissociation/association processes of UO{sub 2}{sup 2+}-Cl{sup −} ion pairs in aqueous solution. Then, the association constant was calculated from this potential. The value we obtained for the association constant is in good agreement with the experimental result (K{sub UO{sub 2Cl{sup +}}} = 1.48 l mol{sup −1}), but the resulting activity coefficient appears to be too low at molar concentration.

  15. Solution of dense systems of linear equations in electromagnetic scattering calculations

    Energy Technology Data Exchange (ETDEWEB)

    Rahola, J. [Center for Scientific Computing, Espoo (Finland)

    1994-12-31

    The discrete-dipole approximation (DDA) is a method for calculating the scattering of light by an irregular particle. The DDA has been used for example in calculations of optical properties of cosmic dust. In this method the particle is approximated by interacting electromagnetic dipoles. Computationally the DDA method includes the solution of large dense systems of linear equations where the coefficient matrix is complex symmetric. In the author`s work, the linear systems of equations are solved by various iterative methods such as the conjugate gradient method applied to the normal equations and QMR. The linear systems have rather low condition numbers due to which many iterative methods perform quite well even without any preconditioning. Some possible preconditioning strategies are discussed. Finally, some fast special methods for computing the matrix-vector product in the iterative methods are considered. In some cases, the matrix-vector product can be computed with the fast Fourier transform, which enables the author to solve dense linear systems of hundreds of thousands of unknowns.

  16. Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory

    CERN Document Server

    Markovich, Tomer; Podgornik, Rudi

    2016-01-01

    We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.

  17. Assessment Of Some Acceleration Schemes In The Solution Of Systems Of Linear Equations.

    Directory of Open Access Journals (Sweden)

    S. Azizu

    2015-06-01

    Full Text Available Abstract In this paper assessment of acceleration schemes in the solution of systems of linear equations has been studied. The iterative methods Jacobi Gauss-Seidel and SOR methods were incorporated into the acceleration scheme Chebyshev extrapolation Residual smoothing Accelerated gradient and Richardson Extrapolation to speed up their convergence. The Conjugate gradient methods of GMRES BICGSTAB and QMR were also assessed. The research focused on Banded systems Tridiagonal systems and Dense Symmetric positive definite systems of linear equations for numerical experiments. The experiments were based on the following performance criteria convergence number of iterations speed of convergence and relative residual of each method. Matlab version 7.0.1 was used for the computation of the resulting algorithms. Assessment of the numerical results showed that the accelerated schemes improved the performance of Jacobi Gauss-Seidel and SOR methods. The Chebyshev and Richardson acceleration methods converged faster than the conjugate gradient methods of GMRES MINRES QMR and BICGSTAB in general.

  18. A Fast Condensing Method for Solution of Linear-Quadratic Control Problems

    DEFF Research Database (Denmark)

    Frison, Gianluca; Jørgensen, John Bagterp

    2013-01-01

    In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...

  19. Existence of Nondecreasing and Continuous Solutions of an Integral Equation with Linear Modification of the Argument

    Institute of Scientific and Technical Information of China (English)

    J. CABALLERO; B. L(ó)PEZ; K. SADARANGANI

    2007-01-01

    We use a technique associated with measures of noncompactness to prove the existence of nondecreasing solutions to an integral equation with linear modification of the argument in the space C[0,1]. In the last thirty years there has been a great deal of work in the field of differential equations with a modified argument. A special class is represented by the differential equation with affine modification of the argument which can be delay differential equations or differential equations with linear modifications of the argument. In this case we study the following integral equation x(t) = a(t) + (Tx)(t)∫σ(t)o u(t,s,x(s),x(λs))ds 0λ1 which can be considered in connection with the following Cauchy problem x'(t) = u(t,s,x(t),x(λt)), t∈[0,1], 0 λ 1 x(0) = uo.

  20. The solution of linear mechanical systems in terms of path superposition

    Science.gov (United States)

    Magrans, Francesc Xavier; Poblet-Puig, Jordi; Rodríguez-Ferran, Antonio

    2017-02-01

    We prove that the solution of any linear mechanical system can be expressed as a linear combination of signal transmission paths. This is done in the framework of the Global Transfer Direct Transfer (GTDT) formulation for vibroacoustic problems. Transmission paths are expressed as powers of the transfer matrix. The key idea of the proof is to generalise the Neumann series of the transfer matrix - which is convergent only if its spectral radius is smaller than one - into a modified Neumann series that is convergent regardless of the eigenvalues of the transfer matrix. The modification consists in choosing the appropriate combination coefficients for the powers of the transfer matrix in the series. A recursive formula for the computation of these factors is derived. The theoretical results are illustrated by means of numerical examples. Finally, we show that the generalised Neumann series can be understood as an acceleration (i.e. convergence speedup) of the Jacobi iterative method.

  1. Nonlinear and linear timescales near kinetic scales in solar wind turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Matthaeus, W. H.; Wan, M.; Shay, M. A. [Department of Physics and Astronomy, University of Delaware, DE 19716 (United States); Oughton, S. [Department of Mathematics, University of Waikato, Hamilton (New Zealand); Osman, K. T.; Chapman, S. C. [Centre for Fusion, Space, and Astrophysics, University of Warwick, Coventry CV4 7AL (United Kingdom); Servidio, S.; Valentini, F. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Gary, S. P. [Space Sciences Institute, Boulder, CO 80301 (United States); Roytershteyn, V.; Karimabadi, H., E-mail: whm@udel.edu [Sciberquest, Inc., Del Mar, CA 92014 (United States)

    2014-08-01

    The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the solar wind these two types of timescales may be directly compared using standard Kolmogorov-style analysis and observational data. The estimated local (in scale) nonlinear magnetohydrodynamic cascade times, evaluated as relevant kinetic scales are approached, remain slower than the cyclotron period, but comparable to or faster than the typical timescales of instabilities, anisotropic waves, and wave damping. The variation with length scale of the turbulence timescales is supported by observations and simulations. On this basis the use of linear theory—which assumes constant parameters to calculate the associated kinetic rates—may be questioned. It is suggested that the product of proton gyrofrequency and nonlinear time at the ion gyroscales provides a simple measure of turbulence influence on proton kinetic behavior.

  2. Field-based observations confirm linear scaling of sand flux with wind stress

    CERN Document Server

    Martin, Raleigh L

    2016-01-01

    Wind-driven sand transport generates atmospheric dust, forms dunes, and sculpts landscapes. However, it remains unclear how the sand flux scales with wind speed, largely because models do not agree on how particle speed changes with wind shear velocity. Here, we present comprehensive measurements from three new field sites and three published studies, showing that characteristic saltation layer heights, and thus particle speeds, remain approximately constant with shear velocity. This result implies a linear dependence of saltation flux on wind shear stress, which contrasts with the nonlinear 3/2 scaling used in most aeolian process predictions. We confirm the linear flux law with direct measurements of the stress-flux relationship occurring at each site. Models for dust generation, dune migration, and other processes driven by wind-blown sand on Earth, Mars, and several other planetary surfaces should be modified to account for linear stress-flux scaling.

  3. High-throughput solution processing of large-scale graphene

    Science.gov (United States)

    Tung, Vincent C.; Allen, Matthew J.; Yang, Yang; Kaner, Richard B.

    2009-01-01

    The electronic properties of graphene, such as high charge carrier concentrations and mobilities, make it a promising candidate for next-generation nanoelectronic devices. In particular, electrons and holes can undergo ballistic transport on the sub-micrometre scale in graphene and do not suffer from the scale limitations of current MOSFET technologies. However, it is still difficult to produce single-layer samples of graphene and bulk processing has not yet been achieved, despite strenuous efforts to develop a scalable production method. Here, we report a versatile solution-based process for the large-scale production of single-layer chemically converted graphene over the entire area of a silicon/SiO2 wafer. By dispersing graphite oxide paper in pure hydrazine we were able to remove oxygen functionalities and restore the planar geometry of the single sheets. The chemically converted graphene sheets that were produced have the largest area reported to date (up to 20 × 40 µm), making them far easier to process. Field-effect devices have been fabricated by conventional photolithography, displaying currents that are three orders of magnitude higher than previously reported for chemically produced graphene. The size of these sheets enables a wide range of characterization techniques, including optical microscopy, scanning electron microscopy and atomic force microscopy, to be performed on the same specimen.

  4. Stable evaluation of differential operators and linear and nonlinear multi-scale filtering

    Directory of Open Access Journals (Sweden)

    Otmar Scherzer

    1997-09-01

    Full Text Available Diffusion processes create multi--scale analyses, which enable the generation of simplified pictures, where for increasing scale the image gets sketchier. In many practical applications the ``scaled image'' can be characterized via a variational formulation as the solution of a minimization problem involving unbounded operators. These unbounded operators can be evaluated by regularization techniques. We show that the theory of stable evaluation of unbounded operators can be applied to efficiently solve these minimization problems.

  5. An overview of solution methods for multi-objective mixed integer linear programming programs

    DEFF Research Database (Denmark)

    Andersen, Kim Allan; Stidsen, Thomas Riis

    Multiple objective mixed integer linear programming (MOMIP) problems are notoriously hard to solve to optimality, i.e. finding the complete set of non-dominated solutions. We will give an overview of existing methods. Among those are interactive methods, the two phases method and enumeration...... methods. In particular we will discuss the existing branch and bound approaches for solving multiple objective integer programming problems. Despite the fact that branch and bound methods has been applied successfully to integer programming problems with one criterion only a few attempts has been made...

  6. Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load

    Institute of Scientific and Technical Information of China (English)

    HUANG De-jin; DING Hao-jiang; CHEN Wei-qiu

    2007-01-01

    The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation.The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.

  7. An overview of solution methods for multi-objective mixed integer linear programming programs

    DEFF Research Database (Denmark)

    Andersen, Kim Allan; Stidsen, Thomas Riis

    Multiple objective mixed integer linear programming (MOMIP) problems are notoriously hard to solve to optimality, i.e. finding the complete set of non-dominated solutions. We will give an overview of existing methods. Among those are interactive methods, the two phases method and enumeration...... methods. In particular we will discuss the existing branch and bound approaches for solving multiple objective integer programming problems. Despite the fact that branch and bound methods has been applied successfully to integer programming problems with one criterion only a few attempts has been made...

  8. Existence of Nontrivial Weak Solutions to Quasi-Linear Elliptic Equations with Exponential Growth

    Institute of Scientific and Technical Information of China (English)

    WANG Chong

    2013-01-01

    In this paper,we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations -△nu+V(x)|u|n-2u-f(x,u)/|x|β,x∈Rn (n≥2),where-△nu=-div(|▽u|n-2▽7u),0≤β < n,V∶ Rn → R is a continuous function,f (x,u)is continuous in Rn × R and behaves like eαun/n-1 as u → +∞.

  9. Linear analysis of the vertical shear instability: outstanding issues and improved solutions (Research Note)

    CERN Document Server

    Umurhan, O M; Gressel, O

    2015-01-01

    The Vertical Shear Instability is one of two known mechanisms potentially active in the so-called dead zones of protoplanetary accretion disks. A recent analysis indicates that a subset of unstable modes shows unbounded growth - both as resolution is increased and when the nominal lid of the atmosphere is extended, possibly indicating ill-posedness in previous attempts of linear analysis. The reduced equations governing the instability are revisited and the generated solutions are examined using both the previously assumed separable forms and an improved non-separable solution form that is herewith introduced. Analyzing the reduced equations using the separable form shows that, while the low-order body modes have converged eigenvalues and eigenfunctions (as both the vertical boundaries of the atmosphere are extended and with increased radial resolution), it is also confirmed that the corresponding high-order body modes and the surface modes do indeed show unbounded growth rates. However, the energy contained ...

  10. Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations

    Directory of Open Access Journals (Sweden)

    Maamar Andasmas

    2016-04-01

    Full Text Available The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z, B (z and F (z are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B, ρ(F} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.

  11. Phantom solution in a non-linear Israel-Stewart theory

    Science.gov (United States)

    Cruz, Miguel; Cruz, Norman; Lepe, Samuel

    2017-06-01

    In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.

  12. Master equation solutions in the linear regime of characteristic formulation of general relativity

    CERN Document Server

    M., C E Cedeño

    2015-01-01

    From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\\"adler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the $J$ metric variable of the Bondi-Sachs metric. Once $\\beta$, another Bondi-Sachs potential, is obtained from the field equations, and $J$ is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, M\\"adler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new sol...

  13. Convergence of Galerkin Solutions for Linear Differential Algebraic Equations in Hilbert Spaces

    Science.gov (United States)

    Matthes, Michael; Tischendorf, Caren

    2010-09-01

    The simulation of complex systems describing different physical effects becomes more and more of interest in various applications. Examples are couplings describing interactions between circuits and semiconductor devices, circuits and electromagnetic fields, fluids and structures. The modeling of such complex processes [1, 2, 3, 4, 7, 8] often leads to coupled systems that are composed of ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs). Such coupled systems can be regarded in the general framework of abstract differential-algebraic equations. Here, we discuss a Galerkin approach for handling linear abstract differential-algebraic equations with monotone operators. It is shown to provide solutions that converge to the unique solution of the abstract differential-algebraic system. Furthermore, the solution is proved to depend continuously on the data. The most interesting point of the Galerkin approach is the choice of basis functions. They have to be chosen in proper subspaces in order to guarantee that the solution satisfies the non-dynamic constraints. In contrast to other approaches as e.g. [5, 6], this approach allows time dependent operators but needs monotonicity.

  14. The velocity shear and vorticity across redshifts and non-linear scales

    CERN Document Server

    Libeskind, Noam I; Gottlöber, Stefan

    2013-01-01

    The evolution of the large scale distribution of matter in the universe is often characterized by the density field. Here we take a complimentary approach and characterize it using the cosmic velocity field, specifically the deformation of the velocity field. The deformation tensor is decomposed into its symmetric component (known as the "shear tensor") and its anti-symmetric part (the "vorticity"). Using a high resolution cosmological simulation we examine the relative orientations of the shear and the vorticity as a function of spatial scale and redshift. The shear is found to be remarkable stable to the choice of scale, while the vorticity is found to quickly decay with increasing spatial scale or redshift. The vorticity emerges out of the linear regime randomly oriented with respect to the shear eigenvectors. Non-linear evolution drives the vorticity to lie within the plane defined by the eigenvector of the fastest collapse. Within that plane the vorticity first gets aligned with the middle eigenvector an...

  15. Nonlinear Helicons ---an analytical solution elucidating multi-scale structure

    CERN Document Server

    Abdelhamid, Hamdi M

    2016-01-01

    The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here we elucidate an intrinsic multi-scale property embodied by the combination of dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

  16. LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF IMPLICIT DIFFERENCE SCHEME FOR A SEMI-LINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    Zhi-zhong Sun; Long-Jun Shen

    2003-01-01

    In this paper, the solution of back-Euler implicit difference scheme for a semi-linearparabolic equation is proved to converge to the solution of difference scheme for the corre-sponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behaviorof its discrete solution is obtained which is analogous to that of its continuous solution. Atlast, a few results are also presented for Crank-Nicolson scheme.

  17. GLOBAL C1 SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LINEARLY DEGENERATE CHARACTERISTICS

    Institute of Scientific and Technical Information of China (English)

    Li Ta-tsien(李大潜); Peng Yue-Jun

    2003-01-01

    Abstract We prove that the C0 boundedness of solution impliesthe global existence and uniqueness of C1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C1 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.

  18. Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy

    Institute of Scientific and Technical Information of China (English)

    Wenrong DAI

    2006-01-01

    In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.

  19. Fast solution of elliptic partial differential equations using linear combinations of plane waves

    Science.gov (United States)

    Pérez-Jordá, José M.

    2016-02-01

    Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

  20. Scaling BPS Solutions and pure-Higgs States

    CERN Document Server

    Bena, Iosif; de Boer, Jan; El-Showk, Sheer; Bleeken, Dieter Van den

    2012-01-01

    Depending on the value of the coupling, BPS states of type II string theory compactified on a Calabi-Yau manifold can be described as multicenter supergravity solutions or as states on the Coulomb or the Higgs branch of a quiver gauge theory. While the Coulomb-branch states can be mapped one-to-one to supergravity states, this is not automatically so for Higgs-branch states. In this paper we explicitly compute the BPS spectrum of the Higgs branch of a three-center quiver with a closed loop, and identify the subset of states that are in one-to-one correspondence with Coulomb/supergravity multicenter states. We also show that there exist additional "pure-Higgs" states, that exist if and only if the charges of the centers can form a scaling solution. Using generating function techniques we compute the large charge degeneracy of the "pure-Higgs" sector and show that it is always exponential. We also construct the map between Higgs- and Coulomb-branch states, discuss its relation to the Higgs-Coulomb map of one of...

  1. A study on the fabrication of main scale of linear encoder using continuous roller imprint method

    Science.gov (United States)

    Fan, Shanjin; Shi, Yongsheng; Yin, Lei; Feng, Long; Liu, Hongzhong

    2013-10-01

    Linear encoder composed of main and index scales has an extensive application in the field of modern precision measurement. The main scale is the key component of linear encoder as measuring basis. In this article, the continuous roller imprint technology is applied to the manufacturing of the main scale, this method can realize the high efficiency and low cost manufacturing of the ultra-long main scale. By means of the plastic deformation of the soft metal film substrate, the grating microstructure on the surface of the cylinder mold is replicated to the soft metal film substrate directly. Through the high precision control of continuous rotational motion of the mold, ultra-long high precision grating microstructure is obtained. This paper mainly discusses the manufacturing process of the high precision cylinder mold and the effects of the roller imprint pressure and roller rotation speed on the imprint replication quality. The above process parameters were optimized to manufacture the high quality main scale. At last, the reading test of a linear encoder contains the main scale made by the above method was conducted to evaluate its measurement accuracy, the result demonstrated the feasibility of the continuous roller imprint method.

  2. An Interactive Decomposition Algorithm for Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters Using TOPSIS Method

    Directory of Open Access Journals (Sweden)

    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.

  3. Linear scaling calculation of an n-type GaAs quantum dot.

    Science.gov (United States)

    Nomura, Shintaro; Iitaka, Toshiaki

    2007-09-01

    A linear scale method for calculating electronic properties of large and complex systems is introduced within a local density approximation. The method is based on the Chebyshev polynomial expansion and the time-dependent method, which is tested on the calculation of the electronic structure of a model n-type GaAs quantum dot.

  4. A trust-region and affine scaling algorithm for linearly constrained optimization

    Institute of Scientific and Technical Information of China (English)

    陈中文; 章祥荪

    2002-01-01

    A new trust-region and affine scaling algorithm for linearly constrained optimization is presentedin this paper. Under no nondegenerate assumption, we prove that any limit point of the sequence generatedby the new algorithm satisfies the first order necessary condition and there exists at least one limit point ofthe sequence which satisfies the second order necessary condition. Some preliminary numerical experiments are reported.

  5. Hardy inequality on time scales and its application to half-linear dynamic equations

    Directory of Open Access Journals (Sweden)

    Řehák Pavel

    2005-01-01

    Full Text Available A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equations is given.

  6. Scale of association: hierarchical linear models and the measurement of ecological systems

    Science.gov (United States)

    Sean M. McMahon; Jeffrey M. Diez

    2007-01-01

    A fundamental challenge to understanding patterns in ecological systems lies in employing methods that can analyse, test and draw inference from measured associations between variables across scales. Hierarchical linear models (HLM) use advanced estimation algorithms to measure regression relationships and variance-covariance parameters in hierarchically structured...

  7. Multi-Repeated Projection Lithography for High-Precision Linear Scale Based on Average Homogenization Effect

    Directory of Open Access Journals (Sweden)

    Dongxu Ren

    2016-04-01

    Full Text Available A multi-repeated photolithography method for manufacturing an incremental linear scale using projection lithography is presented. The method is based on the average homogenization effect that periodically superposes the light intensity of different locations of pitches in the mask to make a consistent energy distribution at a specific wavelength, from which the accuracy of a linear scale can be improved precisely using the average pitch with different step distances. The method’s theoretical error is within 0.01 µm for a periodic mask with a 2-µm sine-wave error. The intensity error models in the focal plane include the rectangular grating error on the mask, static positioning error, and lithography lens focal plane alignment error, which affect pitch uniformity less than in the common linear scale projection lithography splicing process. It was analyzed and confirmed that increasing the repeat exposure number of a single stripe could improve accuracy, as could adjusting the exposure spacing to achieve a set proportion of black and white stripes. According to the experimental results, the effectiveness of the multi-repeated photolithography method is confirmed to easily realize a pitch accuracy of 43 nm in any 10 locations of 1 m, and the whole length accuracy of the linear scale is less than 1 µm/m.

  8. Application of Linear Scale Space and the Spatial Color Model in Microscopy

    NARCIS (Netherlands)

    P. van Osta; K. Verdonck; L. Bols; J. Geysen; J.M. Geusebroek; B. ter Haar Romeny

    2002-01-01

    Structural features and color are used in human vision to distinguish features in light micorscopy. Taking these structural features and color into consideration in machine vision often enables a more robust segmentation than based on intensity tresholding. Linear scale space theory and the spatial

  9. Multi-Repeated Projection Lithography for High-Precision Linear Scale Based on Average Homogenization Effect.

    Science.gov (United States)

    Ren, Dongxu; Zhao, Huiying; Zhang, Chupeng; Yuan, Daocheng; Xi, Jianpu; Zhu, Xueliang; Ban, Xinxing; Dong, Longchao; Gu, Yawen; Jiang, Chunye

    2016-04-14

    A multi-repeated photolithography method for manufacturing an incremental linear scale using projection lithography is presented. The method is based on the average homogenization effect that periodically superposes the light intensity of different locations of pitches in the mask to make a consistent energy distribution at a specific wavelength, from which the accuracy of a linear scale can be improved precisely using the average pitch with different step distances. The method's theoretical error is within 0.01 µm for a periodic mask with a 2-µm sine-wave error. The intensity error models in the focal plane include the rectangular grating error on the mask, static positioning error, and lithography lens focal plane alignment error, which affect pitch uniformity less than in the common linear scale projection lithography splicing process. It was analyzed and confirmed that increasing the repeat exposure number of a single stripe could improve accuracy, as could adjusting the exposure spacing to achieve a set proportion of black and white stripes. According to the experimental results, the effectiveness of the multi-repeated photolithography method is confirmed to easily realize a pitch accuracy of 43 nm in any 10 locations of 1 m, and the whole length accuracy of the linear scale is less than 1 µm/m.

  10. Nonlinear and Linear Timescales near Kinetic Scales in Solar Wind Turbulence

    CERN Document Server

    Matthaeus, W H; Osman, K T; Servidio, S; Wan, M; Gary, S P; Shay, M A; Valentini, F; Roytershteyn, V; Karimabadi, H; Chapman, S C

    2014-01-01

    The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the solar wind these two types of timescales may be directly compared using standard Kolmogorov-style analysis and observational data. The estimated local nonlinear magnetohydrodynamic cascade times, evaluated as relevant kinetic scales are approached, remain slower than the cyclotron period, but comparable to, or faster than, the typical timescales of instabilities, anisotropic waves, and wave damping. The variation with length scale of the turbulence timescales is supported by observations and simulations. On this basis the use of linear theory - which assumes constant parameters to calculate the associated kinetic rates - may be questioned. It is suggested that the product of proton gyrofrequency and nonlinear time at the ion gyroscales provides a simple measure of turbulence influence on...

  11. A divide-and-conquer linear scaling three dimensional fragment method for large scale electronic structure calculations

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Lin-Wang; Zhao, Zhengji; Meza, Juan; Wang, Lin-Wang

    2008-07-11

    We present a new linear scaling ab initio total energy electronic structure calculation method based on the divide-and-conquer strategy. This method is simple to implement, easily to parallelize, and produces very accurate results when compared with the direct ab initio method. The method has been tested using up to 8,000 processors, and has been used to calculate nanosystems up to 15,000 atoms.

  12. Simple and accurate solution for convective-radiative fin with temperature dependent thermal conductivity using double optimal linearization

    Energy Technology Data Exchange (ETDEWEB)

    Bouaziz, M.N. [Department of Mechanical Engineering, University of Medea, BP 164, Medea 26000 (Algeria); Aziz, Abdul, E-mail: aziz@gonzaga.ed [Department of Mechanical Engineering, School of Engineering and Applied Science, Gonzaga University, Spokane, WA 99258 (United States)

    2010-12-15

    A novel concept of double optimal linearization is introduced and used to obtain a simple and accurate solution for the temperature distribution in a straight rectangular convective-radiative fin with temperature dependent thermal conductivity. The solution is built from the classical solution for a pure convection fin of constant thermal conductivity which appears in terms of hyperbolic functions. When compared with the direct numerical solution, the double optimally linearized solution is found to be accurate within 4% for a range of radiation-conduction and thermal conductivity parameters that are likely to be encountered in practice. The present solution is simple and offers superior accuracy compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method. The fin efficiency expression resembles the classical result for the constant thermal conductivity convecting fin. The present results are easily usable by the practicing engineers in their thermal design and analysis work involving fins.

  13. Scalable electron correlation methods I.: PNO-LMP2 with linear scaling in the molecular size and near-inverse-linear scaling in the number of processors.

    Science.gov (United States)

    Werner, Hans-Joachim; Knizia, Gerald; Krause, Christine; Schwilk, Max; Dornbach, Mark

    2015-02-10

    We propose to construct electron correlation methods that are scalable in both molecule size and aggregated parallel computational power, in the sense that the total elapsed time of a calculation becomes nearly independent of the molecular size when the number of processors grows linearly with the molecular size. This is shown to be possible by exploiting a combination of local approximations and parallel algorithms. The concept is demonstrated with a linear scaling pair natural orbital local second-order Møller-Plesset perturbation theory (PNO-LMP2) method. In this method, both the wave function manifold and the integrals are transformed incrementally from projected atomic orbitals (PAOs) first to orbital-specific virtuals (OSVs) and finally to pair natural orbitals (PNOs), which allow for minimum domain sizes and fine-grained accuracy control using very few parameters. A parallel algorithm design is discussed, which is efficient for both small and large molecules, and numbers of processors, although true inverse-linear scaling with compute power is not yet reached in all cases. Initial applications to reactions involving large molecules reveal surprisingly large effects of dispersion energy contributions as well as large intramolecular basis set superposition errors in canonical MP2 calculations. In order to account for the dispersion effects, the usual selection of PNOs on the basis of natural occupation numbers turns out to be insufficient, and a new energy-based criterion is proposed. If explicitly correlated (F12) terms are included, fast convergence to the MP2 complete basis set (CBS) limit is achieved. For the studied reactions, the PNO-LMP2-F12 results deviate from the canonical MP2/CBS and MP2-F12 values by <1 kJ mol(-1), using triple-ζ (VTZ-F12) basis sets.

  14. A linear scale height Chapman model supported by GNSS occultation measurements

    Science.gov (United States)

    Olivares-Pulido, G.; Hernández-Pajares, M.; Aragón-Àngel, A.; Garcia-Rigo, A.

    2016-08-01

    Global Navigation Satellite Systems (GNSS) radio occultations allow the vertical sounding of the Earth's atmosphere, in particular, the ionosphere. The physical observables estimated with this technique permit to test theoretical models of the electron density such as, for example, the Chapman and the Vary-Chap models. The former is characterized by a constant scale height, whereas the latter considers a more general function of the scale height with respect to height. We propose to investigate the feasibility of the Vary-Chap model where the scale height varies linearly with respect to height. In order to test this hypothesis, the scale height data provided by radio occultations from a receiver on board a low Earth orbit (LEO) satellite, obtained by iterating with a local Chapman model at every point of the topside F2 layer provided by the GNSS satellite occultation, are fitted to height data by means of a linear least squares fit (LLS). Results, based on FORMOSAT-3/COSMIC GPS occultation data inverted by means of the Improved Abel transform inversion technique (which takes into account the horizontal electron content gradients) show that the scale height presents a more clear linear trend above the F2 layer peak height, hm, which is in good agreement with the expected linear temperature dependence. Moreover, the parameters of the linear fit obtained during four representative days for all seasons, depend significantly on local time and latitude, strongly suggesting that this approach can significantly contribute to build realistic models of the electron density directly derived from GNSS occultation data.

  15. Generalized scale-invariant solutions to the two-dimensional stationary Navier-Stokes equations

    CERN Document Server

    Guillod, Julien

    2014-01-01

    New explicit solutions to the incompressible Navier-Stokes equations in $\\mathbb{R}^{2}\\setminus\\left\\{ \\boldsymbol{0}\\right\\}$ are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scale-invariant solutions. While the Hamel solutions are parameterized by a discrete parameter $n$, the flux $\\Phi$ and an angle $\\theta_{0}$, the new solutions generalize the Hamel solutions by introducing an additional parameter $a$ which produces a rotation. The new solutions decay like $\\left|\\boldsymbol{x}\\right|^{-1}$ as the Hamel solutions, and exhibit spiral behavior. The new variety of asymptotes induced by the existence of these solutions further emphasizes the difficulties faced when trying to establish the asymptotic behavior of the Navier-Stokes equations in a two-dimensional ...

  16. Semiparametric Analysis of Heterogeneous Data Using Varying-Scale Generalized Linear Models.

    Science.gov (United States)

    Xie, Minge; Simpson, Douglas G; Carroll, Raymond J

    2008-01-01

    This article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically, and develops efficient semiparametric inferences for the parametric components of the models. Such models provide a means to adapt for heterogeneity in the data due to varying exposures, varying levels of aggregation, and so on. The class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases. We present an algorithm to estimate the scale function nonparametrically, and obtain asymptotic distribution theory for regression parameter estimates. In particular, we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound. We also describe bootstrap-based goodness-of-scale test. We illustrate the methodology with simulations, published data, and data from collaborative research on ultrasound safety.

  17. Linear-scaling evaluation of the local energy in quantum MonteCarlo

    Energy Technology Data Exchange (ETDEWEB)

    Austin, Brian; Aspuru-Guzik, Alan; Salomon-Ferrer, Romelia; Lester Jr., William A.

    2006-02-11

    For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size.

  18. A discrete solvent reaction field model for calculating molecular linear response properties in solution

    Science.gov (United States)

    Jensen, Lasse; van Duijnen, Piet Th.; Snijders, Jaap G.

    2003-08-01

    A discrete solvent reaction field model for calculating frequency-dependent molecular linear response properties of molecules in solution is presented. The model combines a time-dependent density functional theory (QM) description of the solute molecule with a classical (MM) description of the discrete solvent molecules. The classical solvent molecules are represented using distributed atomic charges and polarizabilities. All the atomic parameters have been chosen so as to describe molecular gas phase properties of the solvent molecule, i.e., the atomic charges reproduce the molecular dipole moment and the atomic polarizabilities reproduce the molecular polarizability tensor using a modified dipole interaction model. The QM/MM interactions are introduced into the Kohn-Sham equations and all interactions are solved self-consistently, thereby allowing for the solute to be polarized by the solvent. Furthermore, the inclusion of polarizabilities in the MM part allows for the solvent molecules to be polarized by the solute and by interactions with other solvent molecules. Initial applications of the model to calculate the vertical electronic excitation energies and frequency-dependent molecular polarizability of a water molecule in a cluster of 127 classical water molecules are presented. The effect of using different exchange correlation (xc)-potentials is investigated and the results are compared with results from wave function methods combined with a similar solvent model both at the correlated and uncorrelated level of theory. It is shown that accurate results in agreement with correlated wave function results can be obtained using xc-potentials with the correct asymptotic behavior.

  19. EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

    Institute of Scientific and Technical Information of China (English)

    康东升

    2004-01-01

    This paper is concerned with the quasi-linear equation with critical SobolevHardy exponent where Ω RN(N ≥ 3) is a smooth bounded domain, 0 ∈Ω, 0 ≤ s < p, 1 < p < N,p* (s) :=p(N- s)/N-p is the critical Sobolev-Hardy exponent, λ> 0,p ≤ r < p* ,p* := Np/N-p is the critical Sobolev exponent, μ> 0, 0 ≤ t < p, p ≤ q < p* (t) = P(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.

  20. An Integer Linear Programming Solution to the Telescope Network Scheduling Problem

    CERN Document Server

    Lampoudi, Sotiria; Eastman, Jason

    2015-01-01

    Telescope networks are gaining traction due to their promise of higher resource utilization than single telescopes and as enablers of novel astronomical observation modes. However, as telescope network sizes increase, the possibility of scheduling them completely or even semi-manually disappears. In an earlier paper, a step towards software telescope scheduling was made with the specification of the Reservation formalism, through the use of which astronomers can express their complex observation needs and preferences. In this paper we build on that work. We present a solution to the discretized version of the problem of scheduling a telescope network. We derive a solvable integer linear programming (ILP) model based on the Reservation formalism. We show computational results verifying its correctness, and confirm that our Gurobi-based implementation can address problems of realistic size. Finally, we extend the ILP model to also handle the novel observation requests that can be specified using the more advanc...

  1. Linear stability of the Linet - Tian solution with negative cosmological constant

    CERN Document Server

    Gleiser, Reinaldo J

    2016-01-01

    In this paper we analyze the linear stability of the Linet - Tian solution with negative cosmological constant. In the limit of vanishing cosmological constant the Linet - Tian metric reduces to a form of the Levi - Civita metric, and, therefore, it can be considered as a generalization of the former to include a cosmological constant. The gravitational instability of the Levi - Civita metric was recently established, and the purpose of this paper is to investigate what changes result from the introduction of a cosmological constant. A fundamental difference brought about by a (negative) cosmological constant is in the structure at infinity. This introduces an added problem in attempting to define an evolution for the perturbations because the constant time hypersurfaces are not Cauchy surfaces. In this paper we show that under a large set of boundary conditions that lead to a unique evolution of the perturbations, we always find unstable modes, that would generically be present in the evolution of arbitrary ...

  2. A Complete Parametric Solutions of Eigenstructure Assignment by State-Derivative Feedback for Linear Control Systems

    Directory of Open Access Journals (Sweden)

    T. H. S. Abdelaziz

    2005-01-01

    Full Text Available In this paper we introduce a complete parametric approach for solving the problem of eigenstructure assignment via state-derivative feedback for linear systems. This problem is always solvable for any controllable systems iff the open-loop system matrix is nonsingular. In this work, two parametric solutions to the feedback gain matrix are introduced that describe the available degrees of freedom offered by the state-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. Accordingly, the sensitivity of the assigned eigenvalues to perturbations in the system and gain matrix is minimized. Numerical examples are included to show the effectiveness of the proposed approach. 

  3. An automatic multigrid method for the solution of sparse linear systems

    Science.gov (United States)

    Shapira, Yair; Israeli, Moshe; Sidi, Avram

    1993-01-01

    An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

  4. Non-linear dynamics of the passivity breakdown of iron in acidic solutions

    CERN Document Server

    Sazou, D

    2003-01-01

    Breakdown of the iron passivity in acid solutions accompanied by current oscillations was investigated by using electrochemical techniques, which reveal the non-linear dynamical response of the system in the current-potential (I-E) and current-time (I-t) planes. Current oscillations of the Fe-electrolyte electrochemical system were studied in the (a) absence and (b) presence of chlorides. In case (a) two oscillatory regions were distinguished; one at low potentials associated with the formation-dissolution of a ferrous salt and another at higher potentials associated with the formation-breakdown of the oxide film. Chaotic oscillations appear in the former region whereas periodic oscillations of a relaxation type appear in the latter region. In case (b), complex periodic and aperiodic oscillations are induced by small amounts of chlorides due to pitting corrosion. Pitting corrosion is a multistage localized process of a great technological importance. It consists of a local breakdown of the passive oxide film ...

  5. Positive Almost Periodic Solution for Impulsive Nicholson’s Blowflies Model with Linear Harvesting Term on the Bounded Domain

    OpenAIRE

    Yao, Zhijian

    2015-01-01

    In this paper, impulsive Nicholson’s blowflies model with linear harvesting term is studied. By using the contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of a unique positive almost periodic solution. In addition, the exponential convergence of positive almost periodic solution is investigated.

  6. The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

    Institute of Scientific and Technical Information of China (English)

    WU YUE-XIANG; HUO YAN-MEI; WU YA-KUN

    2012-01-01

    The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method.Some new existence results are obtained.

  7. A metahillslope model based on an analytical solution to a linearized Boussinesq equation for temporally variable recharge rates

    Science.gov (United States)

    Pauwels, Valentijn R. N.; Verhoest, Niko E. C.; de Troch, FrançOis P.

    2002-12-01

    In hydrology the slow, subsurface component of the discharge is usually referred to as base flow. One method to model base flow is the conceptual approach, in which the complex physical reality is simplified using hypotheses and assumptions, and the various physical processes are described mathematically. The purpose of this paper is to develop and validate a conceptual method, based on hydraulic theory, to calculate the base flow of a catchment, under observed precipitation rates. The governing groundwater equation, the Boussinesq equation, valid for a unit width sloping aquifer, is linearized and solved for a temporally variable recharge rate. The solution allows the calculation of the transient water table profile in and the outflow from an aquifer under temporally variable recharge rates. When a catchment is considered a metahillslope, the solution can be used, when coupled to a routing model, to calculate the catchment base flow. The model is applied to the Zwalm catchment and four subcatchments in Belgium. The results suggest that it is possible to model base flow at the catchment scale, using a Boussinesq-based metahillslope model. The results further indicate that it is sufficient to use a relatively simple formulation of the infiltration, overland flow, and base flow processes to obtain reasonable estimates of the total catchment discharge.

  8. Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant

    CERN Document Server

    Nungesser, Ernesto

    2014-01-01

    We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.

  9. Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming.

    Science.gov (United States)

    Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami

    2017-08-01

    Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. The software is implemented in Matlab, and is provided as supplementary information . hyunseob.song@pnnl.gov. Supplementary data are available at Bioinformatics online.

  10. HPLC monitoring of spontaneous non-linear peptidization dynamics of selected amino acids in solution.

    Science.gov (United States)

    Godziek, Agnieszka; Maciejowska, Anna; Sajewicz, Mieczysław; Kowalska, Teresa

    2015-03-01

    This is our new study in a series of publications devoted to exploration of applicability of high-performance liquid chromatography (HPLC) to providing answers to difficult questions from the area of the reaction kinetics and mechanisms with non-linear reactions. Although an excellent analytical performance of HPLC is an indisputable fact, so far its performance as a tool in the kinetic and mechanistic studies has been tested to a lesser extent. In our earlier studies, spontaneous peptidization dynamics of amino acids in solution was demonstrated by means of HPLC upon a few amino acid examples, and on that basis a theoretical model has been developed, anticipating an interdependence of dynamics on chemical structures of amino acids involved. In order to expand the spectrum of experimentally investigated amino acid cases, in this study we present the results valid for three novel amino acids of significant life sciences importance, which differ in terms of peptidization dynamics. Experimental evidence originates from the achiral HPLC with the evaporative light scattering detection and MS detection. A conclusion is drawn that different spontaneous peptidization dynamics of amino acids may significantly influence chemical composition of proteins encountered in living organisms. Hence, a need emerges for systematic physicochemical studies on spontaneous non-linear peptidization dynamics of proteinogenic amino acids in liquid abiotic (but also in the biotic) systems.

  11. Estimating WAIS-IV indexes: proration versus linear scaling in a clinical sample.

    Science.gov (United States)

    Umfleet, Laura Glass; Ryan, Joseph J; Gontkovsky, Sam T; Morris, Jeri

    2012-04-01

    We compared the accuracy of proration and linear scaling for estimating Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV), Verbal Comprehension Index (VCI), and Perceptual Reasoning Index (PRI) composites from all possible two subtest combinations. The purpose was to provide practice relevant psychometric results in a clinical sample. The present investigation was an archival study that used mostly within-group comparisons. We analyzed WAIS-IV data of a clinical sample comprising 104 patients with brain damage and 37 with no known neurological impairment. In both clinical samples, actual VCI and PRI scores were highly correlated with estimated index scores based on proration and linear scaling (all rs ≥.95). In the brain-impaired sample, significant mean score differences between the actual and estimated composites were found in two comparisons, but these differences were less than three points; no other significant differences emerged. Overall, findings demonstrate that proration and linear scaling methods are feasible procedures when estimating actual Indexes. There was no advantage of one computational method over the other. © 2012 Wiley Periodicals, Inc.

  12. Recovery of a Sparse Integer Solution to an Underdetermined System of Linear Equations

    CERN Document Server

    Jayram, T S; Arya, Vijay

    2011-01-01

    We consider a system of m linear equations in n variables Ax=b where A is a given m x n matrix and b is a given m-vector known to be equal to Ax' for some unknown solution x' that is integer and k-sparse: x' in {0,1}^n and exactly k entries of x' are 1. We give necessary and sufficient conditions for recovering the solution x exactly using an LP relaxation that minimizes l1 norm of x. When A is drawn from a distribution that has exchangeable columns, we show an interesting connection between the recovery probability and a well known problem in geometry, namely the k-set problem. To the best of our knowledge, this connection appears to be new in the compressive sensing literature. We empirically show that for large n if the elements of A are drawn i.i.d. from the normal distribution then the performance of the recovery LP exhibits a phase transition, i.e., for each k there exists a value m' of m such that the recovery always succeeds if m > m' and always fails if m < m'. Using the empirical data we conjectu...

  13. The efficient solution of the (quietly constrained) noisy, linear regulator problem

    Science.gov (United States)

    Gregory, John; Hughes, H. R.

    2007-09-01

    In a previous paper we gave a new, natural extension of the calculus of variations/optimal control theory to a (strong) stochastic setting. We now extend the theory of this most fundamental chapter of optimal control in several directions. Most importantly we present a new method of stochastic control, adding Brownian motion which makes the problem "noisy." Secondly, we show how to obtain efficient solutions: direct stochastic integration for simpler problems and/or efficient and accurate numerical methods with a global a priori error of O(h3/2) for more complex problems. Finally, we include "quiet" constraints, i.e. deterministic relationships between the state and control variables. Our theory and results can be immediately restricted to the non "noisy" (deterministic) case yielding efficient, numerical solution techniques and an a priori error of O(h2)E In this event we obtain the most efficient method of solving the (constrained) classical Linear Regulator Problem. Our methods are different from the standard theory of stochastic control. In some cases the solutions coincide or at least are closely related. However, our methods have many advantages including those mentioned above. In addition, our methods more directly follow the motivation and theory of classical (deterministic) optimization which is perhaps the most important area of physical and engineering science. Our results follow from related ideas in the deterministic theory. Thus, our approximation methods follow by guessing at an algorithm, but the proof of global convergence uses stochastic techniques because our trajectories are not differentiable. Along these lines, a general drift term in the trajectory equation is properly viewed as an added constraint and extends ideas given in the deterministic case by the first author.

  14. Imprint of non-linear effects on HI intensity mapping on large scales

    CERN Document Server

    Umeh, Obinna

    2016-01-01

    Intensity mapping of the HI brightness temperature provides a unique way of tracing large-scale structures of the Universe up to the largest possible scales. This is achieved by using a low angular resolution radio telescopes to detect emission line from cosmic neutral Hydrogen in the post-reionization Universe. We consider how non-linear effects associated with the HI bias and redshift space distortions contribute to the clustering of cosmic neutral Hydrogen on large scales. We use general relativistic perturbation theory techniques to derive for the first time the full expression for the HI brightness temperature up to third order in perturbation theory without making any plane-parallel approximation. We use this result to show how mode coupling at nonlinear order due to nonlinear bias parameters and redshift space distortions leads to about 10\\% modulation of the HI power spectrum on large scales.

  15. The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

    Science.gov (United States)

    Pang, Haotian; Liu, Han; Vanderbei, Robert

    2014-02-01

    We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

  16. b-Bit Minwise Hashing for Large-Scale Linear SVM

    CERN Document Server

    Li, Ping; Konig, Christian

    2011-01-01

    In this paper, we propose to (seamlessly) integrate b-bit minwise hashing with linear SVM to substantially improve the training (and testing) efficiency using much smaller memory, with essentially no loss of accuracy. Theoretically, we prove that the resemblance matrix, the minwise hashing matrix, and the b-bit minwise hashing matrix are all positive definite matrices (kernels). Interestingly, our proof for the positive definiteness of the b-bit minwise hashing kernel naturally suggests a simple strategy to integrate b-bit hashing with linear SVM. Our technique is particularly useful when the data can not fit in memory, which is an increasingly critical issue in large-scale machine learning. Our preliminary experimental results on a publicly available webspam dataset (350K samples and 16 million dimensions) verified the effectiveness of our algorithm. For example, the training time was reduced to merely a few seconds. In addition, our technique can be easily extended to many other linear and nonlinear machine...

  17. An analytical dynamo solution for large-scale magnetic fields of galaxies

    CERN Document Server

    Chamandy, Luke

    2016-01-01

    We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parameterized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the `no-$z$' approximation and the dynamical $\\alpha$-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted onto galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure (RM) datasets. Further, we explore the properties of our numerical solut...

  18. Self-consistent field theory based molecular dynamics with linear system-size scaling.

    Science.gov (United States)

    Richters, Dorothee; Kühne, Thomas D

    2014-04-01

    We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.

  19. Self-consistent field theory based molecular dynamics with linear system-size scaling

    Energy Technology Data Exchange (ETDEWEB)

    Richters, Dorothee [Institute of Mathematics and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 9, D-55128 Mainz (Germany); Kühne, Thomas D., E-mail: kuehne@uni-mainz.de [Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz (Germany); Technical and Macromolecular Chemistry, University of Paderborn, Warburger Str. 100, D-33098 Paderborn (Germany)

    2014-04-07

    We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.

  20. Screening methods for linear-scaling short-range hybrid calculations on CPU and GPU architectures

    Science.gov (United States)

    Beuerle, Matthias; Kussmann, Jörg; Ochsenfeld, Christian

    2017-04-01

    We present screening schemes that allow for efficient, linear-scaling short-range exchange calculations employing Gaussian basis sets for both CPU and GPU architectures. They are based on the LinK [C. Ochsenfeld et al., J. Chem. Phys. 109, 1663 (1998)] and PreLinK [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 138, 134114 (2013)] methods, but account for the decay introduced by the attenuated Coulomb operator in short-range hybrid density functionals. Furthermore, we discuss the implementation of short-range electron repulsion integrals on GPUs. The introduction of our screening methods allows for speedups of up to a factor 7.8 as compared to the underlying linear-scaling algorithm, while retaining full numerical control over the accuracy. With the increasing number of short-range hybrid functionals, our new schemes will allow for significant computational savings on CPU and GPU architectures.

  1. A field-theoretic approach to linear scaling \\textit{ab-initio} molecular dynamics

    CERN Document Server

    Richters, Dorothee; Kühne, Thomas D

    2012-01-01

    We present a field-theoretic method suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is solved by means of a properly modified Langevin equation. The predictive power of this approach is illustrated using the example of liquid methane under extreme conditions.

  2. 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.

  3. Parametric macromodelling of linear high-frequency systems using multiple frequency scaling and sequential sampling

    OpenAIRE

    Chemmangat Manakkal Cheriya, Krishnan; Ferranti, Francesco; Dhaene, Tom; Knockaert, Luc

    2014-01-01

    An enhanced parametric macromodelling scheme is presented for linear high-frequency systems based on the use of multiple frequency scaling coefficients and a sequential sampling algorithm to fully automate the entire modelling process. The proposed method is applied on a ring resonator bandpass filter example and compared with another state-of-the-art macromodelling method to show its improved modelling capability and reduced setup time.

  4. Simple, explicitly time-dependent and regular solutions of the linearized vacuum Einstein equations on a null cone

    CERN Document Server

    Mädler, Thomas

    2012-01-01

    Perturbations of the linearized vacuum Einstein equations on a null cone in the Bondi-Sachs formulation of General Relativity can be derived from a single master function with spin weight two which is determined by a simple wave equation. Utilizing a standard spin representation of the tensors on a sphere and two different approaches to solve the master equation, we are able to determine two simple and explicitly time-dependent solutions. Both solutions, of which one is asymptotically flat, comply with the regularity conditions at the vertex of the null cone. For the asymptotically flat solution we calculate the corresponding linearized perturbations, describing all multipoles of spin-2 waves that propagate on a Minkowskian background space-time. We also analyze the asymptotic behavior of this solution at null infinity using a Penrose compactification, and calculate the Weyl scalar \\Psi_4. Because of its simplicity, the asymptotically flat solution presented here is ideally suited for testbed calculations in ...

  5. The Quasi-Linear Solution of Vertical Infiltration; La solucion cuasi-lineal de la infiltracion vertical

    Energy Technology Data Exchange (ETDEWEB)

    Fuentes, Carlos [Instituto Mexicano de Tecnologia del Agua, Jiutepec, Morelos (Mexico); Parlangue, Jean-Yves [Departamento de Agricultura e Ingenieria Biologica (United States); Haverkamp, Randel; Vauclin, Michael [Laboratorio de Estudio de las Transferencias en Hidrologia y Medio ambiente (France)

    2001-12-01

    The exact solution of the one-dimensional vertical infiltration equation is deducted, when the hydraulic diffusivity is considered constant and the hydraulic conductivity is a combination of both a linear and quadratic functions of the soil water content. This quasi-linear solution includes as particular cases, both the classical solution known as linear soil and the Knight solution. The cumulative infiltrated water as a function of time provided by the quasi-linear solution has been compared with the cumulative infiltrated water obtained from the numerical solution of the Richards equation on three different soils of contrasting hydrodynamic properties. The good agreement between the two solutions has shown that the quasi-linear solution can be used on soils where the accepted hypothesis, on hydraulic diffusivity and hydraulic conductivity, for its deduction is not satisfied. [Spanish] Se deduce la solucion exacta de la ecuacion de la infiltracion unidimensional vertical cuando la difusividad hidraulica es considerada constante y la conductividad hidraulica es una combinacion de una funcion lineal y una cuadratica del contenido volumetrico de agua. Esta solucion cuasi-lineal de la infiltracion contiene, como casos particulares, la solucion clasica conocida como suelo lineal y la solucion de Knight. La lamina infiltrada acumulada en funcion del tiempo proporcionada por la solucion cuasi-lineal se ha comparado con la lamina infiltrada proporcionada por la solucion numerica de la ecuacion de Richards en tres suelos de propiedades hidrodinamicas contrastantes. El buen acuerdo entre las laminas infiltradas ha mostrado que la solucion cuasi-lineal puede utilizarse en suelos donde la difusividad y la conductividad hidraulicas no satisfacen los supuestos de la deduccion.

  6. Superlinearly Convergent Affine Scaling Interior Trust-Region Method for Linear Constrained LC1 Minimization

    Institute of Scientific and Technical Information of China (English)

    De Tong ZHU

    2008-01-01

    We extend the classical affine scaling interior trust region algorithm for the linear con-strained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in associ-ation with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.

  7. AN APPLICATION OF DOUBLE-SCALE METHOD TO THE STUDY OF NON-LINEAR DISSIPATIVE WAVES IN JEFFREYS MEDIA

    Directory of Open Access Journals (Sweden)

    Adelina Georgescu

    2011-07-01

    Full Text Available In previous papers we sketched out the general use of the doublescalemethod to nonlinear hyperbolic partial differential equations(PDEs in order to study the asymptotic waves and as an examplethe model governing the motion of a rheological medium (Maxwellmedium with one mechanical internal variable was studied. In thispaper the double scale method is applied to investigate non-linear dissipative waves in viscoanelastic media without memory of order one(Jeffreys media, that were studied by one of the authors (L. R. inmore classical way. For these media the equations of motion includesecond order derivative terms multiplied by a very small parameter. We give a physical interpretation of the new (fast variable, related to the surfaces across which the solutions or/and some of their derivatives vary steeply. The paper concludes with one-dimensional application containing original results.

  8. Small scale effect on linear vibration of buckled size-dependent FG nanobeams

    Directory of Open Access Journals (Sweden)

    Sima Ziaee

    2015-06-01

    The present study is an attempt to present linear free vibration of buckled FG nano-beams. It is assumed that the material properties of FGMs are graded in the thickness direction. The partial differential equation of motion is derived based on Euler–Bernoulli beam theory, von-Karman geometric nonlinearity and Eringen’s nonlocal elasticity theory. The exact solution of the post-buckling configurations of FG nano-beams and polynomial-based differential quadrature method are employed to study the linear behaviour of vibrated nano-beams around their post-buckling configurations. The results show the important role of compressive axial force exerted on FG nano-beams in nonlocal behaviour of vibrating FG nano-beams.

  9. Linear Analytical Solutions of Mechanical Sensitivity in Large Deflection of Unsymmetrically Layered Piezoelectric Plate under Pretension

    Directory of Open Access Journals (Sweden)

    Chun-Fu Chen

    2014-03-01

    Full Text Available Linear analytical study on the mechanical sensitivity in large deflection of unsymmetrically layered and laterally loaded piezoelectric plate under pretension is conducted. von Karman plate theory for large deflection is utilized but extended to the case of an unsymmetrically layered plate embedded with a piezoelectric layer. The governing equations thus obtained are simplified by omitting the arising nonlinear terms, yielding a Bessel or modified Bessel equation for the lateral slope. Depending on the relative magnitude of the piezoelectric effect, for both cases, analytical solutions of various geometrical responses are developed and formulated via Bessel and modified Bessel functions. The associated ultimate radial stresses are further derived following lamina constitutive law to evaluate the mechanical sensitivity of the considered plate. For a nearly monolithic plate under a very low applied voltage, the results are in good agreement with those for a single-layered case due to pure mechanical load available in literature, and thus the present approach is checked. For a two-layered unsymmetric plate made of typical silicon-based materials, a sound piezoelectric effect is illustrated particularly in a low pretension condition.

  10. Linear stability analysis in the numerical solution of initial value problems

    Science.gov (United States)

    van Dorsselaer, J. L. M.; Kraaijevanger, J. F. B. M.; Spijker, M. N.

    This article addresses the general problem of establishing upper bounds for the norms of the nth powers of square matrices. The focus is on upper bounds that grow only moderately (or stay constant) where n, or the order of the matrices, increases. The so-called resolvant condition, occuring in the famous Kreiss matrix theorem, is a classical tool for deriving such bounds.Recently the classical upper bounds known to be valid under Kreiss's resolvant condition have been improved. Moreover, generalizations of this resolvant condition have been considered so as to widen the range of applications. The main purpose of this article is to review and extend some of these new developments.The upper bounds for the powers of matrices discussed in this article are intimately connected with the stability analysis of numerical processes for solving initial(-boundary) value problems in ordinary and partial linear differential equations. The article highlights this connection.The article concludes with numerical illustrations in the solution of a simple initial-boundary value problem for a partial differential equation.

  11. Adding salt to a surfactant solution: Linear rheological response of the resulting morphologies

    Energy Technology Data Exchange (ETDEWEB)

    Gaudino, Danila; Pasquino, Rossana, E-mail: r.pasquino@unina.it; Grizzuti, Nino [DICMaPI, Università degli Studi di Napoli Federico II, P.le Tecchio 80, 80125 Napoli (Italy)

    2015-11-15

    The micellar system composed of Cetylpyridinium Chloride-Sodium Salicylate (CPyCl-NaSal) in brine aqueous solutions has been studied by systematically changing the salt concentration, in order to investigate the rheology of the arising morphologies. In particular, the zero-shear viscosity and the linear viscoelastic response have been measured as a function of the NaSal concentration (with [CPyCl] = 100 mM). The Newtonian viscosity shows a nonmonotonic dependence upon concentration, passing through a maximum at NaSal/CPyCl ≈ 0.6, and eventually dropping at higher salt concentrations. The progressive addition of salt determines first a transition from a Newtonian to a purely Maxwell-like behavior as the length of the micelles significantly increases. Beyond the peak viscosity, the viscoelastic data show two distinct features. On the one hand, the main relaxation time of the system strongly decreases, while the plateau modulus remains essentially constant. Calculations based on the rheological data show that, as the binding salt concentration increases, there is a decrease in micelles breaking rate and a decrease in their average length. On the other hand, in the same concentration region, a low-frequency elastic plateau is measured. Such a plateau is considered as the signature of a tenuous, but persistent branched network, whose existence is confirmed by cryo-transmission electron microscopy images.

  12. Iterative solution of dense linear systems arising from the electrostatic integral equation in MEG

    Energy Technology Data Exchange (ETDEWEB)

    Rahola, Jussi [Simulintu Oy, Espoo (Finland); Tissari, Satu [CSC - Scientific Computing Ltd, Espoo (Finland)]. E-mail: satu.tissari@csc.fi

    2002-03-21

    We study the iterative solution of dense linear systems that arise from boundary element discretizations of the electrostatic integral equation in magnetoencephalography (MEG). We show that modern iterative methods can be used to decrease the total computation time by avoiding the time-consuming computation of the LU decomposition of the coefficient matrix. More importantly, the modern iterative methods make it possible to avoid the explicit formation of the coefficient matrix which is needed when a large number of unknowns are used. To study the convergence of iterative solvers we examine the eigenvalue distributions of the coefficient matrices. For the sphere we show how the eigenvalues of the integral operator are approximated by the eigenvalues of the coefficient matrix when the collocation and Galerkin methods are used as discretization methods. The collocation method approximates the eigenvalues of the integral operator directly. The Galerkin method produces a coefficient matrix that needs to be preconditioned in order to maintain optimal convergence speed. With the ILU(0) preconditioner iterative methods converge fast and independent of the number of discretization points for both the collocation and Galerkin approaches. The preconditioner has no significant effect on the total computational time. (author)

  13. Continuous dependence of solutions of abstract generalized linear differential equations with potential converging uniformly with a weight

    OpenAIRE

    Monteiro, G.; Tvrdý, M. (Milan)

    2014-01-01

    In this paper we continue our research on continuous dependence on a parameter of solutions to generalized linear differential equations. These equations are described by linear integral equations containing the abstract Kurzweil-Stieltjes integral. In particular, we are interested in the situation when the kernels of these equations need not have uniformly bounded variations. Our main goal is the extension of our previous results to the nonhomogeneous case. Applications to second order syste...

  14. Dynamical Solution of the SGEMP Electron Boundary Layer for Linearly Rising and Constant X-Ray Time Histories

    Science.gov (United States)

    1976-12-01

    The time dependent solution is presented for the dynamical behavior of the one dimensional electron boundary layer formed when X-rays knock photoelectrons out of a material surface. The X-ray flux is taken to be either linearly rising in time or constant in time . Two electron energy spectra are considered-exponential and linear-times-exponential. The electrons are assumed to have a cos theta

  15. Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics

    CERN Document Server

    Lam, F

    2013-01-01

    A vorticity theory for incompressible fluid flows in the absence of solid boundaries is proposed. Some apriori bounds are established. They are used in an interpolation theory to show the well-posedness of the vorticity Cauchy problem. A non-linear integral equation for vorticity is derived and its solution is expressed in an expansion. Interpretations of flow evolutions starting from given initial data are given and elaborated. The kinetic theory for Maxwellian molecules with cut-off is revisited in order to link microscopic properties to flow characters on the continuum.

  16. Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

    Directory of Open Access Journals (Sweden)

    Sukhpreet Kaur Sidhu

    2014-01-01

    Full Text Available The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

  17. Wind-invariant saltation heights imply linear scaling of aeolian saltation flux with shear stress.

    Science.gov (United States)

    Martin, Raleigh L; Kok, Jasper F

    2017-06-01

    Wind-driven sand transport generates atmospheric dust, forms dunes, and sculpts landscapes. However, it remains unclear how the flux of particles in aeolian saltation-the wind-driven transport of sand in hopping trajectories-scales with wind speed, largely because models do not agree on how particle speeds and trajectories change with wind shear velocity. We present comprehensive measurements, from three new field sites and three published studies, showing that characteristic saltation layer heights remain approximately constant with shear velocity, in agreement with recent wind tunnel studies. These results support the assumption of constant particle speeds in recent models predicting linear scaling of saltation flux with shear stress. In contrast, our results refute widely used older models that assume that particle speed increases with shear velocity, thereby predicting nonlinear 3/2 stress-flux scaling. This conclusion is further supported by direct field measurements of saltation flux versus shear stress. Our results thus argue for adoption of linear saltation flux laws and constant saltation trajectories for modeling saltation-driven aeolian processes on Earth, Mars, and other planetary surfaces.

  18. Large-Scale Structure Formation: from the first non-linear objects to massive galaxy clusters

    CERN Document Server

    Planelles, S; Bykov, A M

    2014-01-01

    The large-scale structure of the Universe formed from initially small perturbations in the cosmic density field, leading to galaxy clusters with up to 10^15 Msun at the present day. Here, we review the formation of structures in the Universe, considering the first primordial galaxies and the most massive galaxy clusters as extreme cases of structure formation where fundamental processes such as gravity, turbulence, cooling and feedback are particularly relevant. The first non-linear objects in the Universe formed in dark matter halos with 10^5-10^8 Msun at redshifts 10-30, leading to the first stars and massive black holes. At later stages, larger scales became non-linear, leading to the formation of galaxy clusters, the most massive objects in the Universe. We describe here their formation via gravitational processes, including the self-similar scaling relations, as well as the observed deviations from such self-similarity and the related non-gravitational physics (cooling, stellar feedback, AGN). While on i...

  19. High-performance small-scale solvers for linear Model Predictive Control

    DEFF Research Database (Denmark)

    Frison, Gianluca; Sørensen, Hans Henrik Brandenborg; Dammann, Bernd

    2014-01-01

    In Model Predictive Control (MPC), an optimization problem needs to be solved at each sampling time, and this has traditionally limited use of MPC to systems with slow dynamic. In recent years, there has been an increasing interest in the area of fast small-scale solvers for linear MPC......, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach...... problems 2 to 8 times faster than the current state-of-the-art solver for this class of problems, and the high-performance is maintained for MPC problems with up to a few hundred states....

  20. Pore-scale and Continuum Simulations of Solute Transport Micromodel Benchmark Experiments

    Energy Technology Data Exchange (ETDEWEB)

    Oostrom, Martinus; Mehmani, Yashar; Romero Gomez, Pedro DJ; Tang, Y.; Liu, H.; Yoon, Hongkyu; Kang, Qinjun; Joekar Niasar, Vahid; Balhoff, Matthew; Dewers, T.; Tartakovsky, Guzel D.; Leist, Emily AE; Hess, Nancy J.; Perkins, William A.; Rakowski, Cynthia L.; Richmond, Marshall C.; Serkowski, John A.; Werth, Charles J.; Valocchi, Albert J.; Wietsma, Thomas W.; Zhang, Changyong

    2016-08-01

    Four sets of micromodel nonreactive solute transport experiments were conducted with flow velocity, grain diameter, pore-aspect ratio, and flow focusing heterogeneity as the variables. The data sets were offered to pore-scale modeling groups to test their simulators. Each set consisted of two learning experiments, for which all results was made available, and a challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing, and considerably enhanced mixing due to flow focusing. Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice-Boltzmann (LB) approach, and one employed a computational fluid dynamics (CFD) technique. The learning experiments were used by the PN models to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used these experiments to appropriately discretize the grid representations. The continuum model use published non-linear relations between transverse dispersion coefficients and Peclet numbers to compute the required dispersivity input values. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values and, resulting in less dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models needed up to several days on supercomputers to resolve the more complex problems.

  1. Methods for accurate analysis of galaxy clustering on non-linear scales

    Science.gov (United States)

    Vakili, Mohammadjavad

    2017-01-01

    Measurements of galaxy clustering with the low-redshift galaxy surveys provide sensitive probe of cosmology and growth of structure. Parameter inference with galaxy clustering relies on computation of likelihood functions which requires estimation of the covariance matrix of the observables used in our analyses. Therefore, accurate estimation of the covariance matrices serves as one of the key ingredients in precise cosmological parameter inference. This requires generation of a large number of independent galaxy mock catalogs that accurately describe the statistical distribution of galaxies in a wide range of physical scales. We present a fast method based on low-resolution N-body simulations and approximate galaxy biasing technique for generating mock catalogs. Using a reference catalog that was created using the high resolution Big-MultiDark N-body simulation, we show that our method is able to produce catalogs that describe galaxy clustering at a percentage-level accuracy down to highly non-linear scales in both real-space and redshift-space.In most large-scale structure analyses, modeling of galaxy bias on non-linear scales is performed assuming a halo model. Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as assembly bias. Standard large-scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. However, modeling of galaxy bias can face systematic effects if the number of galaxies are correlated with other halo properties. Using the Small MultiDark-Planck high resolution N-body simulation and the clustering measurements of Sloan Digital Sky Survey DR7 main galaxy sample, we investigate the extent to which the dependence of galaxy bias on halo concentration can improve our modeling of galaxy clustering.

  2. Investigation of the Validity of the Universal Scaling Law on Linear Chains of Silver Nanoparticles

    Directory of Open Access Journals (Sweden)

    Mohammed Alsawafta

    2015-01-01

    Full Text Available Due to the wide range of variation in the plasmonic characteristics of the metallic nanoparticles arranged in linear arrays, the optical spectra of these arrays provide a powerful platform for spectroscopic studies and biosensing applications. Due to the coupling effect between the interacting nanoparticles, the excited resonance mode is shifted with the interparticle separation. The change in the resonance energy of the coupled mode is expressed by the fractional plasmon shift which would normally follow a universal scaling behavior. Such a universal law has been successfully applied on a system of dimers under parallel polarization. It has been found that the plasmon shift decays exponentially over interparticle spacing. The decay length is independent of both the nanoparticle and dielectric properties of the surrounding medium. In this paper, the discrete dipole approximation (DDA is used to examine the validity of extending the universal scaling law to linear chains of several interacting nanoparticles embedded in various host media for both parallel and perpendicular polarizations. Our calculations reveal that the decay length of both the coupled longitudinal mode (LM and transverse modes (TM is strongly dependent on the refractive index of the surrounding medium nm. The decay constant of the LM is linearly proportional to nm while the corresponding constant of the TM decays exponentially with nm. Upon changing the nanoparticle size, the change in the peak position of the LM decreases exponentially with the interparticle separation and hence, it obeys the universal law. The sensitivity of coupled LM to the nanoparticle size is more pronounced at both smaller nanoparticle sizes and separations. The sensitivity of the coupled TM to the nanoparticle size on the other hand changes linearly with the separation and therefore, the universal law does not apply in the case of the excited TM.

  3. [Application of wavenumber-linear scaling to the calculated Raman frequencies of polyenes and carotenoids].

    Science.gov (United States)

    Liu, Wei-Long; Jiang, Li-Lin; Wang, Yang; He, Xing; Song, Yun-Fei; Zheng, Zhi-Ren; Yang, Yan-Qiang; Zhao, Lian-Cheng

    2013-08-01

    Raman spectra of two typical carotenoids (beta-carotene and lutein) and some short (n = 2-5) polyenes were calculated using density functional theory. The wavenumber-linear scaling (WLS) and other frequency scaling methods were used to calibrate the calculated frequencies. It was found that the most commonly used uniform scaling (UFS) method can only calibrate several individual frequencies perfectly, and the systematic result of this method is not very good. The fitting parameters obtained by the WLS method are upsilon(obs)/upsilon(calc)) = 0.999 9-0.000 027 4upsilon(calc) and upsilon(obs)/upsilon(calc)= 0.993 8-0.000 024 8upsilon(calc) for short polyenes and carotenoids, respectively. The calibration results of the WLS method are much better than the UFS method. This result suggests that the WLS method can be used for the frequency scaling of the molecules as large as carotenoids. The similar fitting parameters for short polyenes and carotenoids indicate that the fitting parameters obtained by WLS for short polyenes can be used for calibrating the calculated vibrational frequencies of carotenoids. This presents a new frequency scaling method for vibrational spectroscopic analysis of carotenoids.

  4. Efficient linear-scaling calculation of response properties: density matrix-based Laplace-transformed coupled-perturbed self-consistent field theory.

    Science.gov (United States)

    Beer, Matthias; Ochsenfeld, Christian

    2008-06-14

    A density matrix-based Laplace reformulation of coupled-perturbed self-consistent field (CPSCF) theory is presented. It allows a direct, instead of iterative, solution for the integral-independent part of the density matrix-based CPSCF (D-CPSCF) equations [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 127, 054103 (2007)]. In this way, the matrix-multiplication overhead compared to molecular orbital-based solutions is reduced to a minimum, while at the same time, the linear-scaling behavior of D-CPSCF theory is preserved. The present Laplace-based equation solver is expected to be of general applicability.

  5. A non-linear discontinuous Petrov-Galerkin method for removing oscillations in the solution of the time-dependent transport equation

    Energy Technology Data Exchange (ETDEWEB)

    Merton, S. R.; Smedley-Stevenson, R. P. [Computational Physics Group, AWE Aldermaston, Reading, Berkshire RG7 4PR (United Kingdom); Pain, C. C. [Dept. of Earth Science and Engineering, Imperial College London, London SW7 2AZ (United Kingdom)

    2012-07-01

    This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)

  6. A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

    Science.gov (United States)

    Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

    2017-07-01

    Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

  7. Nonmonotonic Recursive Polynomial Expansions for Linear Scaling Calculation of the Density Matrix.

    Science.gov (United States)

    Rubensson, Emanuel H

    2011-05-10

    As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this letter, there is room for improvements. The key is to allow for nonmonotonicity in the recursive polynomial expansion. On the basis of this idea, new purification schemes are proposed that require only half the number of matrix-matrix multiplications compared to previous schemes. The speedup is essentially independent of the location of the chemical potential and increases with decreasing band gap.

  8. Stability Criteria for Large-Scale Linear Systems with Structured Uncertainties

    Institute of Scientific and Technical Information of China (English)

    Cao Dengqing

    1996-01-01

    The robust stability analysis for large-scale linear systems with structured timevarying uncertainties is investigated in this paper. By using the scalar Lyapunov functions and the properties of M-matrix and nonnegative matrix, stability robustness measures are proposed. The robust stability criteria obtained are applied to derive an algebric criterion which is expressed directly in terms of plant parameters and is shown to be less conservative than the existing ones. A numerical example is given to demonstrate the stability criteria obtained and to compare them with the previous ones.

  9. Performance of Linear and Nonlinear Two-Leaf Light Use Efficiency Models at Different Temporal Scales

    Directory of Open Access Journals (Sweden)

    Xiaocui Wu

    2015-02-01

    Full Text Available The reliable simulation of gross primary productivity (GPP at various spatial and temporal scales is of significance to quantifying the net exchange of carbon between terrestrial ecosystems and the atmosphere. This study aimed to verify the ability of a nonlinear two-leaf model (TL-LUEn, a linear two-leaf model (TL-LUE, and a big-leaf light use efficiency model (MOD17 to simulate GPP at half-hourly, daily and 8-day scales using GPP derived from 58 eddy-covariance flux sites in Asia, Europe and North America as benchmarks. Model evaluation showed that the overall performance of TL-LUEn was slightly but not significantly better than TL-LUE at half-hourly and daily scale, while the overall performance of both TL-LUEn and TL-LUE were significantly better (p < 0.0001 than MOD17 at the two temporal scales. The improvement of TL-LUEn over TL-LUE was relatively small in comparison with the improvement of TL-LUE over MOD17. However, the differences between TL-LUEn and MOD17, and TL-LUE and MOD17 became less distinct at the 8-day scale. As for different vegetation types, TL-LUEn and TL-LUE performed better than MOD17 for all vegetation types except crops at the half-hourly scale. At the daily and 8-day scales, both TL-LUEn and TL-LUE outperformed MOD17 for forests. However, TL-LUEn had a mixed performance for the three non-forest types while TL-LUE outperformed MOD17 slightly for all these non-forest types at daily and 8-day scales. The better performance of TL-LUEn and TL-LUE for forests was mainly achieved by the correction of the underestimation/overestimation of GPP simulated by MOD17 under low/high solar radiation and sky clearness conditions. TL-LUEn is more applicable at individual sites at the half-hourly scale while TL-LUE could be regionally used at half-hourly, daily and 8-day scales. MOD17 is also an applicable option regionally at the 8-day scale.

  10. Application of linear and non-linear methods for modeling removal efficiency of textile dyes from aqueous solutions using magnetic Fe3O4 impregnated onto walnut shell

    Science.gov (United States)

    Ashrafi, Motahare; Arab Chamjangali, Mansour; Bagherian, Ghadamali; Goudarzi, Nasser

    2017-01-01

    The performance of the Nano-magnetite Fe3O4 impregnated onto walnut shell (Fe3O4-WNS), which possessed the adsorption features of walnut shell and the magnetic property of Fe3O4, was investigated for the elimination of the methyl violet and Rhodamine 6G from contaminated aqueous solutions. The effects of different experimental variables on the removal efficiency of the cited dyes were examined. Then these variables were used as the inputs to generate linear and non-linear models such as the multiple linear regression, random forest, and artificial neural network to predict the removal efficiency of these dye species at different experimental conditions. The validation studies of these models were performed using the test set, which was not present in the modeling procedure. It was found that ANN had a higher ability to predict the adsorption process under different experimental conditions, and could be applied for the development of an automated dye wastewater removal plant. Also the maximum adsorption capacity (qmax) indicated that the qmax value for Fe3O4-WNS for removal of cationic dyes was comparable or better than that for some reported adsorbents. Also it should be cited that exhausted Fe3O4-WNS was regenerated using dishwashing liquid, and reused for removal of the cited dye species from aqueous solutions.

  11. Linear-scaling density functional theory using the projector augmented wave method

    Science.gov (United States)

    Hine, Nicholas D. M.

    2017-01-01

    Quantum mechanical simulation of realistic models of nanostructured systems, such as nanocrystals and crystalline interfaces, demands computational methods combining high-accuracy with low-order scaling with system size. Blöchl’s projector augmented wave (PAW) approach enables all-electron (AE) calculations with the efficiency and systematic accuracy of plane-wave pseudopotential calculations. Meanwhile, linear-scaling (LS) approaches to density functional theory (DFT) allow for simulation of thousands of atoms in feasible computational effort. This article describes an adaptation of PAW for use in the LS-DFT framework provided by the ONETEP LS-DFT package. ONETEP uses optimisation of the density matrix through in situ-optimised local orbitals rather than the direct calculation of eigenstates as in traditional PAW approaches. The method is shown to be comparably accurate to both PAW and AE approaches and to exhibit improved convergence properties compared to norm-conserving pseudopotential methods.

  12. Non-Existence of Positive Stationary Solutions for a Class of Semi-Linear PDEs with Random Coefficients

    CERN Document Server

    Coville, Jerome; Luckhaus, Stephan; 10.3934/nhm.2010.5.745

    2011-01-01

    We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative stationary solution, which implies that an interface that was flat originally cannot get stationary. The absence of global stationary solutions is shown by proving lower bounds on the growth of stationary solutions on large domains with Dirichlet boundary conditions. Difficulties arise because the

  13. Effect of linear sorption on solute transport in a coupled fracture-matrix system with sinusoidal fracture geometry

    Directory of Open Access Journals (Sweden)

    N.Natarajan

    2010-10-01

    Full Text Available Modeling of solute transport through fractured rock is an important component of in many disciplines especially groundwater contamination and nuclear waste disposal. Several studies have been conducted on single rock fracture using parallel plate model and recently solute and thermal transport has been numerically modeled in the sinusoidal fracture matrix coupled system. The effect of linear sorption has been studied on the same. Results suggest the high matrix porosity and matrix diffusion coefficient enhance the sorption process and reduce the matrix diffusion of solutes. The velocity of the fluid reduces with increment in fracture aperture.

  14. Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

    Science.gov (United States)

    Ryo, Ikehata

    Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

  15. High Order A-stable Continuous General Linear Methods for Solution of Systems of Initial Value Problems in ODEs

    Directory of Open Access Journals (Sweden)

    Dauda GuliburYAKUBU

    2012-12-01

    Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.

  16. A probabilistic solution of robust H∞ control problem with scaled matrices

    Science.gov (United States)

    Xie, R.; Gong, J. Y.

    2016-07-01

    This paper addresses the robust H∞ control problem with scaled matrices. It is difficult to find a global optimal solution for this non-convex optimisation problem. A probabilistic solution, which can achieve globally optimal robust performance within any pre-specified tolerance, is obtained by using the proposed method based on randomised algorithm. In the proposed method, the scaled H∞ control problem is divided into two parts: (1) assume the scaled matrices be random variables, the scaled H∞ control problem is converted to a convex optimisation problem for the fixed sample of the scaled matrix and a optimal solution corresponding to the fixed sample is obtained; (2) a probabilistic optimal solution is obtained by using the randomised algorithm based on a finite number N optimal solutions, which are obtained in part (1). The analysis shows that the worst case complexity of proposed method is a polynomial.

  17. Solution Properties of Linear Descriptor (Singular Matrix Differential Systems of Higher Order with (Non- Consistent Initial Conditions

    Directory of Open Access Journals (Sweden)

    Athanasios A. Pantelous

    2010-01-01

    Full Text Available In some interesting applications in control and system theory, linear descriptor (singular matrix differential equations of higher order with time-invariant coefficients and (non- consistent initial conditions have been used. In this paper, we provide a study for the solution properties of a more general class of the Apostol-Kolodner-type equations with consistent and nonconsistent initial conditions.

  18. On the Iterated Exponent of Convergence of Solutions of Linear Differential Equations with Entire and Meromorphic Coefficients

    Directory of Open Access Journals (Sweden)

    Rabab Bouabdelli

    2013-01-01

    Full Text Available We investigate the zeros of the difference of the derivative of solutions of the higher-order linear differential equations f(k+Ak-1(zf(k-1+⋯+A1(zf′+A0(zf=0 and small functions, where A0(z,…,Ak-1(z are entire or meromorphic functions of finite iterated p order.

  19. A SYMBOLIC COMPUTATION METHOD TO DECIDE THE COMPLETENESS OF THE SOLUTIONS TO THE SYSTEM OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    张鸿庆; 谢福鼎; 陆斌

    2002-01-01

    A symbolic computation method to decide whether the solutions to the system of linear partial differential equation is complete via using differential algebra and characteristic set is presented.This is a mechanization method, and it can be carried out on the computer in the Maple environment.

  20. Scaling BPS Solutions and pure-Higgs states

    NARCIS (Netherlands)

    I. Bena; M. dr Berkooz; J. de Boer; S. El-Showk; D. van den Bleeken

    2012-01-01

    Depending on the value of the coupling, BPS states of type II string theory compactified on a Calabi-Yau manifold can be described as multicenter supergravity solutions or as BPS states in a quiver gauge theory. While states that spread into the Coulomb-branch states can be mapped one-to-one to supe

  1. Scalable fault tolerant algorithms for linear-scaling coupled-cluster electronic structure methods.

    Energy Technology Data Exchange (ETDEWEB)

    Leininger, Matthew L.; Nielsen, Ida Marie B.; Janssen, Curtis L.

    2004-10-01

    By means of coupled-cluster theory, molecular properties can be computed with an accuracy often exceeding that of experiment. The high-degree polynomial scaling of the coupled-cluster method, however, remains a major obstacle in the accurate theoretical treatment of mainstream chemical problems, despite tremendous progress in computer architectures. Although it has long been recognized that this super-linear scaling is non-physical, the development of efficient reduced-scaling algorithms for massively parallel computers has not been realized. We here present a locally correlated, reduced-scaling, massively parallel coupled-cluster algorithm. A sparse data representation for handling distributed, sparse multidimensional arrays has been implemented along with a set of generalized contraction routines capable of handling such arrays. The parallel implementation entails a coarse-grained parallelization, reducing interprocessor communication and distributing the largest data arrays but replicating as many arrays as possible without introducing memory bottlenecks. The performance of the algorithm is illustrated by several series of runs for glycine chains using a Linux cluster with an InfiniBand interconnect.

  2. On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media

    Science.gov (United States)

    Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo

    2013-04-01

    A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.

  3. Linear and Non-linear Numerical Sea-keeping Evaluation of a Fast Monohull Ferry Compared to Full Scale Measurements

    DEFF Research Database (Denmark)

    Wang, Zhaohui; Folsø, Rasmus; Bondini, Francesca

    1999-01-01

    , full-scale measurements have been performed on board a 128 m monohull fast ferry. This paper deals with the results from these full-scale measurements. The primary results considered are pitch motion, midship vertical bending moment and vertical acceleration at the bow. Previous comparisons between...

  4. Bringing about matrix sparsity in linear-scaling electronic structure calculations.

    Science.gov (United States)

    Rubensson, Emanuel H; Rudberg, Elias

    2011-05-01

    The performance of linear-scaling electronic structure calculations depends critically on matrix sparsity. This article gives an overview of different strategies for removal of small matrix elements, with emphasis on schemes that allow for rigorous control of errors. In particular, a novel scheme is proposed that has significantly smaller computational overhead compared with the Euclidean norm-based truncation scheme of Rubensson et al. (J Comput Chem 2009, 30, 974) while still achieving the desired asymptotic behavior required for linear scaling. Small matrix elements are removed while ensuring that the Euclidean norm of the error matrix stays below a desired value, so that the resulting error in the occupied subspace can be controlled. The efficiency of the new scheme is investigated in benchmark calculations for water clusters including up to 6523 water molecules. Furthermore, the foundation of matrix sparsity is investigated. This includes a study of the decay of matrix element magnitude with distance between basis function centers for different molecular systems and different methods. The studied methods include Hartree–Fock and density functional theory using both pure and hybrid functionals. The relation between band gap and decay properties of the density matrix is also discussed.

  5. Parallel Solutions for Large—Scale General Sparse Nonlinear Systems of Equations

    Institute of Scientific and Technical Information of China (English)

    胡承毅

    1996-01-01

    In solving application problems,many large-scale nonlinear systems of equaions result in sparse Jacobian matrices.Such nonlinear systems are called sparse nonlinear systems.The irregularity of the locations of nonzrero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner.To overcome this difficulty,we define a new storage scheme for general sparse matrices in this paper,With the new storage scheme,we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.I n Section 1,we provide an introduction to the addressed problem and the interval Newton's methods.In Section 2,some currently used storage schemes for sparse systems are reviewed.In Section 3,new index schemes to store general sparse matrices are reported.In Section 4,we present a parallel algorithm to evaluate a general sparse Jacobian matrix.In Section 5,we present a parallel algorithm to solve the corresponding interval linear system by the all-row preconditioned scheme.Conclusions and future work are discussed in Section 6.

  6. Non linear Euler-Poisson system. Part 1: global existence of low entropy solutions; Systeme Euler - Poisson non lineaire. Partie 1: existence globale de solutions faibles entropiques

    Energy Technology Data Exchange (ETDEWEB)

    Cordier, S.

    1995-05-01

    In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs.

  7. Scale-invariant solutions to partial differential equations of fractional order with a moving boundary condition

    Energy Technology Data Exchange (ETDEWEB)

    Li Xicheng; Xu Mingyu [Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100 (China); Wang Shaowei [Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)], E-mail: xichengli@yahoo.com.cn

    2008-04-18

    In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given.

  8. Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

    DEFF Research Database (Denmark)

    Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

    2012-01-01

    to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...

  9. Iterative solution of linear systems in the 20­th century

    NARCIS (Netherlands)

    Saad, Y.; Vorst, H.A. van der

    2001-01-01

    This paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century. Although iterative methods for solving linear systems find their origin in the early nineteenth century (work by Gauss), the field has seen an explosion of activi

  10. Solution and applications of a class of general linear variational inequalities

    Institute of Scientific and Technical Information of China (English)

    何炳生

    1996-01-01

    Many problems in mathematical programming can be described as a general linear variational inequality of the following form: find a vector u*, such thatSome iterative methods for solving a class of general linear variational inequalities have been presented. It is pointed out that the methods can be used to solve some practical extended programming problems.

  11. A Hamiltonian-based solution to the linear quadratic consensus control problem

    NARCIS (Netherlands)

    Weiss, M.

    2012-01-01

    The Linear Quadratic Consensus Control (LQCC) problem is a relaxation of the classical Linear Quadratic Regulation (LQR) problem, that consists of asymptotically driving the state of the system to a "consensus" point in which all coordinates are equal, in such a way that a quadratic cost function on

  12. Deriving robust and globalized robust solutions of uncertain linear programs having general convex uncertainty sets

    NARCIS (Netherlands)

    Gorissen, B.L.; Blanc, J.P.C.; den Hertog, D.; Ben-Tal, A.

    We propose a new way to derive tractable robust counterparts of a linear program based on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First we obtain a new convex reformulation of the dual problem of a robust linear program, and then show how to construct

  13. Application of the linear/exponential hybrid force field scaling scheme to the bond length alternation modes of polyacetylene

    Science.gov (United States)

    Yang, Shujiang; Kertesz, Miklos

    2006-12-01

    The two bond length alternation related backbone carbon-carbon stretching Raman active normal modes of polyacetylene are notoriously difficulty to predict theoretically. We apply our new linear/exponential scaled quantum mechanical force field scheme to tackle this problem by exponentially adjusting the decay of the coupling force constants between backbone stretchings based on their distance which extends over many neighbors. With transferable scaling parameters optimized by least squares fitting to the experimental vibrational frequencies of short oligoenes, the scaled frequencies of trans-polyacetylene and its isotopic analogs agree very well with experiments. The linear/exponential scaling scheme is also applicable to the cis-polyacetylene case.

  14. Speedy standing wave design, optimization, and scaling rules of simulated moving bed systems with linear isotherms.

    Science.gov (United States)

    Weeden, George S; Wang, Nien-Hwa Linda

    2017-04-14

    Simulated Moving Bed (SMB) systems with linear adsorption isotherms have been used for many different separations, including large-scale sugar separations. While SMBs are much more efficient than batch operations, they are not widely used for large-scale production because there are two key barriers. The methods for design, optimization, and scale-up are complex for non-ideal systems. The Speedy Standing Wave Design (SSWD) is developed here to reduce these barriers. The productivity (PR) and the solvent efficiency (F/D) are explicitly related to seven material properties and 13 design parameters. For diffusion-controlled systems, the maximum PR or F/D is controlled by two key dimensionless material properties, the selectivity (α) and the effective diffusivity ratio (η), and two key dimensionless design parameters, the ratios of step time/diffusion time and pressure-limited convection time/diffusion time. The optimum column configuration for maximum PR or F/D is controlled by the weighted diffusivity ratio (η/α(2)). In general, high α and low η/α(2) favor high PR and F/D. The productivity is proportional to the ratio of the feed concentration to the diffusion time. Small particles and high diffusivities favor high productivity, but do not affect solvent efficiency. Simple scaling rules are derived from the two key dimensionless design parameters. The separation of acetic acid from glucose in biomass hydrolysate is used as an example to show how the productivity and the solvent efficiency are affected by the key dimensionless material and design parameters. Ten design parameters are optimized for maximum PR or minimum cost in one minute on a laptop computer. If the material properties are the same for different particle sizes and the dimensionless groups are kept constant, then lab-scale testing consumes less materials and can be done four times faster using particles with half the particle size. Copyright © 2017 Elsevier B.V. All rights reserved.

  15. Trace Conserving Purification for Linear Scaling [O(N)] Methods: A First Enhancement to CP2K

    Science.gov (United States)

    2014-09-01

    purification scheme times in CP2K. Timings are normalized to TRS4 for each band gap. 5 Fig. 2 Graphical representation of the 1024 water box...Trace Conserving Purification for Linear Scaling [O(N)] Methods: A First Enhancement to CP2K by Jonathan Mullin ARL-CR-0746 September...Proving Ground, MD 21005-5069 ARL-CR-0746 September 2014 Trace Conserving Purification for Linear Scaling [O(N)] Methods: A First

  16. The Front-End Readout as an Encoder IC for Magneto-Resistive Linear Scale Sensors

    Science.gov (United States)

    Tran, Trong-Hieu; Chao, Paul Chang-Po; Chien, Ping-Chieh

    2016-01-01

    This study proposes a front-end readout circuit as an encoder chip for magneto-resistance (MR) linear scales. A typical MR sensor consists of two major parts: one is its base structure, also called the magnetic scale, which is embedded with multiple grid MR electrodes, while another is an “MR reader” stage with magnets inside and moving on the rails of the base. As the stage is in motion, the magnetic interaction between the moving stage and the base causes the variation of the magneto-resistances of the grid electrodes. In this study, a front-end readout IC chip is successfully designed and realized to acquire temporally-varying resistances in electrical signals as the stage is in motions. The acquired signals are in fact sinusoids and co-sinusoids, which are further deciphered by the front-end readout circuit via newly-designed programmable gain amplifiers (PGAs) and analog-to-digital converters (ADCs). The PGA is particularly designed to amplify the signals up to full dynamic ranges and up to 1 MHz. A 12-bit successive approximation register (SAR) ADC for analog-to-digital conversion is designed with linearity performance of ±1 in the least significant bit (LSB) over the input range of 0.5–2.5 V from peak to peak. The chip was fabricated by the Taiwan Semiconductor Manufacturing Company (TSMC) 0.35-micron complementary metal oxide semiconductor (CMOS) technology for verification with a chip size of 6.61 mm2, while the power consumption is 56 mW from a 5-V power supply. The measured integral non-linearity (INL) is −0.79–0.95 LSB while the differential non-linearity (DNL) is −0.68–0.72 LSB. The effective number of bits (ENOB) of the designed ADC is validated as 10.86 for converting the input analog signal to digital counterparts. Experimental validation was conducted. A digital decoder is orchestrated to decipher the harmonic outputs from the ADC via interpolation to the position of the moving stage. It was found that the displacement measurement

  17. The Front-End Readout as an Encoder IC for Magneto-Resistive Linear Scale Sensors.

    Science.gov (United States)

    Tran, Trong-Hieu; Chao, Paul Chang-Po; Chien, Ping-Chieh

    2016-09-02

    This study proposes a front-end readout circuit as an encoder chip for magneto-resistance (MR) linear scales. A typical MR sensor consists of two major parts: one is its base structure, also called the magnetic scale, which is embedded with multiple grid MR electrodes, while another is an "MR reader" stage with magnets inside and moving on the rails of the base. As the stage is in motion, the magnetic interaction between the moving stage and the base causes the variation of the magneto-resistances of the grid electrodes. In this study, a front-end readout IC chip is successfully designed and realized to acquire temporally-varying resistances in electrical signals as the stage is in motions. The acquired signals are in fact sinusoids and co-sinusoids, which are further deciphered by the front-end readout circuit via newly-designed programmable gain amplifiers (PGAs) and analog-to-digital converters (ADCs). The PGA is particularly designed to amplify the signals up to full dynamic ranges and up to 1 MHz. A 12-bit successive approximation register (SAR) ADC for analog-to-digital conversion is designed with linearity performance of ±1 in the least significant bit (LSB) over the input range of 0.5-2.5 V from peak to peak. The chip was fabricated by the Taiwan Semiconductor Manufacturing Company (TSMC) 0.35-micron complementary metal oxide semiconductor (CMOS) technology for verification with a chip size of 6.61 mm², while the power consumption is 56 mW from a 5-V power supply. The measured integral non-linearity (INL) is -0.79-0.95 LSB while the differential non-linearity (DNL) is -0.68-0.72 LSB. The effective number of bits (ENOB) of the designed ADC is validated as 10.86 for converting the input analog signal to digital counterparts. Experimental validation was conducted. A digital decoder is orchestrated to decipher the harmonic outputs from the ADC via interpolation to the position of the moving stage. It was found that the displacement measurement error is within

  18. The Front-End Readout as an Encoder IC for Magneto-Resistive Linear Scale Sensors

    Directory of Open Access Journals (Sweden)

    Trong-Hieu Tran

    2016-09-01

    Full Text Available This study proposes a front-end readout circuit as an encoder chip for magneto-resistance (MR linear scales. A typical MR sensor consists of two major parts: one is its base structure, also called the magnetic scale, which is embedded with multiple grid MR electrodes, while another is an “MR reader” stage with magnets inside and moving on the rails of the base. As the stage is in motion, the magnetic interaction between the moving stage and the base causes the variation of the magneto-resistances of the grid electrodes. In this study, a front-end readout IC chip is successfully designed and realized to acquire temporally-varying resistances in electrical signals as the stage is in motions. The acquired signals are in fact sinusoids and co-sinusoids, which are further deciphered by the front-end readout circuit via newly-designed programmable gain amplifiers (PGAs and analog-to-digital converters (ADCs. The PGA is particularly designed to amplify the signals up to full dynamic ranges and up to 1 MHz. A 12-bit successive approximation register (SAR ADC for analog-to-digital conversion is designed with linearity performance of ±1 in the least significant bit (LSB over the input range of 0.5–2.5 V from peak to peak. The chip was fabricated by the Taiwan Semiconductor Manufacturing Company (TSMC 0.35-micron complementary metal oxide semiconductor (CMOS technology for verification with a chip size of 6.61 mm2, while the power consumption is 56 mW from a 5-V power supply. The measured integral non-linearity (INL is −0.79–0.95 LSB while the differential non-linearity (DNL is −0.68–0.72 LSB. The effective number of bits (ENOB of the designed ADC is validated as 10.86 for converting the input analog signal to digital counterparts. Experimental validation was conducted. A digital decoder is orchestrated to decipher the harmonic outputs from the ADC via interpolation to the position of the moving stage. It was found that the displacement

  19. Examining item-position effects in large-scale assessment using the Linear Logistic Test Model

    Directory of Open Access Journals (Sweden)

    CHRISTINE HOHENSINN

    2008-09-01

    Full Text Available When administering large-scale assessments, item-position effects are of particular importance because the applied test designs very often contain several test booklets with the same items presented at different test positions. Establishing such position effects would be most critical; it would mean that the estimated item parameters do not depend exclusively on the items’ difficulties due to content but also on their presentation positions. As a consequence, item calibration would be biased. By means of the linear logistic test model (LLTM, item-position effects can be tested. In this paper, the results of a simulation study demonstrating how LLTM is indeed able to detect certain position effects in the framework of a large-scale assessment are presented first. Second, empirical item-position effects of a specific large-scale competence assessment in mathematics (4th grade students are analyzed using the LLTM. The results indicate that a small fatigue effect seems to take place. The most important consequence of the given paper is that it is advisable to try pertinent simulation studies before an analysis of empirical data takes place; the reason is, that for the given example, the suggested Likelihood-Ratio test neither holds the nominal type-I-risk, nor qualifies as “robust”, and furthermore occasionally shows very low power.

  20. Acceleration in the linear non-scaling fixed-field alternating-gradient accelerator EMMA

    Science.gov (United States)

    Machida, S.; Barlow, R.; Berg, J. S.; Bliss, N.; Buckley, R. K.; Clarke, J. A.; Craddock, M. K.; D'Arcy, R.; Edgecock, R.; Garland, J. M.; Giboudot, Y.; Goudket, P.; Griffiths, S.; Hill, C.; Hill, S. F.; Hock, K. M.; Holder, D. J.; Ibison, M. G.; Jackson, F.; Jamison, S. P.; Johnstone, C.; Jones, J. K.; Jones, L. B.; Kalinin, A.; Keil, E.; Kelliher, D. J.; Kirkman, I. W.; Koscielniak, S.; Marinov, K.; Marks, N.; Martlew, B.; McIntosh, P. A.; McKenzie, J. W.; Méot, F.; Middleman, K. J.; Moss, A.; Muratori, B. D.; Orrett, J.; Owen, H. L.; Pasternak, J.; Peach, K. J.; Poole, M. W.; Rao, Y.-N.; Saveliev, Y.; Scott, D. J.; Sheehy, S. L.; Shepherd, B. J. A.; Smith, R.; Smith, S. L.; Trbojevic, D.; Tzenov, S.; Weston, T.; Wheelhouse, A.; Williams, P. H.; Wolski, A.; Yokoi, T.

    2012-03-01

    In a fixed-field alternating-gradient (FFAG) accelerator, eliminating pulsed magnet operation permits rapid acceleration to synchrotron energies, but with a much higher beam-pulse repetition rate. Conceived in the 1950s, FFAGs are enjoying renewed interest, fuelled by the need to rapidly accelerate unstable muons for future high-energy physics colliders. Until now a `scaling' principle has been applied to avoid beam blow-up and loss. Removing this restriction produces a new breed of FFAG, a non-scaling variant, allowing powerful advances in machine characteristics. We report on the first non-scaling FFAG, in which orbits are compacted to within 10mm in radius over an electron momentum range of 12-18MeV/c. In this strictly linear-gradient FFAG, unstable beam regions are crossed, but acceleration via a novel serpentine channel is so rapid that no significant beam disruption is observed. This result has significant implications for future particle accelerators, particularly muon and high-intensity proton accelerators.

  1. Analytical scalings of the linear Richtmyer-Meshkov instability when a rarefaction is reflected

    Science.gov (United States)

    Cobos-Campos, F.; Wouchuk, J. G.

    2017-07-01

    The Richtmyer-Meshkov instability for the case of a reflected rarefaction is studied in detail following the growth of the contact surface in the linear regime and providing explicit analytical expressions for the asymptotic velocities in different physical limits. This work is a continuation of the similar problem when a shock is reflected [Phys. Rev. E 93, 053111 (2016), 10.1103/PhysRevE.93.053111]. Explicit analytical expressions for the asymptotic normal velocity of the rippled surface (δ vi∞ ) are shown. The known analytical solution of the perturbations growing inside the rarefaction fan is coupled to the pressure perturbations between the transmitted shock front and the rarefaction trailing edge. The surface ripple growth (ψi) is followed from t =0 + up to the asymptotic stage inside the linear regime. As in the shock reflected case, an asymptotic behavior of the form ψi(t ) ≅ψ∞+δ vi∞t is observed, where ψ∞ is an asymptotic ordinate to the origin. Approximate expressions for the asymptotic velocities are given for arbitrary values of the shock Mach number. The asymptotic velocity field is calculated at both sides of the contact surface. The kinetic energy content of the velocity field is explicitly calculated. It is seen that a significant part of the motion occurs inside a fluid layer very near the material surface in good qualitative agreement with recent simulations. The important physical limits of weak and strong shocks and high and low preshock density ratio are also discussed and exact Taylor expansions are given. The results of the linear theory are compared to simulations and experimental work [R. L. Holmes et al., J. Fluid Mech. 389, 55 (1999), 10.1017/S0022112099004838; C. Mariani et al., Phys. Rev. Lett. 100, 254503 (2008), 10.1103/PhysRevLett.100.254503]. The theoretical predictions of δ vi∞ and ψ∞ show good agreement with the experimental and numerical reported values.

  2. Simple Hybrid Scaling-Free CORDIC Solution for FPGAs

    Directory of Open Access Journals (Sweden)

    Leonid Moroz

    2014-01-01

    Full Text Available COordinate Rotation DIgital Computer (CORDIC is an effective method that is used in digital signal processing applications for computing various trigonometric, hyperbolic, linear, and transcendental functions. This paper presents the theoretical basis and practical implementation of circular (sine-cosine CORDIC-based generator. Synthesis results of this generator based on Altera Stratix III FPGA (EP3SL340F1517C2 using Quartus II version 9.0 show that the proposed hybrid FPGA architecture significantly reduces latency (42% reduction with a small area overhead, compared to the conventional version. The proposed algorithm has been simulated for sine and cosine function evaluation, and it has been verified that the accuracy is comparable with conventional algorithm.

  3. A Formula of Solution for a Class of Linear Recurence with Two Indices

    Institute of Scientific and Technical Information of China (English)

    YU Changan

    2006-01-01

    It is very difficult, sometimes impossible, to get a formula solution of recurrence relation, even for the case of homogeneous recurrence with one indice. In this paper, according to the principle of soluting algebraic equation, we present the formula of solution for a class of recurrnce relations with two indices by appling iteration and induction. It provides a concrete model to solve the concerning problems with modem computing tools.

  4. Proof of the nonexistence of a linear solution for the CR2 injection region of the CLIC drive beam

    CERN Document Server

    Apsimon, Robert

    2014-01-01

    In this paper we present a mathematical proof to show that there exists no linear system of optics which can simultaneously close an orbit bump and correct the dispersion in the CR2 injection region. Due to the requirements of the CR2 injection region, several different trajectories will exist through the injection region which are off-axis; therefore the orbit and dispersion functions need to be corrected. In this paper, we determine the properties of a hypothetical linear lattice which is capable of closing the orbit and dispersion functions and then show that the resulting solutions are either unphysical or trivial. Geneva.

  5. Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method

    Directory of Open Access Journals (Sweden)

    H. M. Abdelhafez

    2016-03-01

    Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.

  6. Massive-scale data management using standards-based solutions

    CERN Document Server

    Shiers, J

    1999-01-01

    In common with many large institutes, CERN has traditionally developed and maintained its own data management solutions. Recently, a significant change of direction has taken place and we have now adopted commercial tools, together with a small amount of site- specific code, for this task. The solutions chosen were originally studied as part of research and development projects oriented towards the Large Hadron Collider (LHC), which is currently under construction at CERN. They have since been adopted not only by the LHC collaborations, which are due to take production data starting in 2005, but also by numerous current experiments, both at CERN and at other High Energy Physics laboratories. Previous experiments, that used data management tools developed in-house, are also studying a possible move to the new environment. To meet the needs of today's experiments, data rates of up to 35 MB/second and data volumes of many hundred TB per experiment must be supported. Data distribution to multiple sites must be pr...

  7. An analytical dynamo solution for large-scale magnetic fields of galaxies

    Science.gov (United States)

    Chamandy, Luke

    2016-11-01

    We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parametrized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the `no-z' approximation and the dynamical α-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted on to galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure data sets. Further, we explore the properties of our numerical solutions, and their dependence on certain parameter values. We illustrate and assess the degree to which numerical solutions based on various levels of approximation, common in the dynamo literature, agree with one another.

  8. Exact solution to the one-dimensional Dirac equation of linear potential

    Institute of Scientific and Technical Information of China (English)

    Long Chao-Yun; Qin Shui-Jie

    2007-01-01

    In this paper the one-dimensional Dirac equation with linear potential has been solved by the method of canonical transformation. The bound-state wavefunctions and the corresponding energy spectrum have been obtained for all bound states.

  9. Linear-scaling generation of potential energy surfaces using a double incremental expansion

    CERN Document Server

    König, Carolin

    2016-01-01

    We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced FALCON (Flexible Adaptation of Local COordinates of Nuclei) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examples of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave fun...

  10. Mixed-Mode Oscillations in a piecewise linear system with multiple time scale coupling

    Science.gov (United States)

    Fernández-García, S.; Krupa, M.; Clément, F.

    2016-10-01

    In this work, we analyze a four dimensional slow-fast piecewise linear system with three time scales presenting Mixed-Mode Oscillations. The system possesses an attractive limit cycle along which oscillations of three different amplitudes and frequencies can appear, namely, small oscillations, pulses (medium amplitude) and one surge (largest amplitude). In addition to proving the existence and attractiveness of the limit cycle, we focus our attention on the canard phenomena underlying the changes in the number of small oscillations and pulses. We analyze locally the existence of secondary canards leading to the addition or subtraction of one small oscillation and describe how this change is globally compensated for or not with the addition or subtraction of one pulse.

  11. An Accurate and Linear Scaling Method to Calculate Charge-Transfer Excitation Energies and Diabatic Couplings

    CERN Document Server

    Pavanello, Michele; Visscher, Lucas; Neugebauer, Johannes

    2012-01-01

    Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the Frozen Density Embedding formulation of subsystem Density-Functional Theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against Coupled-Cluster calculations and achieves chemical accuracy for the systems considered...

  12. ON DECENTRALIZED STABILIZATION OF LINEAR LARGE SCALE SYSTEMS WITH SYMMETRIC CIRCULANT STRUCTURE

    Institute of Scientific and Technical Information of China (English)

    金朝永; 张湘伟

    2004-01-01

    The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied. A few sufficient conditions on decentralized stabilization of such systems were proposed. For the continuous systems, by introducing a concept called the magnitude of interconnected structure, a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given. So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem,no matter how complicated the interconnected structure of the overall system is. A algorithm for obtaining decentralized state feedback to stabilize the overall system is given. The discrete systems were also discussed. The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.

  13. Ligand Discrimination in Myoglobin from Linear-Scaling DFT+U

    CERN Document Server

    Cole, Daniel J; Payne, Mike C

    2013-01-01

    Myoglobin modulates the binding of diatomic molecules to its heme group via hydrogen-bonding and steric interactions with neighboring residues, and is an important benchmark for computational studies of biomolecules. We have performed calculations on the heme binding site and a significant proportion of the protein environment (more than 1000 atoms) using linear-scaling density functional theory and the DFT+U method to correct for self-interaction errors associated with localized 3d states. We confirm both the hydrogen-bonding nature of the discrimination effect (3.6 kcal/mol) and assumptions that the relative strain energy stored in the protein is low (less than 1 kcal/mol). Our calculations significantly widen the scope for tackling problems in drug design and enzymology, especially in cases where electron localization, allostery or long-ranged polarization influence ligand binding and reaction.

  14. Non-linear shrinkage estimation of large-scale structure covariance

    Science.gov (United States)

    Joachimi, Benjamin

    2017-03-01

    In many astrophysical settings, covariance matrices of large data sets have to be determined empirically from a finite number of mock realizations. The resulting noise degrades inference and precludes it completely if there are fewer realizations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimizing its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor of ∼50 less realizations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at a negligible computational cost.

  15. Is the pain visual analogue scale linear and responsive to change? An exploration using Rasch analysis.

    Directory of Open Access Journals (Sweden)

    Paula Kersten

    Full Text Available OBJECTIVES: Pain visual analogue scales (VAS are commonly used in clinical trials and are often treated as an interval level scale without evidence that this is appropriate. This paper examines the internal construct validity and responsiveness of the pain VAS using Rasch analysis. METHODS: Patients (n = 221, mean age 67, 58% female with chronic stable joint pain (hip 40% or knee 60% of mechanical origin waiting for joint replacement were included. Pain was scored on seven daily VASs. Rasch analysis was used to examine fit to the Rasch model. Responsiveness (Standardized Response Means, SRM was examined on the raw ordinal data and the interval data generated from the Rasch analysis. RESULTS: Baseline pain VAS scores fitted the Rasch model, although 15 aberrant cases impacted on unidimensionality. There was some local dependency between items but this did not significantly affect the person estimates of pain. Daily pain (item difficulty was stable, suggesting that single measures can be used. Overall, the SRMs derived from ordinal data overestimated the true responsiveness by 59%. Changes over time at the lower and higher end of the scale were represented by large jumps in interval equivalent data points; in the middle of the scale the reverse was seen. CONCLUSIONS: The pain VAS is a valid tool for measuring pain at one point in time. However, the pain VAS does not behave linearly and SRMs vary along the trait of pain. Consequently, Minimum Clinically Important Differences using raw data, or change scores in general, are invalid as these will either under- or overestimate true change; raw pain VAS data should not be used as a primary outcome measure or to inform parametric-based Randomised Controlled Trial power calculations in research studies; and Rasch analysis should be used to convert ordinal data to interval data prior to data interpretation.

  16. Exponents of non-linear clustering in scale-free one dimensional cosmological simulations

    CERN Document Server

    Benhaiem, David; Sicard, François

    2012-01-01

    One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \\gamma depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter \\kappa controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which \\gamma depends strongly on both n and \\kappa and where it agrees very well with a simple general...

  17. A linear systems analysis of the yaw dynamics of a dynamically scaled insect model.

    Science.gov (United States)

    Dickson, William B; Polidoro, Peter; Tanner, Melissa M; Dickinson, Michael H

    2010-09-01

    Recent studies suggest that fruit flies use subtle changes to their wing motion to actively generate forces during aerial maneuvers. In addition, it has been estimated that the passive rotational damping caused by the flapping wings of an insect is around two orders of magnitude greater than that for the body alone. At present, however, the relationships between the active regulation of wing kinematics, passive damping produced by the flapping wings and the overall trajectory of the animal are still poorly understood. In this study, we use a dynamically scaled robotic model equipped with a torque feedback mechanism to study the dynamics of yaw turns in the fruit fly Drosophila melanogaster. Four plausible mechanisms for the active generation of yaw torque are examined. The mechanisms deform the wing kinematics of hovering in order to introduce asymmetry that results in the active production of yaw torque by the flapping wings. The results demonstrate that the stroke-averaged yaw torque is well approximated by a model that is linear with respect to both the yaw velocity and the magnitude of the kinematic deformations. Dynamic measurements, in which the yaw torque produced by the flapping wings was used in real-time to determine the rotation of the robot, suggest that a first-order linear model with stroke-average coefficients accurately captures the yaw dynamics of the system. Finally, an analysis of the stroke-average dynamics suggests that both damping and inertia will be important factors during rapid body saccades of a fruit fly.

  18. Soil properties and preferential solute transport at the field scale

    DEFF Research Database (Denmark)

    Koestel, J K; Minh, Luong Nhat; Nørgaard, Trine

    An important fraction of water flow and solute transport through soil takes place through preferential flow paths. Although this had been already observed in the nineteenth century, it had been forgotten by the scientific community until it was rediscovered during the 1970s. The awareness...... of the relevance of preferential flow was broadly re-established in the community by the early 1990s. However, since then, the notion remains widespread among soil scientists that the occurrence and strength of preferential flow cannot be predicted from measurable proxy variables such as soil properties or land...... management practices (e.g. Beven, K., 1991, modeling preferential flow - an uncertain future, Preferential Flow, 1-11). In our study, we present evidence that disproves this notion. We evaluated breakthrough curve experiments under a constant irrigation rate of 1 cm/h conducted on 65 soil columns (20 cm...

  19. Synthesis of a highly hydrophobic cyclic decapeptide by solid-phase synthesis of linear peptide and cyclization in solution

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    A general method was described to synthesize a highly hydrophobic cyclic peptide,cyclo[LWLWLWLWLQ]where underlines indicate D-configuration of the amino acid,by a two-step solid-phase/solution synthesis strategy.The linear decapeptide was assembled by standard Boc chemistry on solid-phase and subsequently cyclized in solution with high efficiency and reproducibility. In subsequent purification by semi-preparative HPLC,50%(v/v) DMF/H_2O was employed as the solvent to overcome the difficulty of solubilizat...

  20. Invariant and partially invariant solutions of integro-differential equations for linear thermoviscoelastic aging materials with memory

    Science.gov (United States)

    Zhou, Long-Qiao; Meleshko, Sergey V.

    2017-01-01

    A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.

  1. Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay

    Directory of Open Access Journals (Sweden)

    J. Diblík

    2012-01-01

    Full Text Available We study a frequently investigated class of linear difference equations Δv(n=−p(nv(n−k with a positive coefficient p(n and a single delay k. Recently, it was proved that if the function p(n is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n is bounded above and below by certain functions.

  2. Exact solutions of SO(3) non-linear sigma model in a conic space background

    CERN Document Server

    Bezerra, V B; Romero, C

    2005-01-01

    We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski spacetime. This enables us to apply the same methods for obtaining exact solutions in Minkowski spacetime to the case of a conic spacetime. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.

  3. Effect of cellulosic fiber scale on linear and non-linear mechanical performance of starch-based composites.

    Science.gov (United States)

    Karimi, Samaneh; Abdulkhani, Ali; Tahir, Paridah Md; Dufresne, Alain

    2016-10-01

    Cellulosic nanofibers (NFs) from kenaf bast were used to reinforce glycerol plasticized thermoplastic starch (TPS) matrices with varying contents (0-10wt%). The composites were prepared by casting/evaporation method. Raw fibers (RFs) reinforced TPS films were prepared with the same contents and conditions. The aim of study was to investigate the effects of filler dimension and loading on linear and non-linear mechanical performance of fabricated materials. Obtained results clearly demonstrated that the NF-reinforced composites had significantly greater mechanical performance than the RF-reinforced counterparts. This was attributed to the high aspect ratio and nano dimension of the reinforcing agents, as well as their compatibility with the TPS matrix, resulting in strong fiber/matrix interaction. Tensile strength and Young's modulus increased by 313% and 343%, respectively, with increasing NF content from 0 to 10wt%. Dynamic mechanical analysis (DMA) revealed an elevational trend in the glass transition temperature of amylopectin-rich domains in composites. The most eminent record was +18.5°C shift in temperature position of the film reinforced with 8% NF. This finding implied efficient dispersion of nanofibers in the matrix and their ability to form a network and restrict mobility of the system.

  4. On obtaining spectrally accurate solutions of linear differential equations with complex interfaces using the immersed interface method

    Science.gov (United States)

    Ray, Sudipta; Saha, Sandeep

    2016-11-01

    Numerical solution of engineering problems with interfacial discontinuities requires exact implementation of the jump conditions else the accuracy deteriorates significantly; particularly, achieving spectral accuracy has been limited due to complex interface geometry and Gibbs phenomenon. We adopt a novel implementation of the immersed-interface method that satisfies the jump conditions at the interfaces exactly, in conjunction with the Chebyshev-collocation method. We consider solutions to linear second order ordinary and partial differential equations having a discontinuity in their zeroth and first derivatives across an interface traced by a complex curve. The solutions obtained demonstrate the ability of the proposed method to achieve spectral accuracy for discontinuous solutions across tortuous interfaces. The solution methodology is illustrated using two model problems: (i) an ordinary differential equation with jump conditions forced by an infinitely differentiable function, (ii) Poisson's equation having a discontinuous solution across interfaces that are ellipses of varying aspect ratio. The use of more polynomials in the direction of the major axis than the minor axis of the ellipse increases the convergence rate of the solution.

  5. Solute transport predicts scaling of surface reaction rates in porous media: Applications to silicate weathering

    CERN Document Server

    Hunt, Allen G; Ghanbarian, Behzad

    2013-01-01

    We apply our theory of conservative solute transport, based on concepts from percolation theory, directly and without modification to reactive solute transport. This theory has previously been shown to predict the observed range of dispersivity values for conservative solute transport over ten orders of magnitude of length scale. We now show that the temporal dependence derived for the solute velocity accurately predicts the time-dependence for the weathering of silicate minerals over nine orders of magnitude of time scale, while its predicted length dependence agrees with data obtained for reaction rates over five orders of magnitude of length scale. In both cases, it is possible to unify lab and field results. Thus, net reaction rates appear to be limited by solute transport velocities. We suggest the possible relevance of our results to landscape evolution of the earth's terrestrial surface.

  6. Computational solutions to large-scale data management and analysis.

    Science.gov (United States)

    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.

  7. ILUBCG2-11: Solution of 11-banded nonsymmetric linear equation systems by a preconditioned biconjugate gradient routine

    Science.gov (United States)

    Chen, Y.-M.; Koniges, A. E.; Anderson, D. V.

    1989-10-01

    The biconjugate gradient method (BCG) provides an attractive alternative to the usual conjugate gradient algorithms for the solution of sparse systems of linear equations with nonsymmetric and indefinite matrix operators. A preconditioned algorithm is given, whose form resembles the incomplete L-U conjugate gradient scheme (ILUCG2) previously presented. Although the BCG scheme requires the storage of two additional vectors, it converges in a significantly lesser number of iterations (often half), while the number of calculations per iteration remains essentially the same.

  8. Homotopy perturbation Laplace transform solution of fractional non-linear reaction diffusion system of Lotka-Volterra type differential equation

    Directory of Open Access Journals (Sweden)

    M.H. Tiwana

    2017-04-01

    Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.

  9. Operational method of solution of linear non-integer ordinary and partial differential equations.

    Science.gov (United States)

    Zhukovsky, K V

    2016-01-01

    We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

  10. Biogeochemical Filtering of Solute Signals Explored as a Function of Transport and Reaction Time Scales

    Science.gov (United States)

    Zanardo, S.; Basu, N. B.; Rao, P. C.

    2009-12-01

    Catchment biogeochemical responses are the result of superposition of diverse dynamic components, which can be related to climate forcing, water flow, and biogeochemical reactions. The interactions among these components are highly non-linear and contribute to the generation of emergent patterns at multiple spatial and temporal scales. The aim of this work is to explore the following biogeochemical signatures arising from such interactions: (1) the relationship between contaminant loads (L) and discharge (Q) at the annual timescale, leading to an apparent chemostatic relationship (i.e., linear L-Q plots) for different contaminants and at different spatial scales; (2) spatial patterns in the slope and the scatter of the L-Q relationships; and (3) correlation between the intra-annual flow duration curves (FDC) and the load duration curves (LDC). Exploring this relationship necessitates the use of a parsimonious model, with few spatially uniform time constants, that can generate synthetic time series of load and flow at the outlet of river basins. The Mass Response Functions (MRF) approach (Rinaldo et al., 2006), lends itself suitable for the purpose since it relies on the assumption that the evolution of solute concentration in the water pulses depends only on the residence time, and not on its trajectory - thus space is replaced by time. The model simulates the episodic delivery of water and contaminant pulses from the hillslopes to the stream network in response to temporally random but spatially uniform effective rainfall patterns. The domain is described by an immobile source zone in which first order biogeochemical reactions (degradation rate constant ke) alter the solute mass, while multiple mobile rainfall pulses exchange mass with the source zone following linear kinetics (mass transfer rate constant α). The biogeochemical module of MRF, that was originally written to simulate non-reactive tracer and nitrate transport, was modified to include the more

  11. Linear-scaling source-sink algorithm for simulating time-resolved quantum transport and superconductivity

    Science.gov (United States)

    Weston, Joseph; Waintal, Xavier

    2016-04-01

    We report on a "source-sink" algorithm which allows one to calculate time-resolved physical quantities from a general nanoelectronic quantum system (described by an arbitrary time-dependent quadratic Hamiltonian) connected to infinite electrodes. Although mathematically equivalent to the nonequilibrium Green's function formalism, the approach is based on the scattering wave functions of the system. It amounts to solving a set of generalized Schrödinger equations that include an additional "source" term (coming from the time-dependent perturbation) and an absorbing "sink" term (the electrodes). The algorithm execution time scales linearly with both system size and simulation time, allowing one to simulate large systems (currently around 106 degrees of freedom) and/or large times (currently around 105 times the smallest time scale of the system). As an application we calculate the current-voltage characteristics of a Josephson junction for both short and long junctions, and recover the multiple Andreev reflection physics. We also discuss two intrinsically time-dependent situations: the relaxation time of a Josephson junction after a quench of the voltage bias, and the propagation of voltage pulses through a Josephson junction. In the case of a ballistic, long Josephson junction, we predict that a fast voltage pulse creates an oscillatory current whose frequency is controlled by the Thouless energy of the normal part. A similar effect is found for short junctions; a voltage pulse produces an oscillating current which, in the absence of electromagnetic environment, does not relax.

  12. Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data

    Science.gov (United States)

    Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

    2017-01-01

    Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods. PMID:28166542

  13. An Integral-Direct Linear-Scaling Second-Order Møller-Plesset Approach.

    Science.gov (United States)

    Nagy, Péter R; Samu, Gyula; Kállay, Mihály

    2016-10-11

    An integral-direct, iteration-free, linear-scaling, local second-order Møller-Plesset (MP2) approach is presented, which is also useful for spin-scaled MP2 calculations as well as for the efficient evaluation of the perturbative terms of double-hybrid density functionals. The method is based on a fragmentation approximation: the correlation contributions of the individual electron pairs are evaluated in domains constructed for the corresponding localized orbitals, and the correlation energies of distant electron pairs are computed with multipole expansions. The required electron repulsion integrals are calculated directly invoking the density fitting approximation; the storage of integrals and intermediates is avoided. The approach also utilizes natural auxiliary functions to reduce the size of the auxiliary basis of the domains and thereby the operation count and memory requirement. Our test calculations show that the approach recovers 99.9% of the canonical MP2 correlation energy and reproduces reaction energies with an average (maximum) error below 1 kJ/mol (4 kJ/mol). Our benchmark calculations demonstrate that the new method enables MP2 calculations for molecules with more than 2300 atoms and 26000 basis functions on a single processor.

  14. Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Tait, E. W.; Ratcliff, L. E.; Payne, M. C.; Haynes, P. D.; Hine, N. D. M.

    2016-04-20

    Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.

  15. Finite-time scaling via linear driving: application to the two-dimensional Potts model.

    Science.gov (United States)

    Huang, Xianzhi; Gong, Shurong; Zhong, Fan; Fan, Shuangli

    2010-04-01

    We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.

  16. Spatially variable water table recharge and the hillslope hydrologic response: Analytical solutions to the linearized hillslope Boussinesq equation

    Science.gov (United States)

    Dralle, David N.; Boisramé, Gabrielle F. S.; Thompson, Sally E.

    2014-11-01

    The linearized hillslope Boussinesq equation, introduced by Brutsaert (1994), describes the dynamics of saturated, subsurface flow from hillslopes with shallow, unconfined aquifers. In this paper, we use a new analytical technique to solve the linearized hillslope Boussinesq equation to predict water table dynamics and hillslope discharge to channels. The new solutions extend previous analytical treatments of the linearized hillslope Boussinesq equation to account for the impact of spatiotemporal heterogeneity in water table recharge. The results indicate that the spatial character of recharge may significantly alter both steady state subsurface storage characteristics and the transient hillslope hydrologic response, depending strongly on similarity measures of controls on the subsurface flow dynamics. Additionally, we derive new analytical solutions for the linearized hillslope-storage Boussinesq equation and explore the interaction effects of recharge structure and hillslope morphology on water storage and base flow recession characteristics. A theoretical recession analysis, for example, demonstrates that decreasing the relative amount of downslope recharge has a similar effect as increasing hillslope convergence. In general, the theory suggests that recharge heterogeneity can serve to diminish or enhance the hydrologic impacts of hillslope morphology.

  17. Solution for integer linear bilevel programming problems using orthogonal genetic algorithm

    Institute of Scientific and Technical Information of China (English)

    Hong Li; Li Zhang; Yongchang Jiao

    2014-01-01

    An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit program-ming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the ortho-gonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as off-spring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algo-rithm.

  18. An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

    KAUST Repository

    Bourantas, Georgios

    2013-07-01

    A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

  19. SOLUTION RHEOLOGY OF HYPERBRANCHED POLYESTERS AND THEIR BLENDS WITH LINEAR POLYMERS

    Science.gov (United States)

    In this study, the rheological properties of different generations of hyperbranched polyesters in 1-methyl-2-pyrrolidinone solvent and their blends with poly(2-hydroxyethyl methacrylate) have ben investigated. All the hyperbranched polyester solutions exhibited Newtonian behavior...

  20. SOLUTION RHEOLOGY OF HYPERBRANCHED POLYESTERS AND THEIR BLENDS WITH LINEAR POLYMERS

    Science.gov (United States)

    In this study, the rheological properties of different generations of hyperbranched polyesters in 1-methyl-2-pyrrolidinone solvent and their blends with poly(2-hydroxyethyl methacrylate) have ben investigated. All the hyperbranched polyester solutions exhibited Newtonian behavior...

  1. ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.

  2. Grid Interface Challenges and Candidate Solutions for the Compact Linear Collider’s (CLIC) Klystron Modulators

    CERN Document Server

    Aguglia, D; Watson, A; Clare, J; Wheeler, P

    2014-01-01

    The Compact Linear Collider (CLIC) is a linear electron-positron accelerator under study at CERN, in view of exploring a new leptons collision energy region (0.5TeV to 5TeV). This complex requires ~1600 klystrons fed by highly efficient and controllable power electronics for a convenient power connection to the utility grid. This paper presents the challenges and evaluates several possible structures for the power system. Discussion are provided regarding the candidate topologies according to the converters’ ratings / number and considering reliability, modularity, and redundancy.

  3. Drag reduction by linear viscosity model in turbulent channel flow of polymer solution

    Institute of Scientific and Technical Information of China (English)

    吴桂芬; 李昌烽; 黄东升; 赵作广; 冯晓东; 王瑞

    2008-01-01

    A further numerical study of the theory that the drag reduction in the turbulence is related to the viscosity profile growing linearly with the distance from the wall was performed.The constant viscosity in the Navier-Stokes equations was replaced using this viscosity model.Some drag reduction characteristics were shown comparing with Virk’s phenomenology.The mean velocity and Reynolds stress profiles are consistent with the experimental and direct numerical simulation results.A drag reduction level of 45% was obtained.It is reasonable for this linear viscosity model to explain the mechanism of turbulence drag reduction in some aspects.

  4. Numerical solution of linear models in economics: The SP-DG model revisited

    OpenAIRE

    T. Andrade, G. Faria, V. Leite, F. Verona, M. Viegas; Afonso, O.; P.B. Vasconcelos

    2007-01-01

    In general, complex and large dimensional models are needed to solve real economic problems. Due to these characteristics, there is either no analytical solution for them or they are not attainable. As a result, solutions can be only obtained through numerical methods. Thus, the growing importance of computers in Economics is not surprising. This paper focuses on an implementation of the SP-DG model, using Matlab,developed by the students as part of the Computational Economics course. We also...

  5. Segmented linear modeling of CHO fed‐batch culture and its application to large scale production

    Science.gov (United States)

    Ben Yahia, Bassem; Gourevitch, Boris; Malphettes, Laetitia

    2016-01-01

    ABSTRACT We describe a systematic approach to model CHO metabolism during biopharmaceutical production across a wide range of cell culture conditions. To this end, we applied the metabolic steady state concept. We analyzed and modeled the production rates of metabolites as a function of the specific growth rate. First, the total number of metabolic steady state phases and the location of the breakpoints were determined by recursive partitioning. For this, the smoothed derivative of the metabolic rates with respect to the growth rate were used followed by hierarchical clustering of the obtained partition. We then applied a piecewise regression to the metabolic rates with the previously determined number of phases. This allowed identifying the growth rates at which the cells underwent a metabolic shift. The resulting model with piecewise linear relationships between metabolic rates and the growth rate did well describe cellular metabolism in the fed‐batch cultures. Using the model structure and parameter values from a small‐scale cell culture (2 L) training dataset, it was possible to predict metabolic rates of new fed‐batch cultures just using the experimental specific growth rates. Such prediction was successful both at the laboratory scale with 2 L bioreactors but also at the production scale of 2000 L. This type of modeling provides a flexible framework to set a solid foundation for metabolic flux analysis and mechanistic type of modeling. Biotechnol. Bioeng. 2017;114: 785–797. © 2016 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc. PMID:27869296

  6. Segmented linear modeling of CHO fed-batch culture and its application to large scale production.

    Science.gov (United States)

    Ben Yahia, Bassem; Gourevitch, Boris; Malphettes, Laetitia; Heinzle, Elmar

    2017-04-01

    We describe a systematic approach to model CHO metabolism during biopharmaceutical production across a wide range of cell culture conditions. To this end, we applied the metabolic steady state concept. We analyzed and modeled the production rates of metabolites as a function of the specific growth rate. First, the total number of metabolic steady state phases and the location of the breakpoints were determined by recursive partitioning. For this, the smoothed derivative of the metabolic rates with respect to the growth rate were used followed by hierarchical clustering of the obtained partition. We then applied a piecewise regression to the metabolic rates with the previously determined number of phases. This allowed identifying the growth rates at which the cells underwent a metabolic shift. The resulting model with piecewise linear relationships between metabolic rates and the growth rate did well describe cellular metabolism in the fed-batch cultures. Using the model structure and parameter values from a small-scale cell culture (2 L) training dataset, it was possible to predict metabolic rates of new fed-batch cultures just using the experimental specific growth rates. Such prediction was successful both at the laboratory scale with 2 L bioreactors but also at the production scale of 2000 L. This type of modeling provides a flexible framework to set a solid foundation for metabolic flux analysis and mechanistic type of modeling. Biotechnol. Bioeng. 2017;114: 785-797. © 2016 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc. © 2016 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc.

  7. ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION ON TIME SCALES

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.

  8. Field-scale water flow and solute transport : Swap model concepts, parameter estimation and case studies

    NARCIS (Netherlands)

    Dam, van J.C.

    2000-01-01

    Water flow and solute transport in top soils are important elements in many environmental studies. The agro- and ecohydrological model SWAP (Soil-Water-Plant-Atmosphere) has been developed to simulate simultaneously water flow, solute transport, heat flow and crop growth at field scale level. The ma

  9. Minimizing the effects of filtering on catchment scale GRACE solutions

    Science.gov (United States)

    Dutt Vishwakarma, Bramha; Devaraju, Balaji; Sneeuw, Nico

    2016-08-01

    The Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided time variable gravity information since its launch in 2002. Due to short-wavelength noise, the total water storage variations over a catchment observed from GRACE are usable only after filtering. Filtering smooths both the signal and the noise, inevitably changing the nature of the estimated total water storage change. The filtered estimates suffer from attenuation and leakage, which changes the signal characteristics. Several studies have mainly focused on correcting the changed amplitude with the aid of hydrological models. In this study, it is demonstrated that in addition to the amplitude loss, also significant phase change in the time series of total water storage over a region can occur. The phase change due to leakage from nearby catchments can be around 20° to 30° for catchments with moderate size, which makes it difficult to retrieve signal by only scaling. We propose a strategy to approach the true time series with improved phase and amplitude. The strategy is independent of any hydrological model. It is first demonstrated in a closed-loop environment over 32 catchments, where we show that the performance of our method is consistent and better than other model-dependent approaches. Then we also discuss the limitations of our approach. Finally we apply our method to the GRACE level 2 products for 32 catchments.

  10. A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

    NARCIS (Netherlands)

    Botchev, M.A.

    2013-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of th

  11. A block Krylov subspace time-exact solution method for linear ODE systems

    NARCIS (Netherlands)

    Botchev, M.A.

    2012-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approxim

  12. Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

    Science.gov (United States)

    Seaman, Brian; Osler, Thomas J.

    2004-01-01

    A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

  13. Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s)

    NARCIS (Netherlands)

    Collignon, T.P.; Van Gijzen, M.B.

    IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly

  14. Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s)

    NARCIS (Netherlands)

    Collignon, T.P.; Van Gijzen, M.B.

    IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly

  15. A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

    NARCIS (Netherlands)

    Bochev, Mikhail A.

    2013-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

  16. A block Krylov subspace time-exact solution method for linear ODE systems

    NARCIS (Netherlands)

    Bochev, Mikhail A.

    We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial

  17. Progress in solutions of the non-linear Boussinesq groundwater equation (Invited)

    Science.gov (United States)

    Dias, N. L.; Chor, T. L.; de Zarate, A. R.

    2013-12-01

    An existing truncated series solution, previously obtained from inversion techniques from the solution for the Blasius boundary-layer equation, is obtained directly for the Boussinesq equation in terms of a recurrence relation. The series is found to have a finite radius of convergence, which also explains why previous approximations to the solution of the Boussinesq equation had to resort to a combination of series/Padé expressions for small values of the independent variable and asymptotic approximations for large ones. The radius of convergence is obtained numerically to a high accuracy by means of path integration techniques that are able to identify the complex-plane singularities which determine that radius. New variable transformations are proposed for numerical integration of the equation that avoid singularities at the origin, and further asymptotic approximations, which remain necessary due to the finite radius of convergence, are also obtained. The approach can be extended to non-homogeneous boundary conditions at the origin, which is important in realistic scenarios where an aquifer discharges into a channel of finite-depth. Further recurrence relations are found for series solutions of the non-homogeneous case, as well as their radii of convergence and corresponding asymptotic approximations. Results obtained by joining ten terms of the series solution and the asymptotic approximation obtained by Heaslet and Alksne (1961).

  18. Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Meng Hu

    2012-01-01

    Full Text Available By using the theory of calculus on time scales and M-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.

  19. Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales

    OpenAIRE

    Meng Hu; Lili Wang

    2012-01-01

    By using the theory of calculus on time scales and M-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.

  20. Factor solutions of the Social Phobia Scale (SPS) and the Social Interaction Anxiety Scale (SIAS) in a Swedish population.

    Science.gov (United States)

    Mörtberg, Ewa; Reuterskiöld, Lena; Tillfors, Maria; Furmark, Tomas; Öst, Lars-Göran

    2017-06-01

    Culturally validated rating scales for social anxiety disorder (SAD) are of significant importance when screening for the disorder, as well as for evaluating treatment efficacy. This study examined construct validity and additional psychometric properties of two commonly used scales, the Social Phobia Scale and the Social Interaction Anxiety Scale, in a clinical SAD population (n = 180) and in a normal population (n = 614) in Sweden. Confirmatory factor analyses of previously reported factor solutions were tested but did not reveal acceptable fit. Exploratory factor analyses (EFA) of the joint structure of the scales in the total population yielded a two-factor model (performance anxiety and social interaction anxiety), whereas EFA in the clinical sample revealed a three-factor solution, a social interaction anxiety factor and two performance anxiety factors. The SPS and SIAS showed good to excellent internal consistency, and discriminated well between patients with SAD and a normal population sample. Both scales showed good convergent validity with an established measure of SAD, whereas the discriminant validity of symptoms of social anxiety and depression could not be confirmed. The optimal cut-off score for SPS and SIAS were 18 and 22 points, respectively. It is concluded that the factor structure and the additional psychometric properties of SPS and SIAS support the use of the scales for assessment in a Swedish population.

  1. On the Approximate Analytical Solution to Non-Linear Oscillation Systems

    Directory of Open Access Journals (Sweden)

    Mahmoud Bayat

    2013-01-01

    Full Text Available This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation of the Variational Approach (VA is presented to obtain highly accurate analytical solutions to free vibration of conservative oscillators with inertia and static type cubic nonlinearities. In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods.

  2. THE IMPORTANCE OF LIMIT SOLUTIONS & TEMPORAL AND SPATIAL SCALES IN THE TEACHING OF TRANSPORT PHENOMENA

    Directory of Open Access Journals (Sweden)

    SÁVIO LEANDRO BERTOLI

    2016-07-01

    Full Text Available In the engineering courses the field of Transport Phenomena is of significant importance and it is in several disciplines relating to Fluid Mechanics, Heat and Mass Transfer. In these disciplines, problems involving these phenomena are mathematically formulated and analytical solutions are obtained whenever possible. The aim of this paper is to emphasize the possibility of extending aspects of the teaching-learning in this area by a method based on time scales and limit solutions. Thus, aspects relative to the phenomenology naturally arise during the definition of the scales and / or by determining the limit solutions. Aspects concerning the phenomenology of the limit problems are easily incorporated into the proposed development, which contributes significantly to the understanding of physics inherent in the mathematical modeling of each limiting case studied. Finally the study aims to disseminate the use of the limit solutions and of the time scales in the general fields of engineering.

  3. Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

    KAUST Repository

    Claudel, Christian G.

    2014-01-01

    This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

  4. Solute specific scaling of inorganic nitrogen and phosphorus uptake in streams

    OpenAIRE

    2013-01-01

    Stream ecosystem processes such as nutrient cycling may vary with stream position in the watershed. Using a scaling approach, we examined the relationship between stream size and nutrient uptake length, which represents the mean distance that a dissolved solute travels prior to removal from the water column. Ammonium uptake length increased proportionally with stream size measured as specific discharge (discharge/stream width) with a scaling exponent = 1.01. In contrast, the scaling ex...

  5. Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2012-01-01

    Full Text Available This paper centres on the application of the new piecewise successive linearization method (PSLM in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.

  6. The solution of the optimization problem of small energy complexes using linear programming methods

    Science.gov (United States)

    Ivanin, O. A.; Director, L. B.

    2016-11-01

    Linear programming methods were used for solving the optimization problem of schemes and operation modes of distributed generation energy complexes. Applicability conditions of simplex method, applied to energy complexes, including installations of renewable energy (solar, wind), diesel-generators and energy storage, considered. The analysis of decomposition algorithms for various schemes of energy complexes was made. The results of optimization calculations for energy complexes, operated autonomously and as a part of distribution grid, are presented.

  7. Non-linear and transient absorption spectroscopy of magnesium(II)-tetrabenzoporphyrin in solution

    Science.gov (United States)

    Stiel, H.; Volkmer, A.; Rückmann, I.; Zeug, A.; Ehrenberg, B.; Röder, B.

    1998-10-01

    The excited state properties of magnesium(II)-tetrabenzoporphyrin (Mg-TBP) were studied by using intensity dependent transmission (non-linear absorption), ps-transient absorption and time resolved luminescence spectroscopy. It was found that there is a strong excited absorption in the region around 500 nm. Because there is no or little ground state absorption in this region the dye is suitable as an optical limiter.

  8. Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions

    Energy Technology Data Exchange (ETDEWEB)

    Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2012-05-15

    We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.

  9. General linear methods and friends: Toward efficient solutions of multiphysics problems

    Science.gov (United States)

    Sandu, Adrian

    2017-07-01

    Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

  10. Scale Mismatches in Social-Ecological Systems: Causes, Consequences, and Solutions

    Directory of Open Access Journals (Sweden)

    Graeme S. Cumming

    2006-06-01

    Full Text Available Scale is a concept that transcends disciplinary boundaries. In ecology and geography, scale is usually defined in terms of spatial and temporal dimensions. Sociological scale also incorporates space and time, but adds ideas about representation and organization. Although spatial and temporal location determine the context for social and ecological dynamics, social-ecological interactions can create dynamic feedback loops in which humans both influence and are influenced by ecosystem processes. We hypothesize that many of the problems encountered by societies in managing natural resources arise because of a mismatch between the scale of management and the scale(s of the ecological processes being managed. We use examples from southern Africa and the southern United States to address four main questions: (1 What is a "scale mismatch?" (2 How are scale mismatches generated? (3 What are the consequences of scale mismatches? (4 How can scale mismatches be resolved? Scale mismatches occur when the scale of environmental variation and the scale of social organization in which the responsibility for management resides are aligned in such a way that one or more functions of the social-ecological system are disrupted, inefficiencies occur, and/or important components of the system are lost. They are generated by a wide range of social, ecological, and linked social-ecological processes. Mismatches between the scales of ecological processes and the institutions that are responsible for managing them can contribute to a decrease in social-ecological resilience, including the mismanagement of natural resources and a decrease in human well-being. Solutions to scale mismatches usually require institutional changes at more than one hierarchical level. Long-term solutions to scale mismatch problems will depend on social learning and the development of flexible institutions that can adjust and reorganize in response to changes in ecosystems. Further research is

  11. A Non-linear Scaling Algorithm Based on chirp-z Transform for Squint Mode FMCW-SAR

    Directory of Open Access Journals (Sweden)

    Yu Bin-bin

    2012-03-01

    Full Text Available A non-linear scaling chirp-z imaging algorithm for squint mode Frequency Modulated Continuous Wave Synthetic Aperture Radar (FMCW-SAR is presented to solve the problem of the focus accuracy decline. Based on the non-linear characteristics in range direction for the echo signal in Doppler domain, a non-linear modulated signal is introduced to perform a non-linear scaling based on chirp-z transform. Then the error due to range compression and range migration correction can be reduced, therefore the range resolution of radar image is improved. By using the imaging algorithm proposed, the imaging performances for point targets, compared with that from the original chirp-z algorithm, are demonstrated to be improved in range resolution and image contrast, and to be maintained the same in azimuth resolution.

  12. An Efficient Implementation of Non-Linear Limit State Analysis Based on Lower-Bound Solutions

    DEFF Research Database (Denmark)

    Damkilde, Lars; Schmidt, Lotte Juhl

    2005-01-01

    Limit State analysis has been used in design for decades e.g. the yield line theory for concrete slabs or slip line solutions in geotechnics. In engineering practice manual methods have been dominating but in recent years the interest in numerical methods has been increasing. In this respect...

  13. Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems.

    Science.gov (United States)

    1980-10-01

    superior to projected SOR and modified block SOR (see TalbIs 5.3 and 6.3, and Section 4). 3. For high accuracy solutions of the discrete LCP, one should use...of variational inequalities. Math. Computation, 28(1974), pp. 963-971. R. GLOWINSKI. La methode de relaxation. Rendiconti di Matematica , 14 (1971

  14. Linear analytical solution to the phase diversity problem for extended objects based on the Born approximation

    NARCIS (Netherlands)

    Andrei, R.M.; Smith, C.S.; Fraanje, P.R.; Verhaegen, M.; Korkiakoski, V.A.; Keller, C.U.; Doelman, N.J.

    2012-01-01

    In this paper we give a new wavefront estimation technique that overcomes the main disadvantages of the phase diversity (PD) algorithms, namely the large computational complexity and the fact that the solutions can get stuck in a local minima. Our approach gives a good starting point for an iterativ

  15. On The Iterated Exponent of Convergence of Solutions of Linear Differential Equations

    Directory of Open Access Journals (Sweden)

    Abdallah EL FARISSI

    2015-03-01

    Full Text Available In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f^{(k}+A_{k-1}f^{(k-1}+...+A₀f=0 for k≥2 and small functions, where A_{j} (j=0,1,...,k-1 are meromorphic functions of finite iterated p-order.

  16. Towards a Robust Solution of the Non-linear Kinematics for the General Stewart Platform with Estimation of Distribution Algorithms

    Directory of Open Access Journals (Sweden)

    Eusebio Eduardo Hernández Martinez

    2013-01-01

    Full Text Available In robotics, solving the direct kinematics problem (DKP for parallel robots is very often more difficult and time consuming than for their serial counterparts. The problem is stated as follows: given the joint variables, the Cartesian variables should be computed, namely the pose of the mobile platform. Most of the time, the DKP requires solving a non‐linear system of equations. In addition, given that the system could be non‐convex, Newton or Quasi‐Newton (Dogleg based solvers get trapped on local minima. The capacity of such kinds of solvers to find an adequate solution strongly depends on the starting point. A well‐known problem is the selection of such a starting point, which requires a priori information about the neighbouring region of the solution. In order to circumvent this issue, this article proposes an efficient method to select and to generate the starting point based on probabilistic learning. Experiments and discussion are presented to show the method performance. The method successfully avoids getting trapped on local minima without the need for human intervention, which increases its robustness when compared with a single Dogleg approach. This proposal can be extended to other structures, to any non‐linear system of equations, and of course, to non‐linear optimization problems.

  17. Systematic Perturbation of Cytoskeletal Function Reveals a Linear Scaling Relationship between Cell Geometry and Fitness

    Directory of Open Access Journals (Sweden)

    Russell D. Monds

    2014-11-01

    Full Text Available Diversification of cell size is hypothesized to have occurred through a process of evolutionary optimization, but direct demonstrations of causal relationships between cell geometry and fitness are lacking. Here, we identify a mutation from a laboratory-evolved bacterium that dramatically increases cell size through cytoskeletal perturbation and confers a large fitness advantage. We engineer a library of cytoskeletal mutants of different sizes and show that fitness scales linearly with respect to cell size over a wide physiological range. Quantification of the growth rates of single cells during the exit from stationary phase reveals that transitions between “feast-or-famine” growth regimes are a key determinant of cell-size-dependent fitness effects. We also uncover environments that suppress the fitness advantage of larger cells, indicating that cell-size-dependent fitness effects are subject to both biophysical and metabolic constraints. Together, our results highlight laboratory-based evolution as a powerful framework for studying the quantitative relationships between morphology and fitness.

  18. Adding a visual linear scale probability to the PIOPED probability of pulmonary embolism.

    Science.gov (United States)

    Christiansen, F; Nilsson, T; Måre, K; Carlsson, A

    1997-05-01

    Reporting a lung scintigraphy diagnosis as a PIOPED categorical probability of pulmonary embolism offers the clinician a wide range of interpretation. Therefore the purpose of this study was to analyze the impact on lung scintigraphy reporting of adding a visual linear scale (VLS) probability assessment to the ordinary PIOPED categorical probability. The study material was a re-evaluation of lung scintigrams from a prospective study of 170 patients. All patients had been examined by lung scintigraphy and pulmonary angiography. The scintigrams were re-evaluated by 3 raters, and the probability of pulmonary embolism was estimated by the PIOPED categorization and by a VLS probability. The test was repeated after 6 months. There was no significant difference (p > 0.05) in the area under the ROC curve between the PIOPED categorization and the VLS for any of the 3 raters. Analysis of agreement among raters and for repeatability demonstrated low agreement in the mid-range of probabilities. A VLS probability estimate did not significantly improve the overall accuracy of the diagnosis compared to the categorical PIOPED probability assessment alone. From the data of our present study we cannot recommend the addition of a VLS score to the PIOPED categorization.

  19. A Steeper than Linear Disk Mass-Stellar Mass Scaling Relation

    Science.gov (United States)

    Pascucci, Ilaria; SLICK, EOS

    2017-01-01

    The disk mass is among the most important input parameter of planet formation models as it determines the number and masses of the planets that can form. I will present an ALMA 887 micron survey of the disk population around objects from 2 to 0.03Msun in the nearby 2 Myr-old Chamaeleon I star-forming region. Assuming isothermal and optically thin emission, we convert the 887 micron flux densities into dust disk masses (Mdust) and show that the Mdust-Mstar scaling relation is steeper than linear. By re-analyzing all millimeter data available for nearby regions in a self-consistent way, we find that the 1-3 Myr-old regions of Taurus, Lupus, and Chamaeleon I share the same Mdust-Mstar relation, while the 10 Myr-old Upper Sco association has an even steeper relation. Theoretical models of grain growth, drift, and fragmentation reproduce this trend and suggest that disks are in the fragmentation-limited regime. In this regime millimeter grains will be located closer in around lower-mass stars, a prediction that can be tested with deeper and higher spatial resolution ALMA observations.

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

    Science.gov (United States)

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

    2016-07-12

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

  1. Laplacian versus topography in the solution of the linear gravimetric boundary value problem by means of successive approximations

    Science.gov (United States)

    Holota, Petr; Nesvadba, Otakar

    2017-04-01

    The aim of this paper is to discuss the solution of the linearized gravimetric boundary value problem by means of the method of successive approximations. We start with the relation between the geometry of the solution domain and the structure of Laplace's operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Laplace's operator has a relatively simple structure in terms of ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from an oblate ellipsoid of revolution, even if it is optimally fitted. Therefore, an alternative is discussed. A system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces is used. Clearly, the structure of Laplace's operator is more complicated in this case. It was deduced by means of tensor calculus and in a sense it represents the topography of the physical surface of the Earth. Nevertheless, the construction of the respective Green's function is more simple, if the solution domain is transformed. This enables the use of the classical Green's function method together with the method of successive approximations for the solution of the linear gravimetric boundary value problem expressed in terms of new coordinates. The structure of iteration steps is analyzed and where useful also modified by means of the integration by parts. Comparison with other methods is discussed.

  2. Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

    Directory of Open Access Journals (Sweden)

    Matthew J Simpson

    Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i the rate at which the domain elongates, (ii the diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

  3. Explosive Solutions of Elliptic Equations with Absorption and Non-Linear Gradient Term

    Indian Academy of Sciences (India)

    Marius Ghergu; Constantin Niculescu; Vicenţiu Rădulescu

    2002-08-01

    Let be a non-decreasing $C^1$-function such that $f > 0$ on $(0, ∞), f(0) = 0, \\int_1^∞ 1/\\sqrt{F(t)}dt < ∞$ and $F(t)/f^{2/a}(t)→ 0$ as $t →∞$, where $F(t) = \\int_0^t f(s)ds$ and $a \\in (0,2]$. We prove the existence of positive large solutions to the equation $ u + q(x)|\

  4. A note on the solution of fuzzy transportation problem using fuzzy linear system

    Directory of Open Access Journals (Sweden)

    P. Senthilkumar

    2013-08-01

    Full Text Available In this paper, we discuss the solution of a fuzzy transportation problem, with fuzzy quantities. The problem is solved in two stages. In the first stage, the fuzzy transportation problem is reduced to crisp system by using the lower and upper bounds of fuzzy quantities. In the second stage, the crisp transportation problems are solved by usual simplex method. The procedure is illustrated with numerical examples.

  5. Analytical Solution of Linear, Quadratic and Cubic Model of PTT Fluid

    Directory of Open Access Journals (Sweden)

    Naeem Faraz

    2015-07-01

    Full Text Available An attempt is made for the first time to solve the quadratic and cubic model of magneto hydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT. Series solution of magneto hydrodynamic (MHD flow is developed by using homotopy perturbation method (HPM. Results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveals many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.

  6. LINEAR STIELTJES EQUATION WITH GENERALIZED RIEMANN INTEGRAL AND EXISTENCE OF REGULATED SOLUTIONS

    Institute of Scientific and Technical Information of China (English)

    L. BARBANTI

    2001-01-01

    In this work we establish an existence theorem of regulated solutions for a class of Stieltjes equations which involve generalized Riemann kind of integrals. The general method applied consists in considering the continuous-time Stieltjes equation as limit of discrete processes. This approach will prove fruitful in the study of the controllability of Stieltjes systems, because it will be possible to get properties on the continuous time equation by transferring properties of the discrete ones.

  7. Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem

    OpenAIRE

    Altürk, Ahmet

    2016-01-01

    Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some ...

  8. Progressive Magnetic Resonance Image Reconstruction Based on Iterative Solution of a Sparse Linear System

    Science.gov (United States)

    Fahmy, Ahmed S.; Gabr, Refaat E.; Heberlein, Keith; Hu, Xiaoping P.

    2006-01-01

    Image reconstruction from nonuniformly sampled spatial frequency domain data is an important problem that arises in computed imaging. Current reconstruction techniques suffer from limitations in their model and implementation. In this paper, we present a new reconstruction method that is based on solving a system of linear equations using an efficient iterative approach. Image pixel intensities are related to the measured frequency domain data through a set of linear equations. Although the system matrix is too dense and large to solve by direct inversion in practice, a simple orthogonal transformation to the rows of this matrix is applied to convert the matrix into a sparse one up to a certain chosen level of energy preservation. The transformed system is subsequently solved using the conjugate gradient method. This method is applied to reconstruct images of a numerical phantom as well as magnetic resonance images from experimental spiral imaging data. The results support the theory and demonstrate that the computational load of this method is similar to that of standard gridding, illustrating its practical utility. PMID:23165034

  9. Linear-scaling time-dependent density-functional theory (TDDFT) beyond the Tamm-Dancoff approximation: obtaining efficiency and accuracy with in situ optimised local orbitals

    CERN Document Server

    Zuehlsdorff, Tim J; Payne, Mike C; Haynes, Peter D

    2015-01-01

    We present a solution of the full TDDFT eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspace with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate-gradients algorithm that is very memory-efficient. The algorithm is validated on a test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll (BChl) i...

  10. Parallel solution of systems of linear equations generated by COMSOL 3.2 using the Sun Performance Library

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Dammann, Bernd; Aage, Niels

    This note investigates the use of the Sun Performance Library for parallel solution of a system of linear equations generated by COMSOL 3.2. In many engineering disciplines this is a computational bottleneck for large problems which are often met in research practice. Most researches are primarily...... for a testproblem run in 2D and 3D. Moreover this note quantifies the performance of COMSOL running on a Sparc ULTRA III processor. The study shows that for small problems such as debugging tasks, teaching exercises etc. the Sun computer is not competitive compared with a standard PC....

  11. On the solution of two-point linear differential eigenvalue problems. [numerical technique with application to Orr-Sommerfeld equation

    Science.gov (United States)

    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.

  12. Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet

    OpenAIRE

    Mohamadali, Meysam; Ashrafi, Nariman

    2016-01-01

    High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an eff...

  13. Investigating the potential of using acoustic frequency on the degradation of linear alkylbenzen sulfonates from aqueous solution

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The effectiveness of using acoustical (sonochemical) reactor for degradation of linear alkylbenzen sulfonate (LAS) from aqueous solution was investigated. LASs are anionic surfactants, found in relatively high amounts in domestic and industrial wastewaters. In this study, experiments on LAS solution were performed using methylene blue active substances (MBAS) method.The effectiveness of acoustical processor reactor for LAS degradation is evaluated with emphasis on the effect of treatment time and initial LAS concentration. Experiments were performed at initial concentrations of 0.2, 0.5, 0.8 and 1.0 mg/L, acoustic frequency of 130 kHz, applied power of 500 W and temperature of 18 ℃~20 ℃. At the conditions involved, LAS degradation was found to increase with increasing sonochemical time. In addition, as the concentration increased, the LAS degradation rate decreased in the acoustical processor reactor.

  14. Solution of the spherically symmetric linear thermoviscoelastic problem in the inertia-free limit

    DEFF Research Database (Denmark)

    Christensen, Tage Emil; Dyre, J. C.

    2008-01-01

    paper-the thermoviscoelastic  problem may be solved analytically in the inertia-free limit, i.e., the limit where the sample is much smaller than the wavelength of sound waves at the frequencies of interest. As for the one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E 75......, 041502 (2007)], the solution is conveniently formulated in terms of the so-called transfer matrix, which directly links to the boundary conditions that can be experimentally controlled. Once the transfer matrix has been calculated, it is fairly easy to deduce the equations describing various...

  15. The reduction of the linear stability of elliptic Euler-Moulton solutions of the n-body problem to those of 3-body problems

    Science.gov (United States)

    Zhou, Qinglong; Long, Yiming

    2017-04-01

    In this paper, we consider the elliptic collinear solutions of the classical n-body problem, where the n bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion is called an elliptic Euler-Moulton collinear solution. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic Euler-Moulton collinear solution of n-bodies splits into (n-1) independent linear Hamiltonian systems, the first one is the linearized Hamiltonian system of the Kepler 2-body problem at Kepler elliptic orbit, and each of the other (n-2) systems is the essential part of the linearized Hamiltonian system at an elliptic Euler collinear solution of a 3-body problem whose mass parameter is modified. Then the linear stability of such a solution in the n-body problem is reduced to those of the corresponding elliptic Euler collinear solutions of the 3-body problems, which for example then can be further understood using numerical results of Martínez et al. on 3-body Euler solutions in 2004-2006. As an example, we carry out the detailed derivation of the linear stability for an elliptic Euler-Moulton solution of the 4-body problem with two small masses in the middle.

  16. Linear collider: a preview

    Energy Technology Data Exchange (ETDEWEB)

    Wiedemann, H.

    1981-11-01

    Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.

  17. SIMULTANEOUSLY SPARSE SOLUTIONS TO LINEAR INVERSE PROBLEMS WITH MULTIPLE SYSTEM MATRICES AND A SINGLE OBSERVATION VECTOR*

    Science.gov (United States)

    ZELINSKI, ADAM C.; GOYAL, VIVEK K.; ADALSTEINSSON, ELFAR

    2010-01-01

    A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that approximately solves the system. We refer to this as the multiple-system single-output (MSSO) simultaneous sparse approximation problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts an initial exploration of algorithms with which to solve it. Greedy algorithms and techniques based on convex relaxation are derived and compared empirically. Experiments involve sparsity pattern recovery in noiseless and noisy settings and MRI RF pulse design. PMID:20445814

  18. A Coded Bit-Loading Linear Precoded Discrete Multitone Solution for Power Line Communication

    CERN Document Server

    Muhammad, Fahad Syed; Hélard, Jean-François; Crussière, Matthieu

    2008-01-01

    Linear precoded discrete multitone modulation (LP-DMT) system has been already proved advantageous with adaptive resource allocation algorithm in a power line communication (PLC) context. In this paper, we investigate the bit and energy allocation algorithm of an adaptive LP-DMT system taking into account the channel coding scheme. A coded adaptive LP-DMT system is presented in the PLC context with a loading algorithm which ccommodates the channel coding gains in bit and energy calculations. The performance of a concatenated channel coding scheme, consisting of an inner Wei's 4-dimensional 16-states trellis code and an outer Reed-Solomon code, in combination with the roposed algorithm is analyzed. Simulation results are presented for a fixed target bit error rate in a multicarrier scenario under power spectral density constraint. Using a multipath model of PLC channel, it is shown that the proposed coded adaptive LP-DMT system performs better than classical coded discrete multitone.

  19. Variational principle and a perturbative solution of non-linear string equations in curved space

    CERN Document Server

    Roshchupkin, S N

    1999-01-01

    String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H

  20. Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics

    DEFF Research Database (Denmark)

    Iwankiewicz, R.; Nielsen, Søren R. K.

    -numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...... of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...

  1. Iterative solution of general sparse linear systems on clusters of workstations

    Energy Technology Data Exchange (ETDEWEB)

    Lo, Gen-Ching; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)

    1996-12-31

    Solving sparse irregularly structured linear systems on parallel platforms poses several challenges. First, sparsity makes it difficult to exploit data locality, whether in a distributed or shared memory environment. A second, perhaps more serious challenge, is to find efficient ways to precondition the system. Preconditioning techniques which have a large degree of parallelism, such as multicolor SSOR, often have a slower rate of convergence than their sequential counterparts. Finally, a number of other computational kernels such as inner products could ruin any gains gained from parallel speed-ups, and this is especially true on workstation clusters where start-up times may be high. In this paper we discuss these issues and report on our experience with PSPARSLIB, an on-going project for building a library of parallel iterative sparse matrix solvers.

  2. Implementation and Performance Evaluation of Distributed Cloud Storage Solutions using Random Linear Network Coding

    DEFF Research Database (Denmark)

    Fitzek, Frank; Toth, Tamas; Szabados, Áron

    2014-01-01

    This paper advocates the use of random linear network coding for storage in distributed clouds in order to reduce storage and traffic costs in dynamic settings, i.e. when adding and removing numerous storage devices/clouds on-the-fly and when the number of reachable clouds is limited. We introduce...... various network coding approaches that trade-off reliability, storage and traffic costs, and system complexity relying on probabilistic recoding for cloud regeneration. We compare these approaches with other approaches based on data replication and Reed-Solomon codes. A simulator has been developed...... to carry out a thorough performance evaluation of the various approaches when relying on different system settings, e.g., finite fields, and network/storage conditions, e.g., storage space used per cloud, limited network use, and limited recoding capabilities. In contrast to standard coding approaches, our...

  3. A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation

    Science.gov (United States)

    Colmenares, José; Galizia, Antonella; Ortiz, Jesús; Clematis, Andrea; Rocchia, Walter

    2014-01-01

    The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs. PMID:25013789

  4. Linear topology in amorphous metal oxide electrochromic networks obtained via low-temperature solution processing

    Science.gov (United States)

    Llordés, Anna; Wang, Yang; Fernandez-Martinez, Alejandro; Xiao, Penghao; Lee, Tom; Poulain, Agnieszka; Zandi, Omid; Saez Cabezas, Camila A.; Henkelman, Graeme; Milliron, Delia J.

    2016-12-01

    Amorphous transition metal oxides are recognized as leading candidates for electrochromic window coatings that can dynamically modulate solar irradiation and improve building energy efficiency. However, their thin films are normally prepared by energy-intensive sputtering techniques or high-temperature solution methods, which increase manufacturing cost and complexity. Here, we report on a room-temperature solution process to fabricate electrochromic films of niobium oxide glass (NbOx) and `nanocrystal-in-glass’ composites (that is, tin-doped indium oxide (ITO) nanocrystals embedded in NbOx glass) via acid-catalysed condensation of polyniobate clusters. A combination of X-ray scattering and spectroscopic characterization with complementary simulations reveals that this strategy leads to a unique one-dimensional chain-like NbOx structure, which significantly enhances the electrochromic performance, compared to a typical three-dimensional NbOx network obtained from conventional high-temperature thermal processing. In addition, we show how self-assembled ITO-in-NbOx composite films can be successfully integrated into high-performance flexible electrochromic devices.

  5. A combined MPI-CUDA parallel solution of linear and nonlinear Poisson-Boltzmann equation.

    Science.gov (United States)

    Colmenares, José; Galizia, Antonella; Ortiz, Jesús; Clematis, Andrea; Rocchia, Walter

    2014-01-01

    The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.

  6. A Combined MPI-CUDA Parallel Solution of Linear and Nonlinear Poisson-Boltzmann Equation

    Directory of Open Access Journals (Sweden)

    José Colmenares

    2014-01-01

    Full Text Available The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.

  7. Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations

    Science.gov (United States)

    Ayhan, Burcu; Ozer, M. Naci; Bekir, Ahmet

    2017-01-01

    Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.

  8. HEIST: An event-scale model of cascading water and solute fronts through the vadose zone (Invited)

    Science.gov (United States)

    Harman, C. J.; Basu, N. B.; Rao, P. C.; Sivapalan, M.

    2009-12-01

    The transport of a sorbing, degrading solute (such as Atrazine) through the soil is largely driven by infiltrating water from storms or irrigation, and so depends on the interactions between the timing and characteristics of the rainfall or irrigation events, the properties of the solute, soil characteristics (e.g, porosity, macropore density etc.), and the antecedent soil moisture conditions. This interaction causes the time series inputs of the solute to be “filtered” prior to reaching the watertable, so that the timing, frequency and magnitude of output events is altered. While many previous studies have examined the movement of solutes through soils for a particular site, few have examined the nature of this filtering in more general terms. In this work we present an elegant 1-D model of solute transport through the soil, driven by infiltration events, that is designed to examine this filtering effect. A unique feature of this model is the event-scale time-stepping. By assuming that infiltration and redistribution processes occur instantaneously during an event, while degradation, mobilization, and evapotranspiration are the only important processes occurring between storms, analytical expressions can be derived for the event-to-event transformations of the input signal within the system. Solutes can be surface applied in recalcitrant and labile forms, with first-order mass transfer between the pools, and linear reversible sorption. Infiltrating water mobilizes the labile dissolved solute, generating a point load that moves through the soil with wetting fronts generated by storm events. The retardation and first-order decay of the point-loads eventually decouples them from the wetting fronts they first entered with, allowing solutes to concentrate in the profile. Because only one timestep is required per storm, the model runs very fast, allowing us to examine the effect of different parameter combinations on the filtering. The results show that

  9. Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

    1994-01-01

    perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...... for multi-degree-of-freedom (MDOF) systems and the method is illustrated for a single-degree-of-freedom (SDOF) oscillator. The results are compared to those of exact results for a random oscillator subject to white noise excitation with random intensity....

  10. A computer package for the design and eigenproblem solution of damped linear multidegree of freedom systems

    Science.gov (United States)

    Ahmadian, M.; Inman, D. J.

    1982-01-01

    Systems described by the matrix differental equation are considered. An interactive design routine is presented for positive definite mass, damping, and stiffness matrices. Designing is accomplished by adjusting the mass, damping, and stiffness matrices to obtain a desired oscillation behavior. The algorithm also features interactively modifying the physical structure of the system, obtaining the matrix structure and a number of other system properties. In case of a general system, where the M, C, and K matrices lack any special properties, a routine for the eigenproblem solution of the system is developed. The latent roots are obtained by computing the characteristic polynomial of the system and solving for its roots. The above routines are prepared in FORTRAN IV and prove to be usable for the machines with low core memory.

  11. Multiple linear regression to develop strength scaled equations for knee and elbow joints based on age, gender and segment mass

    DEFF Research Database (Denmark)

    D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar

    2012-01-01

    and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent...

  12. On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Quanxin Zhang

    2014-01-01

    Full Text Available We discuss oscillation criteria for second-order half-linear neutral delay dynamic equations on time scales by using the generalized Riccati transformation and the inequality technique. Under certain conditions, we establish four new oscillation criteria. Our results in this paper are new even for the cases of =ℝ and =ℤ.

  13. Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

    Science.gov (United States)

    Lorenzo, C F; Hartley, T T; Malti, R

    2013-05-13

    A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

  14. Technical Solutions to Mitigate Reliability Challenges due to Technology Scaling of Charge Storage NVM

    Directory of Open Access Journals (Sweden)

    Meng Chuan Lee

    2013-01-01

    Full Text Available Charge storage nonvolatile memory (NVM is one of the main driving forces in the evolution of IT handheld devices. Technology scaling of charge storage NVM has always been the strategy to achieve higher density NVM with lower cost per bit in order to meet the persistent consumer demand for larger storage space. However, conventional technology scaling of charge storage NVM has run into many critical reliability challenges related to fundamental device characteristics. Therefore, further technology scaling has to be supplemented with novel approaches in order to surmount these reliability issues to achieve desired reliability performance. This paper is focused on reviewing critical research findings on major reliability challenges and technical solutions to mitigate technology scaling challenges of charge storage NVM. Most of these technical solutions are still in research phase while a few of them are more mature and ready for production phase. Three of the mature technical solutions will be reviewed in detail, that is, tunnel oxide top/bottom nitridation, nanocrystal, and phase change memory (PCM. Key advantages and reported reliability challenges of these approaches are thoroughly reviewed in this paper. This paper will serve as a good reference to understand the future trend of innovative technical solutions to overcome the reliability challenges of charge storage NVM due to technology scaling.

  15. Numerical solution of the stochastic collection equation—comparison of the Linear Discrete Method with other methods

    Science.gov (United States)

    Simmel, Martin; Trautmann, Thomas; Tetzlaff, Gerd

    The Linear Discrete Method is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made with the Method of Moments, the Berry-Reinhardt model and the Linear Flux Method. Simulations for all numerical methods are shown for the kernel after Golovin [Bull. Acad. Sci. USSR, Geophys. Ser. 5 (1963) 783] and are compared with the analytical solution for two different initial distributions. BRM seems to give the best results and LDM gives good results, too. LFM overestimates the drop growth for the right tail of the distribution and MOM does the same but over the entire drop spectrum. For the hydrodynamic kernel after Long [J. Atmos. Sci. 31 (1974) 1040], simulations are presented using the four numerical methods (LDM, MOM, BRM, LFM). Especially for high resolutions, the solutions of LDM and LFM approach each other very closely. In addition, LDM simulations using the hydrodynamic kernel after Böhm [Atmos. Res. 52 (1999) 167] are presented, which show good correspondence between low- and high-resolution results. Computation efficiency is especially important when numerical schemes are to be included in larger models. Therefore, the computation times of the four methods were compared for the cases with the Golovin kernel. The result is that LDM is the fastest method by far, needing less time than other methods by a factor of 2-7, depending on the case and the bin resolution. For high resolutions, MOM is the slowest. For the lowest resolution, this holds for LFM.

  16. Sorption of malachite green from aqueous solution by potato peel: Kinetics and equilibrium modeling using non-linear analysis method

    Directory of Open Access Journals (Sweden)

    El-Khamsa Guechi

    2016-09-01

    Full Text Available Potato peel (PP was used as a biosorbent to remove malachite green (MG from aqueous solution under various operating conditions. The effect of the experimental parameters such as initial dye concentration, biosorbent dose, initial pH, stirring speed, temperature, ionic strength and biosorbent particle size was investigated through a number of batch sorption experiments. The sorption kinetic uptake for MG by PP at various initial dye concentrations was analyzed by non-linear method using pseudo-first, pseudo-second and pseudo-nth order models. It was found that the pseudo-nth order kinetic model was the best applicable model to describe the sorption kinetic data and the order n of sorption reaction was calculated in the range from 0.71 to 2.71. Three sorption isotherms namely the Langmuir, Freundlich and Redlich–Peterson isotherms in their non-linear forms were applied to the biosorption equilibrium data. Both the Langmuir and Redlich–Peterson models were found to fit the sorption isotherm data well, but the Redlich–Peterson model was better. Thermodynamic parameters show that the sorption process of MG is endothermic and more effective process at high temperatures. The results revealed that PP is very effective for the biosorption of MG from aqueous solutions.

  17. Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model

    CERN Document Server

    Koroteev, Peter; Vinci, Walter

    2010-01-01

    We study a heterotic two-dimensional N=(0,2) gauged non-linear sigma-model whose target space is a weighted complex projective space. We consider the case with N positively and \\tilde{N}=N_F - N negatively charged fields. This model is believed to give a description of the low-energy physics of a non-Abelian semi-local vortex in a four-dimensional N=2 supersymmetric U(N) gauge theory with N_F > N matter hypermultiplets. The supersymmetry in the latter theory is broken down to N=1 by a mass term for the adjoint fields. We solve the model in the large-N approximation and explore a two-dimensional subset of the mass parameter space for which a discrete Z_{N-\\tilde{N}} symmetry is preserved. Supersymmetry is generically broken, but it is preserved for special values of the masses where a new branch opens up and the model becomes super-conformal.

  18. Programmable Solution for Solving Non-linearity Characteristics of Smart Sensor Applications

    Directory of Open Access Journals (Sweden)

    S. Khan

    2007-10-01

    Full Text Available This paper presents a simple but programmable technique to solve the problem of non-linear characteristics of sensors used in more sensitive applications. The nonlinearity of the output response becomes a very sensitive issue in cases where a proportional increase in the physical quantity fails to bring about a proportional increase in the signal measured. The nonlinearity is addressed by using the interpolation method on the characteristics of a given sensor, approximating it to a set of tangent lines, the tangent points of which are recognized in the code of the processor by IF-THEN code. The method suggested here eliminates the use of external circuits for interfacing, and eases the programming burden on the processor at the cost of proportionally reduced memory requirements. The mathematically worked out results are compared with the simulation and experimental results for an IR sensor selected for the purpose and used for level measurement. This work will be of paramount importance and significance in applications where the controlled signal is required to follow the input signal precisely particularly in sensitive robotic applications.

  19. Fluorine-Containing ABC Linear Triblock Terpolymers: Synthesis and Self-assembly in Solution

    Energy Technology Data Exchange (ETDEWEB)

    He, Lihong [ORNL; Hinestrosa Salazar, Juan P [ORNL; Pickel, Joseph M [ORNL; Kilbey, II, S Michael [ORNL; Mays, Jimmy [ORNL; Zhang, Shanju [Georgia Institute of Technology; Bucknall, David G. [Georgia Institute of Technology; Hong, Kunlun [ORNL

    2011-01-01

    In this paper a fluorine-containing monomer, 2-fluroroethyl methacrylate (2FEMA) was used to synthesize the linear triblock terpolymer poly(n-butyl methacrylate)-poly(methyl methacrylate)-poly(2-fluoroethyl methacrylate) (PnBMA-PMMA-P2FEMA). A kinetic study of the homopolymerization of 2FEMA by reversible addition-fragmentation chain transfer (RAFT) polymerization showed that it demonstrates living character and produces well defined polymers with reasonably narrow polydispersities (~1.30). Triblock terpolymers were prepared sequentially using a purified Macro-CTA at 70 oC, resulting in final terpolymers with high Dp for each block (>150) and with polydispersities between 1.6 and 2.1. The structure and molecular weights of the resultant PnBMA-PMMA-P2FEMA triblock terpolymers were characterized via 1H NMR, 19F NMR, and gel permeation chromatography (GPC). Self-assembly of these polymers was carried out in a selective solvent and the micellar aggregates (MAs) thereby formed were analyzed using scanning electron microscopy (SEM) and dynamic light scattering (DLS). It was confirmed from SEM that these copolymers could directly self-organize into large compound micelles in tetrahydrofuran/methanol with different diameters, depending on polymer composition.

  20. Microscopic structure and dynamics of LiBF4 solutions in cyclic and linear carbonates.

    Science.gov (United States)

    Postupna, O O; Kolesnik, Y V; Kalugin, O N; Prezhdo, O V

    2011-12-15

    Motivated by development of lithium-ion batteries, we study the structure and dynamics of LiBF(4) in pure and mixed solvents with various salt concentrations. For this purpose, we have developed force field models for ethylene carbonate, propylene carbonate, dimethyl carbonate, and dimethoxyethane. We find that Li(+) is preferentially solvated by the cyclic and more polar component of the mixtures, as the electrostatic interaction overcomes possible steric hindrances. The cation coordination number decreases from 6 to 5 with increasing salt concentration due to formation of ion-pairs. The uniform decline of the diffusion coefficients of the two ions is disrupted at mixture compositions that perturb the ion-pair interaction. We show that the Stokes' model of diffusion can be applied to the very small Li(+) ion, provided that the size of the first solvation shell is properly taken into consideration. The strong coordination of the ions by the polar, cyclic components of the solvent mixtures established in our simulations suggests that the less polar linear component can be optimized in order to reduce electrolyte viscosity and to achieve high electrical conductivity.