A note on derivations of Murray-von Neumann algebras.

Science.gov (United States)

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Baltimaade kunstiajaloo isa : Wilhelm Neumann 150 / Jevgeni Kaljundi

Index Scriptorium Estoniae

Kaljundi, Jevgeni, 1931-2011

1999-01-01

Wilhelm Neumann ئ iseõppija. Riias: ilmunud uurimused, töö oma projekti järgi ehitatud Läti kunstimuuseumi direktorina. Neumanni vaid Eesti kunstipärandit käsitlevad uurimused. Neumann ئ muinsuskaitsetegevuse algataja Baltimaadel, tema töid muinsuskaitse alal Eestis. W. Neumann arhitektina

Clarifying the link between von Neumann and thermodynamic entropies

Science.gov (United States)

Deville, Alain; Deville, Yannick

2013-01-01

The state of a quantum system being described by a density operator ρ, quantum statistical mechanics calls the quantity - kTr( ρln ρ), introduced by von Neumann, its von Neumann or statistical entropy. A 1999 Shenker's paper initiated a debate about its link with the entropy of phenomenological thermodynamics. Referring to Gibbs's and von Neumann's founding texts, we replace von Neumann's 1932 contribution in its historical context, after Gibbs's 1902 treatise and before the creation of the information entropy concept, which places boundaries into the debate. Reexamining von Neumann's reasoning, we stress that the part of his reasoning implied in the debate mainly uses thermodynamics, not quantum mechanics, and identify two implicit postulates. We thoroughly examine Shenker's and ensuing papers, insisting upon the presence of open thermodynamical subsystems, imposing us the use of the chemical potential concept. We briefly mention Landau's approach to the quantum entropy. On the whole, it is shown that von Neumann's viewpoint is right, and why Shenker's claim that von Neumann entropy "is not the quantum-mechanical correlate of thermodynamic entropy" can't be retained.

Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map

Energy Technology Data Exchange (ETDEWEB)

Mejri, Youssef, E-mail: josef-bizert@hotmail.fr [Aix Marseille Universite, Toulon Universite, CNRS, CPT, Marseille (France); Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna (Tunisia); Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis (Tunisia)

2016-06-15

In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.

Repulsive Casimir force from fractional Neumann boundary conditions

International Nuclear Information System (INIS)

Lim, S.C.; Teo, L.P.

2009-01-01

This Letter studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a d-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.

Spectral theory and quotients in Von Neumann algebras | West ...

African Journals Online (AJOL)

In this note we consider to what extent the functional calculus and the spectral theory in von Neumann algebras are preserved by the taking of quotients relative to two-sided ideals of the von Neumann algebra. Keywords:von Neumann algebra, functional calculus, spectral theory, quotient algebras. Quaestiones ...

Integral Method of Boundary Characteristics: Neumann Condition

Science.gov (United States)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

Integral representation of a solution of the Neumann problem for the Stokes system

Czech Academy of Sciences Publication Activity Database

Medková, Dagmar

2010-01-01

Roč. 54, č. 4 (2010), s. 459-484 ISSN 1017-1398 R&D Projects: GA AV ČR IAA100190804 Institutional research plan: CEZ:AV0Z10190503 Keywords : Stokes system * Neumann problem * single layer potential * double layer potential * integral equation method * successive approximation Subject RIV: BA - General Mathematics Impact factor: 0.784, year: 2010 http://link.springer.com/article/10.1007%2Fs11075-009-9346-4

Borel reductibility and classification of von neumann algebras

DEFF Research Database (Denmark)

Sasyk, R.; Törnquist, Asger Dag

2009-01-01

We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism relation for separable von Neumann algebras....

Von Neumann Entropy of an Electron in One-Dimensional Determined Potentials

Institute of Scientific and Technical Information of China (English)

GONG Long-Yan; TONG Pei-Qing

2005-01-01

@@ By using the measure of von Neumann entropy, we numerically investigate quantum entanglement of an electronmoving in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. Thedelocalized and localized eigenstates can be distinguished by von Neumann entropy of the individual eigenstates.There are drastic decreases in yon Neumann entropy of the individual eigenstates at mobility edges. In the curveof the spectrum averaged yon Neumann entropy as a function of potential parameter λ, a sharp transition existsat the metal-insulator transition point λc = 2. It is found that the yon Neumann entropy is a good quantity toreflect localization and metal-insulator transition.

A bicategorical approach to Morita equivalence for von Neumann algebras

International Nuclear Information System (INIS)

Brouwer, R. M.

2003-01-01

We relate Morita equivalence for von Neumann algebras to the ''Connes fusion'' tensor product between correspondences. In the purely algebraic setting, it is well known that rings are Morita equivalent if they are equivalent objects in a bicategory whose 1-cells are bimodules. We present a similar result for von Neumann algebras. We show that von Neumann algebras form a bicategory, having Connes's correspondences as 1-morphisms, and (bounded) intertwiners as 2-morphisms. Further, we prove that two von Neumann algebras are Morita equivalent iff they are equivalent objects in the bicategory. The proofs make extensive use of the Tomita-Takesaki modular theory

Pure Jauch-Piron states on von Neumann algebras

International Nuclear Information System (INIS)

Hamhalter, J.

1993-01-01

We study Jauch-Piron states and two-valued measures on von Neumann algebra. We prove as the main result that, under some set-theoretical assumption, a pure state of a von Neumann algebra A not containing a central abelian portion is Jauch-Piron if and only if it is σ-additive. Moreover, we show that this result holds for type I factor indenpendently on the set-theoretical axiomatics. As a consequence we obtain a lucid characterization of pure Jauch-Piron states on von Neumann algebras acting on a Hilbert space with real-nonmeasurable dimension (this can be viewed as a generalization of the paper). We also characterize the von Neumann algebras whose logic of projections is Jauch-Piron. Finally, we prove that every two-valued measure on the projection logic of A, where A contains no type I 2 central portion, has to be concentrated at an abelian direct summand of A. (orig.)

$L^q$-solution of the Neumann, Robin and transmission problem for the scalar Oseen equation

Czech Academy of Sciences Publication Activity Database

Medková, Dagmar

2018-01-01

Roč. 291, č. 4 (2018), s. 682-698 ISSN 0025-584X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : generalized jump problem * Neumann problem * Robin problem Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.742, year: 2016

The classification problem for von Neumann factors

DEFF Research Database (Denmark)

Sasyk, R.; Törnquist, Asger Dag

2009-01-01

We prove that it is not possible to classify separable von Neumann factors of types II, II or III, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants. In particular the isomorphism relation of type II factors is not smooth. We also prove...... that the isomorphism relation for von Neumann II factors is analytic, but is not Borel....

Decision Utility Theory: Back to von Neumann, Morgenstern, and Markowitz

OpenAIRE

Kontek, Krzysztof

2010-01-01

Prospect Theory (1979) and its Cumulative version (1992) argue for probability weighting to explain lottery choices. Decision Utility Theory presents an alternative solution, which makes no use of this concept. The new theory distinguishes decision and perception utility, postulates a double S-shaped decision utility curve similar to one hypothesized by Markowitz (1952), and applies the expected decision utility value similarly to the theory by von Neumann and Morgenstern (1944). Decision Uti...

Von Neumann's impossibility proof: Mathematics in the service of rhetorics

Science.gov (United States)

Dieks, Dennis

2017-11-01

According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen interpretation put the situation to good use by arguing that the completeness of quantum mechanics was undeniable. This state of affairs lasted, so the story continues, until Bell in 1966 exposed von Neumann's proof as obviously wrong. The realization that von Neumann's proof was fallacious then rehabilitated hidden variables and made serious foundational research possible again. It is often added in recent accounts that von Neumann's error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist. We shall attempt to tell a story that is more historically accurate and less ideologically charged. Most importantly, von Neumann never claimed to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann's argument was basically that hidden-variables schemes must violate the ;quantum principle; that physical quantities are to be represented by operators in a Hilbert space. As a consequence, hidden-variables schemes, though possible in principle, necessarily exhibit a certain kind of contextuality. As we shall illustrate, early reactions to Bohm's theory are in agreement with this account. Leading physicists pointed out that Bohm's theory has the strange feature that pre-existing particle properties do not generally reveal themselves in measurements, in accordance with von Neumann's result. They did not conclude that the ;impossible was done; and that von Neumann had been shown wrong.

An accurate von Neumann's law for three-dimensional foams

NARCIS (Netherlands)

Hilgenfeldt, Sascha; Kraynik, Andrew M.; Koehler, Stephan A.; Stone, Howard A.

2001-01-01

The diffusive coarsening of 2D soap froths is governed by von Neumann's law. A statistical version of this law for dry 3D foams has long been conjectured. A new derivation, based on a theorem by Minkowski, yields an explicit analytical von Neumann's law in 3D which is in very good agreement with

Series of Bessel and Kummer-type functions

CERN Document Server

Baricz, Arpad; Pogány, Tibor K

2017-01-01

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Properties of von Neumann entropy

Indian Academy of Sciences (India)

disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the ...

Von Neumann algebras as complemented subspaces of B(H)

DEFF Research Database (Denmark)

Christensen, Erik; Wang, Liguang

2014-01-01

Let M be a von Neumann algebra of type II1 which is also a complemented subspace of B( H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented factor of type II1 on a Hilbert space H, then M is injective...

Iterative numerical solution of scattering problems

International Nuclear Information System (INIS)

Tomio, L.; Adhikari, S.K.

1995-05-01

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10 10 after some-8-10 iterations. (author). 31 refs, 2 tabs

Neumann Casimir effect: A singular boundary-interaction approach

International Nuclear Information System (INIS)

Fosco, C.D.; Lombardo, F.C.; Mazzitelli, F.D.

2010-01-01

Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and transmission coefficients ill-defined because of UV divergences. We present a possible procedure to tame those divergences, by introducing a minimum length scale, related to the nonzero 'width' of a nonlocal term. We then use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriate limits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallel mirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, we discuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially useful in order to compute Casimir energies in theories containing nonlocal potentials; in particular, those which we use to reproduce Neumann boundary conditions.

Iterative numerical solution of scattering problems

Energy Technology Data Exchange (ETDEWEB)

Tomio, L; Adhikari, S K

1995-05-01

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10{sup 10} after some-8-10 iterations. (author). 31 refs, 2 tabs.

John von Neumann selected letters

CERN Document Server

2005-01-01

John von Neuman was perhaps the most influential mathematician of the twentieth century, especially if his broad influence outside mathematics is included. Not only did he contribute to almost all branches of mathematics and created new fields, but he also changed post-World War II history with his work on the design of computers and with being a sought-after technical advisor to many figures in the U.S. military-political establishment in the 1940s and 1950s. The present volume is the first substantial collection of (previously mainly unpublished) letters written by von Neumann to colleagues, friends, government officials, and others. The letters give us a glimpse of the thinking of John von Neumann about mathematics, physics, computer science, science management, education, consulting, politics, and war. Readers of quite diverse backgrounds will find much of interest in this fascinating first-hand look at one of the towering figures of twentieth century science.

von Neumann's hypothesis concerning coherent states

International Nuclear Information System (INIS)

Zak, J

2003-01-01

An orthonormal basis of modified coherent states is constructed. Each member of the basis is an infinite sum of coherent states on a von Neumann lattice. A single state is assigned to each unit cell of area h (Planck constant) in the phase plane. The uncertainties of the coordinate x and the square of the momentum p 2 for these states are shown to be similar to those for the usual coherent states. Expansions in the newly established set are discussed and it is shown that any function in the kq-representation can be written as a sum of two fixed kq-functions. Approximate commuting operators for x and p 2 are defined on a lattice in phase plane according to von Neumann's prescription. (leeter to the editor)

The smooth entropy formalism for von Neumann algebras

International Nuclear Information System (INIS)

Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

2016-01-01

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra

The smooth entropy formalism for von Neumann algebras

Energy Technology Data Exchange (ETDEWEB)

Berta, Mario, E-mail: berta@caltech.edu [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States); Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp [Department of Physics, Graduate School of Science, University of Tokyo, Tokyo, Japan and Institute for Theoretical Physics, Leibniz University Hanover, Hanover (Germany); Scholz, Volkher B., E-mail: scholz@phys.ethz.ch [Institute for Theoretical Physics, ETH Zurich, Zurich (Switzerland)

2016-01-15

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

Molecular quantum control landscapes in von Neumann time-frequency phase space

Science.gov (United States)

Ruetzel, Stefan; Stolzenberger, Christoph; Fechner, Susanne; Dimler, Frank; Brixner, Tobias; Tannor, David J.

2010-10-01

Recently we introduced the von Neumann representation as a joint time-frequency description for femtosecond laser pulses and suggested its use as a basis for pulse shaping experiments. Here we use the von Neumann basis to represent multidimensional molecular control landscapes, providing insight into the molecular dynamics. We present three kinds of time-frequency phase space scanning procedures based on the von Neumann formalism: variation of intensity, time-frequency phase space position, and/or the relative phase of single subpulses. The shaped pulses produced are characterized via Fourier-transform spectral interferometry. Quantum control is demonstrated on the laser dye IR140 elucidating a time-frequency pump-dump mechanism.

δ'-function perturbations and Neumann boundary-conditions by path integration

International Nuclear Information System (INIS)

Grosche, C.

1994-02-01

δ'-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together with a relativistic point interaction. The non-relativistic limit yields either a usual δ-function or a δ'-function perturbation; making their strengths infinitely repulsive one obtains Dirichlet, respectively Neumann boundary conditions in the path integral. (orig.)

Chain segmentation for the Monte Carlo solution of particle transport problems

International Nuclear Information System (INIS)

Ragheb, M.M.H.

1984-01-01

A Monte Carlo approach is proposed where the random walk chains generated in particle transport simulations are segmented. Forward and adjoint-mode estimators are then used in conjunction with the firstevent source density on the segmented chains to obtain multiple estimates of the individual terms of the Neumann series solution at each collision point. The solution is then constructed by summation of the series. The approach is compared to the exact analytical and to the Monte Carlo nonabsorption weighting method results for two representative slowing down and deep penetration problems. Application of the proposed approach leads to unbiased estimates for limited numbers of particle simulations and is useful in suppressing an effective bias problem observed in some cases of deep penetration particle transport problems

Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems

NARCIS (Netherlands)

Austin, T.; Eisner, T.; Tao, T.

2011-01-01

The Furstenberg recurrence theorem (or equivalently Szemerédi’s theorem) can be formulated in the language of von Neumann algebras as follows: given an integer k ≥ 2, an abelian finite von Neumann algebra (M,τ) with an automorphism α : M→M, and a nonnegative a in M with τ(a) > 0, one has liminf

Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement

Science.gov (United States)

Safaiee, Rosa; Golshan, Mohammad Mehdi

2017-06-01

The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals' in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present

Power Series Solution to the Pendulum Equation

Science.gov (United States)

Benacka, Jan

2009-01-01

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

Nash y von Neumann: mundos posibles y juegos de lenguaje

Directory of Open Access Journals (Sweden)

Salazar , Boris

2004-06-01

Full Text Available Este ensayo emplea las nociones de juego de lenguaje y de equivalencia entre juegos para examinar la decisión de John Nash de no jugar el juego coalicional que propuso John von Neumann. El argumento central es que Nash concibió una clase de mundos posibles incompatible con la de von Neumann, y que en el origen de esa divergencia estarían sus distintas nociones de racionalidad.

Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers

CERN Document Server

Auteri, F; Quartapelle, L

2003-01-01

A new Galerkin-Legendre direct spectral solver for the Neumann problem associated with Laplace and Helmholtz operators in rectangular domains is presented. The algorithm differs from other Neumann spectral solvers by the high sparsity of the matrices, exploited in conjunction with the direct product structure of the problem. The homogeneous boundary condition is satisfied exactly by expanding the unknown variable into a polynomial basis of functions which are built upon the Legendre polynomials and have a zero slope at the interval extremes. A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results are given to illustrate the performance of the proposed spectral elliptic solv...

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

Science.gov (United States)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Boundary Equations and Regularity Theory for Geometric Variational Systems with Neumann Data

Science.gov (United States)

Schikorra, Armin

2018-02-01

We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.

On the problem of completeness of QM: von Neumann against Einstein, Podolsky, and Rosen

OpenAIRE

Khrennikov, Andrei

2008-01-01

We performed a comparative analysis of the arguments of Einstein, Podolsky and Rosen -- EPR, 1935 (against the completeness of QM) and the theoretical formalism of QM (due to von Neumann, 1932). We found that the EPR considerations do not match at all with the von Neumann's theory. Thus EPR did not criticize the real theoretical model of QM. The root of EPR's paradoxical conclusion on incompleteness of QM is the misuse of von Neumann's projection postulate. EPR applied this postulate to obser...

Number-conserving cellular automata with a von Neumann neighborhood of range one

International Nuclear Information System (INIS)

Wolnik, Barbara; Dzedzej, Adam; Baetens, Jan M; De Baets, Bernard

2017-01-01

We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions. (paper)

Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions

International Nuclear Information System (INIS)

Eab, C. H.; Lim, S. C.; Teo, L. P.

2007-01-01

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed

Calculation of von Neumann entropy for hydrogen and positronium negative ions

International Nuclear Information System (INIS)

Lin, Chien-Hao; Ho, Yew Kam

2014-01-01

In the present work, we carry out calculations of von Neumann entropies and linear entropies for the hydrogen negative ion and the positronium negative ion. We concentrate on the spatial (electron–electron orbital) entanglement in these ions by using highly correlated Hylleraas functions to represent their ground states, and to take care of correlation effects. We apply the Schmidt decomposition method on the partial-wave expanded two-electron wave functions, and from which the one-particle reduced density matrix can be obtained, leading to the quantifications of linear entropy and von Neumann entropy in the H − and Ps − ions. - Highlights: • We calculate von Neumann entropies and linear entropies for hydrogen and positronium negative ions. • We employ highly correlated Hylleraas functions to take into account of correlation effects. • Spatial (electron–electron orbital) entanglement is quantified using the Schmidt decomposition method. • The eigenvalues of the one-particle reduced density matrix are calculated

Asymptotics with respect to the spectral parameter and Neumann series of Bessel functions for solutions of the one-dimensional Schrödinger equation

Science.gov (United States)

Kravchenko, Vladislav V.; Torba, Sergii M.

2017-12-01

A representation for a solution u(ω, x) of the equation -u″ + q(x)u = ω2u, satisfying the initial conditions u(ω, 0) = 1, u'(ω, 0) = iω, is derived in the form u (ω ,x ) = ei ω x(1 +u/1(x ) ω +u/2(x ) ω2 )+e/-iω xu3(x ) ω2 -1/ω2 ∑n=0 ∞inαn(x ) jn(ω x ) , where um(x), m = 1, 2, 3, are given in a closed form, jn stands for a spherical Bessel function of order n, and the coefficients αn are calculated by a recurrent integration procedure. The following estimate is proved |u (ω ,x ) -uN(ω ,x ) |≤1/|ω|2 ɛ N(x ) √{sinh(2/Imω x ) Imω } for any ω ∈C {0 } , where uN(ω, x) is an approximate solution given by truncating the series in the proposed representation for u(ω, x) and ɛN(x) is a non-negative function tending to zero for all x belonging to a finite interval of interest. In particular, for ω ∈R {0 } , the estimate has the form |u (ω ,x ) -uN(ω ,x ) |≤1/|ω|2 ɛ N(x ) . A numerical illustration of application of the new representation for computing the solution u(ω, x) on large sets of values of the spectral parameter ω with an accuracy nondeteriorating (and even improving) when ω → ±∞ is given.

Rohlin flows on Von Neumann algebras

CERN Document Server

Masuda, Toshihiko

2016-01-01

The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II_1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III_0 factors. Several concrete examples are also studied.

An integrodifferential model for phase transitions: stationary solutions in higher dimensions

Science.gov (United States)

Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi

2008-01-01

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.

Explicit formulas for Neumann coefficients in the plane-wave geometry

International Nuclear Information System (INIS)

He Yanghui; Schwarz, John H.; Spradlin, Marcus; Volovich, Anastasia

2003-01-01

We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter μ. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large μ and find unexpectedly simple results, which are valid to all orders in 1/μ. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling λ ' . A specific example is presented

Physical Realization of von Neumann Lattices in Rotating Bose Gases with Dipole Interatomic Interactions.

Science.gov (United States)

Cheng, Szu-Cheng; Jheng, Shih-Da

2016-08-22

This paper reports a novel type of vortex lattice, referred to as a bubble crystal, which was discovered in rapidly rotating Bose gases with long-range interactions. Bubble crystals differ from vortex lattices which possess a single quantum flux per unit cell, while atoms in bubble crystals are clustered periodically and surrounded by vortices. No existing model is able to describe the vortex structure of bubble crystals; however, we identified a mathematical lattice, which is a subset of coherent states and exists periodically in the physical space. This lattice is called a von Neumann lattice, and when it possesses a single vortex per unit cell, it presents the same geometrical structure as an Abrikosov lattice. In this report, we extend the von Neumann lattice to one with an integral number of flux quanta per unit cell and demonstrate that von Neumann lattices well reproduce the translational properties of bubble crystals. Numerical simulations confirm that, as a generalized vortex, a von Neumann lattice can be physically realized using vortex lattices in rapidly rotating Bose gases with dipole interatomic interactions.

Subroutine for series solutions of linear differential equations

International Nuclear Information System (INIS)

Tasso, H.; Steuerwald, J.

1976-02-01

A subroutine for Taylor series solutions of systems of ordinary linear differential equations is descriebed. It uses the old idea of Lie series but allows simple implementation and is time-saving for symbolic manipulations. (orig.) [de

Existence of solutions for a fourth order eigenvalue problem ] {Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions

Directory of Open Access Journals (Sweden)

Khalil Ben Haddouch

2016-04-01

Full Text Available In this work we will study the eigenvalues for a fourth order elliptic equation with $p(x$-growth conditions $\\Delta^2_{p(x} u=\\lambda |u|^{p(x-2} u$, under Neumann boundary conditions, where $p(x$ is a continuous function defined on the bounded domain with $p(x>1$. Through the Ljusternik-Schnireleman theory on $C^1$-manifold, we prove the existence of infinitely many eigenvalue sequences and $\\sup \\Lambda =+\\infty$, where $\\Lambda$ is the set of all eigenvalues.

Regularity of spectral fractional Dirichlet and Neumann problems

DEFF Research Database (Denmark)

Grubb, Gerd

2016-01-01

Consider the fractional powers and of the Dirichlet and Neumann realizations of a second-order strongly elliptic differential operator A on a smooth bounded subset Ω of . Recalling the results on complex powers and complex interpolation of domains of elliptic boundary value problems by Seeley in ...

Frobenius theory for positive maps of von Neumann algebras

International Nuclear Information System (INIS)

Albeverio, S.; Hoegh-Krohn, R.

1978-01-01

Frobenius theory about the cyclic structure of eigenvalues of irreducible non negative matrices is extended to the case of positive linear maps of von Neumann algebras. Semigroups of such maps and ergodic properties are also considered. (orig.) [de

Introducing formalism in economics: The growth model of John von Neumann

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Gloria-Palermo Sandye

2010-01-01

Full Text Available The objective is to interpret John von Neumann's growth model as a decisive step of the forthcoming formalist revolution of the 1950s in economics. This model gave rise to an impressive variety of comments about its classical or neoclassical underpinnings. We go beyond this traditional criterion and interpret rather this model as the manifestation of von Neumann's involvement in the formalist programme of mathematician David Hilbert. We discuss the impact of Kurt Gödel's discoveries on this programme. We show that the growth model reflects the pragmatic turn of the formalist programme after Gödel and proposes the extension of modern axiomatisation to economics.

On the Clebsch-Gordan series for some Heisenberg groups

International Nuclear Information System (INIS)

Raszillier, H.

1984-11-01

We suggest the use of the Stone-von Neumann theorem for a simple insight into the Clebsch-Gordan series of the Heisenberg groups of quantum mechanics, constructed over the abelian groups Rsup(n) and Fsub(p)sup(n). (orig.)

Born approximation to a perturbative numerical method for the solution of the Schroedinger equation

International Nuclear Information System (INIS)

Adam, Gh.

1978-01-01

A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)

Semiclassical series solution of the generalized phase shift atom--diatom scattering equations

International Nuclear Information System (INIS)

Squire, K.R.; Curtiss, C.F.

1980-01-01

A semiclassical series solution of the previously developed operator form of the generalized phase shift equations describing atom--diatom scattering is presented. This development is based on earlier work which led to a double series in powers of Planck's constant and a scaling parameter of the anisotropic portion of the intermolecular potential. The present solution is similar in that it is a double power series in Planck's constant and in the difference between the spherical radial momentum and a first order approximation. The present series solution avoids difficulties of the previous series associated with the classical turning point

Evaluation of recent GRACE monthly solution series with an ice sheet perspective

Science.gov (United States)

Horwath, Martin; Groh, Andreas

2016-04-01

GRACE monthly global gravity field solutions have undergone a remarkable evolution, leading to the latest (Release 5) series by CSR, GFZ, and JPL, to new series by other processing centers, such as ITSG and AIUB, as well as to efforts to derive combined solutions, particularly by the EGSIEM (European Gravity Service for Improved Emergency Management) project. For applications, such as GRACE inferences on ice sheet mass balance, the obvious question is on what GRACE solution series to base the assessment. Here we evaluate different GRACE solution series (including the ones listed above) in a unified framework. We concentrate on solutions expanded up to degree 90 or higher, since this is most appropriate for polar applications. We empirically assess the error levels in the spectral as well as in the spatial domain based on the month-to-month scatter in the high spherical harmonic degrees. We include empirical assessment of error correlations. We then apply all series to infer Antarctic and Greenland mass change time series and compare the results in terms of apparent signal content and noise level. We find that the ITSG solutions show lowest noise level in the high degrees (above 60). A preliminary combined solution from the EGSIEM project shows lowest noise in the degrees below 60. This virtue maps into the derived ice mass time series, where the EGSIEM-based results show the lowest noise in most cases. Meanwhile, there is no indication that any of the considered series systematically dampens actual geophysical signals.

Minimum Moduli in Von Neumann Algebras | Gopalraj | Quaestiones ...

African Journals Online (AJOL)

In this paper we answer a question raised in [12] in the affirmative, namely that the essential minimum modulus of an element in a von. Neumann algebra, relative to any norm closed two-sided ideal, is equal to the minimum modulus of the element perturbed by an element from the ideal. As a corollary of this result, we ...

Current status of Uganda Kob (Kobus Kob Thomasi Neumann) in ...

African Journals Online (AJOL)

Current status of Uganda Kob (Kobus Kob Thomasi Neumann) in Toro Game Reserve, Uganda. ... As part of a biological assessment of Toro Game Reserve, the status of Uganda kob Kobus kob Thomasi ... AJOL African Journals Online.

Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir

Directory of Open Access Journals (Sweden)

Junfeng Ding

2018-04-01

Full Text Available Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions.

Characterizing ξ-Lie Multiplicative Isomorphisms on Von Neumann Algebras

Directory of Open Access Journals (Sweden)

Yamin Song

2014-01-01

Full Text Available Let ℳ and be von Neumann algebras without central summands of type I1. Assume that ξ∈ℂ with ξ≠1. In this paper, all maps Φ:ℳ→ satisfying ΦAB-ξBA=ΦAΦB-ξΦBΦ(A are characterized.

A paradox of rationality à la von Neumann-Morgenstern

NARCIS (Netherlands)

Ismail, M.S.

2015-01-01

We show that there are games and decision situations in which it is not possible for the decision maker to be rational a la von Neumann-Morgenstern in both situations simultaneously, which is the source of the paradox presented in this note. We provide an assumption which is the necessary and

Path integral solution of linear second order partial differential equations I: the general construction

International Nuclear Information System (INIS)

LaChapelle, J.

2004-01-01

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

Interpolatability distinguishes LOCC from separable von Neumann measurements

International Nuclear Information System (INIS)

Childs, Andrew M.; Leung, Debbie; Mančinska, Laura; Ozols, Maris

2013-01-01

Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations

KK -theory and spectral flow in von Neumann algebras

DEFF Research Database (Denmark)

Kaad, Jens; Nest, Ryszard; Rennie, Adam

2012-01-01

We present a definition of spectral flow for any norm closed ideal J in any von Neumann algebra N. Given a path of selfadjoint operators in N which are invertible in N/J, the spectral flow produces a class in Ko (J). Given a semifinite spectral triple (A, H, D) relative to (N, t) with A separable...

A bicategorical approach to Morita equivalence for Von Neumann algebras

NARCIS (Netherlands)

R.M. Brouwer (Rachel)

2003-01-01

textabstractWe relate Morita equivalence for von Neumann algebras to the ``Connes fusion'' tensor product between correspondences. In the purely algebraic setting, it is well known that rings are Morita equivalent if and only if they are equivalent objects in a bicategory whose 1-cells are

A series solution for horizontal infiltration in an initially dry aquifer

Science.gov (United States)

Furtak-Cole, Eden; Telyakovskiy, Aleksey S.; Cooper, Clay A.

2018-06-01

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment.

Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces

Directory of Open Access Journals (Sweden)

Young Chel Kwun

2016-07-01

Full Text Available Abstract Let C N J ( B $\\mathcal{C}_{NJ} ( \\mathcal{B} $ and J ( B $J ( \\mathcal{B} $ be the generalized von Neumann-Jordan and James constants of a quasi-Banach space B $\\mathcal{B}$ , respectively. In this paper we shall show the relation between C N J ( B $\\mathcal {C}_{NJ} ( \\mathcal{B} $ , J ( B $J ( \\mathcal{B} $ , and the modulus of convexity. Also, we show that if B $\\mathcal{B}$ is not uniform non-square then J ( B = C N J ( B = 2 $J ( \\mathcal{B} =\\mathcal{C}_{NJ} ( \\mathcal{B} =2$ . Moreover, we give an equivalent formula for the generalized von Neumann-Jordan constant.

A von Neumann type inequality for certain domains in Cn

Czech Academy of Sciences Publication Activity Database

Ambrozie, Calin-Grigore; Timotin, D.

2002-01-01

Roč. 131, č. 3 (2002), s. 859-869 ISSN 0002-9939 R&D Projects: GA ČR GA201/03/0041 Institutional research plan: CEZ:AV0Z1019905 Keywords : von Neumann inequality * multioperators * Nevanlinna-Pick problem Subject RIV: BA - General Mathematics Impact factor: 0.334, year: 2002

Computational Error Estimate for the Power Series Solution of Odes ...

African Journals Online (AJOL)

This paper compares the error estimation of power series solution with recursive Tau method for solving ordinary differential equations. From the computational viewpoint, the power series using zeros of Chebyshevpolunomial is effective, accurate and easy to use. Keywords: Lanczos Tau method, Chebyshev polynomial, ...

A Neumann problem with the $q$-Laplacian on a solid torus in the critical of supercritical case

Directory of Open Access Journals (Sweden)

Nikos Labropoulos

2007-11-01

Full Text Available Following the work of Ding [21] we study the existence of a nontrivial positive solution to the nonlinear Neumann problem $$displaylines{ Delta_qu+a(xu^{q-1}=lambda f(xu^{p-1}, quad u>0quad hbox{on } T,cr abla u|^{q-2}frac{partial u}{partial u}+b(x u^{q-1} =lambda g(xu^{ilde{p}-1} quadhbox{on }{partial T},cr p =frac{2q}{2-q}>6,quad ilde{p}=frac{q}{2-q}>4,quad frac{3}{2}solutions that exhibit no radial symmetries. First we find the best constants in the Sobolev inequalities for the supercritical case (the critical of supercritical.

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

International Nuclear Information System (INIS)

Kościk, Przemysław

2015-01-01

We study one-dimensional systems of N particles in a one-dimensional harmonic trap with an inverse power law interaction ∼|x| −d . Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of N. A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on N is discussed for the systems with d=1 (charged particles) and with d=3 (dipolar particles). - Highlights: • We study confined systems of N particles with an inverse power law interaction. • We apply the harmonic approximation to the systems. • We derive closed form expressions for the asymptotic von Neumann entropy. • The asymptotic von Neumann entropy grows monotonically as N increases

Magnetic bottles for the Neumann problem: The case of dimension 3

Indian Academy of Sciences (India)

M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22

2 in our previous work and will be analysed in the case of dimension 3 in a future paper. Keywords. Spectral .... in x1 > 0 and with Neumann condition on x1 = 0. The bottom the ..... University of Hong-Kong) December 6–11 (1999). [LuPa5] ...

Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data

Directory of Open Access Journals (Sweden)

Abderrahmane El Hachimi

2007-11-01

$$ \\frac{\\partial u}{\\partial t}-\\triangle_{p}u+\\alpha(u=f \\quad \\text{in } ]0,\\ T[\\times\\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.

Factorization and dilation problems for completely positive maps on von Neumann algebras

DEFF Research Database (Denmark)

Haagerup, Uffe; Musat, Magdalena

2011-01-01

We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been...

Pipe-anchor discontinuity analysis utilizing power series solutions, Bessel functions, and Fourier series

International Nuclear Information System (INIS)

Williams, Dennis K.; Ranson, William F.

2003-01-01

One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an

Ampere-Neumann electrodynamics of metals

International Nuclear Information System (INIS)

Graneau, P.

1985-01-01

Maxwell described Ampere's force law as the cardinal formula of electrodynamics. This law predicts longitudinal mechanical forces along current streamlines in metallic conductors. The Ampere forces set up tension in wires and busbars and compression in liquid metal. At normal current densities they are negligible but, increasing with the square of current, they become dominant in pulse power circuits. Ampere tension and compression have been revealed by exploding wire experiments, in liquid metal jets at solid - liquid interfaces, and with an electrodynamic pendulum. Ampere stresses are already playing an important role in the development of railguns, fuses, current limiters, opening switches, pulse magnets, and a host of other pulse-power devices. This book outlines the electrodynamic action-at-a-distance theory developed by Ampere, Neumann, Weber and, to some extent, by Maxwell. One chapter describes the 20th century extensions of the theory by Graneau and others

Contact angles on a soft solid: from Young's law to Neumann's law.

Science.gov (United States)

Marchand, Antonin; Das, Siddhartha; Snoeijer, Jacco H; Andreotti, Bruno

2012-12-07

The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles differently from those predicted by Neumann's law, which applies when the drop is floating on another liquid. Here, we derive an elastocapillary model for contact angles on a soft solid by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of a vanishing elastic modulus yields Neumann's law or a variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit to the soft limit appears when the length scale defined by the ratio of surface tension to elastic modulus γ/E reaches the range of molecular interactions.

Dissipative quantum mechanics: The generalization of the canonical quantization and von Neumann equation

International Nuclear Information System (INIS)

Tarasov, V.E.

1994-07-01

Sedov variational principle, which is the generalization of the least actional principle for the dissipative processes is used to generalize the canonical quantization and von Neumann equation for dissipative systems (particles and strings). (author). 66 refs, 1 fig

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Science.gov (United States)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Classical solutions of two dimensional Stokes problems on non smooth domains. 1: The Radon integral operators

International Nuclear Information System (INIS)

Lubuma, M.S.

1991-05-01

The applicability of the Neumann indirect method of potentials to the Dirichlet and Neumann problems for the two-dimensional Stokes operator on a non smooth boundary Γ is subject to two kinds of sufficient and/or necessary conditions on Γ. The first one, occurring in electrostatic, is equivalent to the boundedness on C(Γ) of the velocity double layer potential W as well as to the existence of jump relations of potentials. The second condition, which forces Γ to be a simple rectifiable curve and which, compared to the Laplacian, is a stronger restriction on the corners of Γ, states that the Fredholm radius of W is greater than 2. Under these conditions, the Radon boundary integral equations defined by the above mentioned jump relations are solvable by the Fredholm theory; the double (for Dirichlet) and the single (for Neumann) layer potentials corresponding to their solutions are classical solutions of the Stokes problems. (author). 48 refs

Anomalies free E-infinity from von Neumann's continuous geometry

International Nuclear Information System (INIS)

El Naschie, M.S.

2008-01-01

Von Neumann's continuous geometry has been considerably developed by Connes and is characterized by two fundamental concepts. First it is formulated without any direct reference to points and second it possesses a dimensional function. The present work explores the relevance of these two points to string theory as well as E-infinity theory. In particular we show that point-lessness and dimensional function implies fractality. In turn fractality leads to the concept of average or fuzzy symmetry and the elimination of gauge anomalies

Stability estimates for solution of IBVP to fractional parabolic differential and difference equations

Science.gov (United States)

Ashyralyev, Allaberen; Cakir, Zafer

2016-08-01

In this work, we investigate initial-boundary value problems for fractional parabolic equations with the Neumann boundary condition. Stability estimates for the solution of this problem are established. Difference schemes for approximate solution of initial-boundary value problem are constructed. Furthermore, we give theorem on coercive stability estimates for the solution of the difference schemes.

Book Review: John von Neumann and the foundations of quantum physics. (Vienna Circle Institute yearbook (2000), 8) Miklos Redei and Michael Stoltzner (Eds.); Kluwer Academic Publishers, Dordrecht, 2001, pp., US 125, ISBN 0792368126

Science.gov (United States)

Lupher, Tracy

2003-12-01

Some people may be surprised to learn that John von Neumann's work on the foundations of quantum physics went far beyond what is contained within the pages of his Mathematical Foundations of Quantum Mechanics (MFQM) (von Neumann, 1955). However, this narrow focus often ignores von Neumann's later work on quantum logic and what are now called in his honor, von Neumann algebras. This volume honoring von Neumann's contributions to physics is unique in that, while it contains 12 papers that examine various aspects of von Neumann's work, it also contains two of his previously unpublished papers and some of his previously unpublished correspondence.

Application of stochastic Liouville–von Neumann equation to electronic energy transfer in FMO complex

International Nuclear Information System (INIS)

Imai, Hajime; Ohtsuki, Yukiyoshi; Kono, Hirohiko

2015-01-01

Highlights: • Stochastic Liouville–von Neumann equation is applied to energy transfer dynamics. • Noise generation methods for dealing with exciton in FMO complexes are proposed. • Structured spectral densities could better support coherent population dynamics. - Abstract: A stochastic Liouville–von Neumann approach to solving a spin-boson model is applied to electronic energy transfer in Fenna–Matthews–Olson (FMO) complexes as a case study of the dynamics in biological systems. We modify a noise generation method to treat an experimentally obtained highly structured spectral density. By considering the population dynamics in a two-site system with a model structured spectral density, we numerically observe two kinds of coherent motions associated with inter-site coupling and system–bath coupling, the latter of which is mainly attributed to the peak structure of the spectral density

Inadequacy of von Neumann entropy for characterizing extractable work

International Nuclear Information System (INIS)

Dahlsten, Oscar C O; Renner, Renato; Rieper, Elisabeth; Vedral, Vlatko

2011-01-01

The lack of knowledge that an observer has about a system limits the amount of work it can extract. This lack of knowledge is normally quantified using the Gibbs/von Neumann entropy. We show that this standard approach is, surprisingly, only correct in very specific circumstances. In general, one should use the recently developed smooth entropy approach. For many common physical situations, including large but internally correlated systems, the resulting values for the extractable work can deviate arbitrarily from those suggested by the standard approach.

Global solution branches for a nonlocal Allen-Cahn equation

Science.gov (United States)

Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji

2018-05-01

We consider the Neumann problem of a 1D stationary Allen-Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric solutions which bifurcates from a point on the branch of odd-symmetric solutions. This paper derives the global behavior of the branch of asymmetric solutions, and moreover, determines the set of all solutions to the nonlocal Allen-Cahn equation. Our proof is based on a level set analysis for an integral map associated with the nonlocal term.

Spin chain from membrane and the Neumann-Rosochatius integrable system

International Nuclear Information System (INIS)

Bozhilov, P.

2007-01-01

We find membrane configurations in AdS 4 xS 7 , which correspond to the continuous limit of the SU(2) integrable spin chain, considered as a limit of the SU(3) spin chain, arising in N=4 SYM in four dimensions, dual to strings in AdS 5 xS 5 . We also discuss the relationship with the Neumann-Rosochatius integrable system at the level of Lagrangians, comparing the string and membrane cases

High Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

Science.gov (United States)

Scott, James R.; Martini, Michael C.

2008-01-01

Taylor series integration is implemented in a spacecraft trajectory analysis code-the Spacecraft N-body Analysis Program (SNAP) - and compared with the code s existing eighth-order Runge-Kutta Fehlberg time integration scheme. Nine trajectory problems, including near Earth, lunar, Mars and Europa missions, are analyzed. Head-to-head comparison at five different error tolerances shows that, on average, Taylor series is faster than Runge-Kutta Fehlberg by a factor of 15.8. Results further show that Taylor series has superior convergence properties. Taylor series integration proves that it can provide rapid, highly accurate solutions to spacecraft trajectory problems.

The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide

Czech Academy of Sciences Publication Activity Database

Krejčiřík, David; Zuazua, E.

2011-01-01

Roč. 250, č. 5 (2011), s. 2334-2346 ISSN 0022-0396 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : Laplacian * Dirichlet and Neumann boundary conditions * Twist Subject RIV: BE - Theoretical Physics Impact factor: 1.277, year: 2011

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

Science.gov (United States)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

Monotonicity of the von Neumann entropy expressed as a function of R\\'enyi entropies

OpenAIRE

Fannes, Mark

2013-01-01

The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\\'enyi entropies, is monotonically increasing in R\\'enyi entropies of even order and decreasing in those of odd order.

Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

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Yaobing Zhao

2014-01-01

Full Text Available This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.

An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

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Moh’d Khier Al-Srihin

2017-01-01

Full Text Available In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.

Ultraweak Continuity of σ-derivations on von Neumann Algebras

International Nuclear Information System (INIS)

Mirzavaziri, Madjid; Moslehian, Mohammad Sal

2009-01-01

Let σ be a surjective ultraweakly continuous *-linear mapping and d be a σ-derivation on a von Neumann algebra. We show that there are a surjective ultraweakly continuous *-homomorphism and a Σ-derivation such that D is ultraweakly continuous if and only if so is d. We use this fact to show that the σ-derivation d is automatically ultraweakly continuous. We also prove the converse in the sense that if σ is a linear mapping and d is an ultraweakly continuous *-σ-derivation, then there is an ultraweakly continuous linear mapping such that d is a *-Σ-derivation

A three-dimensional semi-analytical solution for predicting drug release through the orifice of a spherical device.

Science.gov (United States)

Simon, Laurent; Ospina, Juan

2016-07-25

Three-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica(®). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. Copyright © 2016 Elsevier B.V. All rights reserved.

Hypercontractivity in group Von Neumann algebras

CERN Document Server

Junge, Marius; Parcet, Javier

2017-01-01

In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive L_2 \\to L_q inequalities with respect to the Markov process given by the word length and with q an even integer. Interpolation and differentiation also yield general L_p \\to L_q hypercontrativity for 1 < p \\le q < \\infty via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part-which varies from one group to another-is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) L_p \\to L_q hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a condit...

Computational stability of the Von Neumann--Richtmyer method for the case of the ideal gas law

International Nuclear Information System (INIS)

Hicks, D.L.

1978-07-01

Two stability concepts are of interest for partial difference equations--one arises in theory--the other in practice. The theoretical kind, referred to here as asymptotic stability, is essentially just asymptotic (as Δt, Δx → 0) boundedness of the discrete solution. The other kind, referred to here as computational stability, is stability for a fixed Δt and Δx--computational instability is indicated in practice by oscillatory behavior of the discrete approximation--in particular, oscillations of period 2Δx. This report is concerned with computational stability. Only approximate stability analyses of the von Neumann-Richtmyer scheme have been done for the case of the ideal gas law. Herein a more rigorous computational stability analysis is sought. The analysis leads to a recommendation for the improvement of the time step restriction in WONDY for the case of the ideal gas law

The Integral Equation Method and the Neumann Problem for the Poisson Equation on NTA Domains

Czech Academy of Sciences Publication Activity Database

Medková, Dagmar

2009-01-01

Roč. 63, č. 21 (2009), s. 227-247 ISSN 0378-620X Institutional research plan: CEZ:AV0Z10190503 Keywords : Poisson equation * Neumann problem * integral equation method Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2009

von Neumann entropy associated with the haldane exclusion statistics

International Nuclear Information System (INIS)

Rajagopal, A.K.

1995-01-01

We obtain the von Neumann entropy per state of the Haldane exclusion statistics with parameter g in terms of the mean occupation number bar n{wlnw-(1+w)ln(1+w)}, where w=(1-bar n). This reduces correctly to the well known expressions in the limiting cases of Bose (g=0) and Fermi (g=1) statistics. We have derived the second and third order fluctuations in the occupation numbers for arbitrary g. An elegant general duality relationship between the w factor associated with the particle and that associated with the hole at the reciprocal g is deduced along with the attendant relationship between the two respective entropies

General Series Solutions for Stresses and Displacements in an Inner-fixed Ring

Science.gov (United States)

Jiao, Yongshu; Liu, Shuo; Qi, Dexuan

2018-03-01

The general series solution approach is provided to get the stress and displacement fields in the inner-fixed ring. After choosing an Airy stress function in series form, stresses are expressed by infinite coefficients. Displacements are obtained by integrating the geometric equations. For an inner-fixed ring, the arbitrary loads acting on outer edge are extended into two sets of Fourier series. The zero displacement boundary conditions on inner surface are utilized. Then the stress (and displacement) coefficients are expressed by loading coefficients. A numerical example shows the validity of this approach.

The Laplace series solution for local fractional Korteweg-de Vries equation

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Ye Shan-Shan

2016-01-01

Full Text Available In this paper, we consider a new application of the local fractional Laplace series expansion method to handle the local fractional Korteweg-de Vries equation. The obtained solution with non-differentiable type shows that the technology is accurate and efficient.

A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yong Chen; Qi Wang

2005-01-01

In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained

Shape differentiability of the Neumann problem of the Laplace equation in the half-space

Czech Academy of Sciences Publication Activity Database

Amrouche, Ch.; Nečasová, Šárka; Sokolowski, J.

2008-01-01

Roč. 37, č. 4 (2008), s. 748-769 ISSN 0324-8569 R&D Projects: GA ČR GA201/05/0005; GA ČR GA201/08/0012 Institutional research plan: CEZ:AV0Z10190503 Keywords : shape optimization * Neumann problem * half space * material derivative Subject RIV: BA - General Mathematics Impact factor: 0.689, year: 2008

On Dirichlet-to-Neumann Maps and Some Applications to Modified Fredholm Determinants

OpenAIRE

Gesztesy, Fritz; Mitrea, Marius; Zinchenko, Maxim

2010-01-01

We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrodinger operators in $L^2(\\Omega; d^n x)$, $n=2,3$, where $\\Omega$ is an open set with a compact, nonempty boundary satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of modified Fredholm perturbation determinants associated with operators in $L^2(\\Omega; d^n x)$ to modified Fredholm perturbation determinants associated with operators in $L^2(\\partial\\Om...

Die Mathematik und andere Kurzsprachen : Über John von Neumann, The Computer and the Brain

NARCIS (Netherlands)

Leydesdorff, L.; Baecker, D.

2016-01-01

Das Buch The Computer and the Brain (1958, dt. 1991; im Folgenden wird nach der deutschen Übersetzung zitiert) ist die gedruckte Version der Silliman Lectures, die zu halten John von Neumann 1956 nach Yale eingeladen worden war. Obwohl sie bis zum März 1956 vorbereitet waren, wurden sie nie

Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

Science.gov (United States)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

International Nuclear Information System (INIS)

Loubenets, Elena R.

2015-01-01

We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)

Entanglement in random pure states: spectral density and average von Neumann entropy

Energy Technology Data Exchange (ETDEWEB)

Kumar, Santosh; Pandey, Akhilesh, E-mail: skumar.physics@gmail.com, E-mail: ap0700@mail.jnu.ac.in [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067 (India)

2011-11-04

Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt eigenvalues. We derive here closed expressions for the spectral density of Schmidt eigenvalues for all three invariant classes of random matrix ensembles. We also obtain exact results for average von Neumann entropy. We find that maximum average entanglement is achieved if the system belongs to the symplectic invariant class. (paper)

Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition : exact results

NARCIS (Netherlands)

B.J. Meulenbroek (Bernard); U. M. Ebert (Ute); L. Schäfer

2005-01-01

textabstractThe dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

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Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

Regularization of moving boundaries in a Laplacian field by a mixed dirichlet-neumann boundary condition: Exact results

NARCIS (Netherlands)

Meulenbroek, B.; Ebert, U.; Schäfer, L.

2005-01-01

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive

A series solution of the Falkner-Skan equation using the crocco-wang transformation

Science.gov (United States)

Asaithambi, Asai

A direct series solution for the Falkner-Skan equation is obtained by first transforming the problem using the Crocco-Wang transformation. The transformation converts the third-order problem to a second-order two-point boundary value problem. The method first constructs a series involving the unknown skin-friction coefficient α. Then, α is determined by using the secant method or Newton’s method. The derivative needed for Newton’s method is also computed using a series derived from the transformed differential equation. The method is validated by solving the Falkner-Skan equation for several cases reported previously in the literature.

Exact series solution to the two flavor neutrino oscillation problem in matter

International Nuclear Information System (INIS)

Blennow, Mattias; Ohlsson, Tommy

2004-01-01

In this paper, we present a real nonlinear differential equation for the two flavor neutrino oscillation problem in matter with an arbitrary density profile. We also present an exact series solution to this nonlinear differential equation. In addition, we investigate numerically the convergence of this solution for different matter density profiles such as constant and linear profiles as well as the Preliminary Reference Earth Model describing the Earth's matter density profile. Finally, we discuss other methods used for solving the neutrino flavor evolution problem

On the summability of divergent power series solutions for certain first-order linear PDEs

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Masaki Hibino

2015-01-01

Full Text Available This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.

On the rate of convergence in von Neumann's ergodic theorem with continuous time

International Nuclear Information System (INIS)

Kachurovskii, A G; Reshetenko, Anna V

2010-01-01

The rate of convergence in von Neumann's mean ergodic theorem is studied for continuous time. The condition that the rate of convergence of the ergodic averages be of power-law type is shown to be equivalent to requiring that the spectral measure of the corresponding dynamical system have a power-type singularity at 0. This forces the estimates for the convergence rate in the above ergodic theorem to be necessarily spectral. All the results obtained have obvious exact analogues for wide-sense stationary processes. Bibliography: 7 titles.

Stability analysis of WONDY (a hydrocode based on the artifical viscosity method of von Neumann and Richtmyer) for a special case of Maxwell's Law

International Nuclear Information System (INIS)

Hicks, D.L.

1978-01-01

The artification viscosity method of von Neumann and Richtmyer was originally designed and analyzed for stability in the case when the material was an ideal gas. Recently a hydrocode (WONDY) based on the von Neumann-Richymyer scheme was used in calculating wave progagation problems in materials obeying a form of Maxwell's material law; signs of an unstable difference scheme appeared. A stability analysis shows that the timestep restrictions required for stability in certain cases can be more stringent for material laws of the Maxwell type than they are for material laws of the ideal gas type

IMPSOR, 3-D Boundary Problems Solution for Thermal Conductivity Calculation

International Nuclear Information System (INIS)

Wilson, D.G.; Williams, M.A.

1994-01-01

1 - Description of program or function: IMPSOR implements finite difference methods for multidimensional moving boundary problems with Dirichlet or Neumann boundary conditions. The geometry of the spatial domain is a rectangular parallelepiped with dimensions specified by the user. Dirichlet or Neumann boundary conditions may be specified on each face of the box independently. The user defines the initial and boundary conditions as well as the thermal and physical properties of the problem and several parameters for the numerical method, e.g. degree of implicitness, time-step size. 2 - Method of solution: The spatial domain is partitioned and the governing equation discretized, which yields a nonlinear system of equations at each time-step. This nonlinear system is solved using a successive over-relaxation (SOR) algorithm. For a given node, the previous iteration's temperature and thermal conductivity values are used for advanced points with current values at previous points. This constitutes a Gauss-Seidel iteration. Most of the computing time used by the numerical method is spent in the iterative solution of the nonlinear system. The SOR scheme employed is designed to accommodate vectorization on a Cray X-MP. 3 - Restrictions on the complexity of the problem: Maximum of 70,000 nodes

Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series

Directory of Open Access Journals (Sweden)

Xiang-Chao Shi

2014-01-01

Full Text Available Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.

Ocorrência de Amblyomma fuscum Neumann, 1899 e Amblyomma humerale Koch, 1844 (Acari: Ixodidae em Bufo arenalis no estado de São Paulo, Brasil Occurence of Amblyomma fuscum Neumann, 1899 and Amblyomma humerale Koch, 1844 (Acari: Ixodidae in Bufo arenalis in the state of São Paulo, Brazil

Directory of Open Access Journals (Sweden)

Afonso Lodovico Sinkoc

1997-06-01

Full Text Available O objetivo deste trabalho é relatar a ocorrência do parasitismo monoespecífico de A. fuscum NEUMANN, 1899 e A. humerale KOCH, 1844 em sapos (Bufo arenalis no Município de Rosana, Estado de São Paulo, Brasil. Este relato caracteriza um novo hospedeiro e uma nova localização geográfica para estas duas espécies de carrapatos.The objective of this work is to describe the occurence of the monoespecific parasitism of A. fuscum NEUMANN, 1899 and A. humerale KOCH, 1844 in toads (Bufo arenalis from the County of Rosana, State of São Paulo, Brazil. This is the description of a new host and new geographic site for those two species.

Motion of particles in solar and galactic systems by using Neumann boundary condition

Science.gov (United States)

Shenavar, Hossein

2016-12-01

A new equation of motion, which is derived previously by imposing Neumann boundary condition on cosmological perturbation equations (Shenavar in Astrophys. Space Sci., 2016a, doi: 10.1007/s10509-016-2676-5), is investigated. By studying the precession of perihelion, it is shown that the new equation of motion suggests a small, though detectable, correction in orbits of solar system objects. Then a system of particles is surveyed to have a better understanding of galactic structures. Also the general form of the force law is introduced by which the rotation curve and mass discrepancy of axisymmetric disks of stars are derived. In addition, it is suggested that the mass discrepancy as a function of centripetal acceleration becomes significant near a constant acceleration 2c1a0 where c1 is the Neumann constant and a0 = 6.59 ×10^{-10} m/s2 is a fundamental acceleration. Furthermore, it is shown that a critical surface density equal to σ0=a0/G, in which G is the Newton gravitational constant, has a significant role in rotation curve and mass discrepancy plots. Also, the specific form of NFW mass density profile at small radii, ρ∝1/r, is explained too. Finally, the present model will be tested by using a sample of 39 LSB galaxies for which we will show that the rotation curve fittings are generally acceptable. The derived mass to light ratios too are found within the plausible bound except for the galaxy F571-8.

Conditional expectations on the von Neumann algebras and causal independence of quantized fields

International Nuclear Information System (INIS)

Dadashyan, K.Yu.; Khoruzhij, S.S.

1981-01-01

Implementation of the condition of casual independence of quantized fields has been established for a number of quantum-field systems. Implementation of a property of the Haag-Castler casual independence has been proved for a net of the von Neumann local algebras in a number of models of free and quantized fields interacting in the Fock local way. In particular, proved is a theorem of meeting the condition of casual independence with the net of local albegras of the Dirac free field. A new method based on the techniques of noncommutative probability law has been used for the proof [ru

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

Science.gov (United States)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Analysis of the susceptibility in a fluid system with Neumann – plus boundary conditions

Directory of Open Access Journals (Sweden)

Djondjorov Peter

2018-01-01

Full Text Available The behaviour of the local and total susceptibilities of a fluid system bounded by different surfaces is studied in the framework of the Ginsburg-Landau Ising type model. The case of a plain geometry, Neumann-infinity boundary conditions under variations of the temperature and an external ordering field is considered. Exact analytic expressions for the order parameter, local and total susceptibilities in such a system are presented. They are used to analyse the phase behaviour of fluids confined in regions close to the bulk critical point of the respective infinite system.

Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

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SURE KÖME

2014-12-01

Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

Correlação da aferição manual e digital da distância interespinhosa pelo método de newmann em fraturas toracolombares do tipo explosão Correlación entre calibrado manual y digital de la distancia interespinhosa por el método de neumann en fracturas toracolombares tipo explosión Correlation between manual and digital measurement of inter-spinous dis tance by neumann method in burst thoracolumbar fracture

Directory of Open Access Journals (Sweden)

João Paulo Machado Bergamaschi

2011-01-01

: The manual and digital measurements of the inter-spinous distance by the Neumann method presented high correlation and high reproducibility in this series.

Schelling, von Neumann, and the Event that Didn’t Occur

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Alexander J. Field

2014-02-01

Full Text Available Thomas Schelling was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. However, although he makes frequent references in his writings to this approach, his main explorations and insights depend upon and require acknowledgment of its limitations. One of his principal concerns was how a country could engage in successful deterrence. If the behavioral assumptions that commonly underpin game theory are taken seriously and applied consistently, however, nuclear adversaries are almost certain to engage in devastating conflict, as John von Neumann forcefully asserted. The history of the last half century falsified von Neumann’s prediction, and the “event that didn’t occur” formed the subject of Schelling’s Nobel lecture. The answer to the question “why?” is the central concern of this paper.

Existence of solutions to supercritical Neumann problems via a new variational principle

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Craig Cowan

2017-09-01

-\\int_{B_1} \\frac{ a(|x| |u|^p}{p} \\,dx. $$ The novelty of using I instead of E is the hidden symmetry in I generated by $ \\frac{1}{p} \\int_{B_1} a(|x| |u|^p\\,dx $ and its Fenchel dual. Additionally we are able to prove the existence of a positive nonconstant solution, in the case a(|x|=1, relatively easy and without needing to cut off the supercritical nonlinearity. Finally, we use this new approach to prove existence results for gradient systems with supercritical nonlinearities.

Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions

International Nuclear Information System (INIS)

Ohtani, Nobuo

1976-01-01

A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)

One Measure Does Not a Construct Make: Directions toward Reinvigorating Psychopathy Research--Reply to Hare and Neumann (2010)

Science.gov (United States)

Skeem, Jennifer L.; Cooke, David J.

2010-01-01

In our article (J. L. Skeem & D. J. Cooke, 2010), we outlined the dangers inherent in conflating the Psychopathy Checklist-Revised (PCL-R; R. Hare, 1991) with psychopathy itself. In their response, R. Hare and C. Neumann (2010) seemed to agree with key points that the PCL-R should not be confused with psychopathy and that criminal behavior is not…

Novel approach to the Helmholtz integral equation solution by Fourier series expansion for acoustic radiation and scattering problems

CSIR Research Space (South Africa)

Shatalov, MY

2006-01-01

Full Text Available -scale structure to guarantee the numerical accuracy of solution. In the present paper the authors propose to use a novel method of solution of the Helmholtz integral equation, which is based on expansion of the integrands in double Fourier series. The main...

Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals

International Nuclear Information System (INIS)

Baranov, Anton D

2009-01-01

We study properties of the embedding operators of model subspaces K p Θ (defined by inner functions) in the Hardy space H p (coinvariant subspaces of the shift operator). We find a criterion for the embedding of K p Θ in L p (μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in K p Θ . We investigate measures μ such that the embedding operator belongs to some Schatten-von Neumann ideal.

A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

Science.gov (United States)

Andrade, D.; Nachbin, A.

2018-06-01

Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two dimensional free surface. The corresponding Fourier-type operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care and a Galerkin method is provided accordingly. One dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large amplitude, rapidly varying topography. An alternative, conformal mapping based, method is used for benchmarking. A two dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three dimensional DtN operator.

Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation

International Nuclear Information System (INIS)

Wei, T; Qin, H H; Shi, R

2008-01-01

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method

A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach

DEFF Research Database (Denmark)

Karlstrom, O.; Emary, C.; Zedler, P.

2013-01-01

We investigate the second-order von Neumann approach from a diagrammatic point of view and demonstrate its equivalence with the resonant tunneling approximation. The investigation of higher order diagrams shows that the method correctly reproduces the equation of motion for the single-particle re...... in a two-level dot, a phenomenon that requires the inclusion of electron–electron interaction as well as higher order tunneling processes....

The unbounded solution of a periodic mixed Sturm–Liouville problem in an infinite strip for the Laplacian

Directory of Open Access Journals (Sweden)

M.G. Elsheikh

2013-10-01

Full Text Available The unbounded solution, at the points where the boundary conditions change, for a mixed Sturm–Liouville problem of the Dirichlet–Neumann type can be obtained using the method of the integral equation formulation. Since this formulation is usually reduced to an infinite algebraic system in which the unknowns are the Fourier coefficients of the unknown unbounded entity, a study of ℓp-solutions imposes itself concerning the influence of the truncation on such systems. This study is achieved and the well-known theorem on the ℓ2-solutions of the infinite algebraic systems is generalized.

The Photon Shell Game and the Quantum von Neumann Architecture with Superconducting Circuits

Science.gov (United States)

Mariantoni, Matteo

2012-02-01

Superconducting quantum circuits have made significant advances over the past decade, allowing more complex and integrated circuits that perform with good fidelity. We have recently implemented a machine comprising seven quantum channels, with three superconducting resonators, two phase qubits, and two zeroing registers. I will explain the design and operation of this machine, first showing how a single microwave photon | 1 > can be prepared in one resonator and coherently transferred between the three resonators. I will also show how more exotic states such as double photon states | 2 > and superposition states | 0 >+ | 1 > can be shuffled among the resonators as well [1]. I will then demonstrate how this machine can be used as the quantum-mechanical analog of the von Neumann computer architecture, which for a classical computer comprises a central processing unit and a memory holding both instructions and data. The quantum version comprises a quantum central processing unit (quCPU) that exchanges data with a quantum random-access memory (quRAM) integrated on one chip, with instructions stored on a classical computer. I will also present a proof-of-concept demonstration of a code that involves all seven quantum elements: (1), Preparing an entangled state in the quCPU, (2), writing it to the quRAM, (3), preparing a second state in the quCPU, (4), zeroing it, and, (5), reading out the first state stored in the quRAM [2]. Finally, I will demonstrate that the quantum von Neumann machine provides one unit cell of a two-dimensional qubit-resonator array that can be used for surface code quantum computing. This will allow the realization of a scalable, fault-tolerant quantum processor with the most forgiving error rates to date. [4pt] [1] M. Mariantoni et al., Nature Physics 7, 287-293 (2011.)[0pt] [2] M. Mariantoni et al., Science 334, 61-65 (2011).

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Wang, Jie

2015-01-01

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Wang, Jie, E-mail: wangjie@iun.edu [Department of Computer Information Systems, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2015-07-15

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.

Problems in Analyzing Time Series with Gaps and Their Solution with the WinABD Software Package

Science.gov (United States)

Desherevskii, A. V.; Zhuravlev, V. I.; Nikolsky, A. N.; Sidorin, A. Ya.

2017-12-01

Technologies for the analysis of time series with gaps are considered. Some algorithms of signal extraction (purification) and evaluation of its characteristics, such as rhythmic components, are discussed for series with gaps. Examples are given for the analysis of data obtained during long-term observations at the Garm geophysical test site and in other regions. The technical solutions used in the WinABD software are considered to most efficiently arrange the operation of relevant algorithms in the presence of observational defects.

A solid solution series of atacamite type Ni{sub 2x}Mg{sub 2−2x}Cl(OH){sub 3}

Energy Technology Data Exchange (ETDEWEB)

Bette, Sebastian [TU Bergakademie Freiberg, Institute of Inorganic Chemistry, Leipziger Strasse 29, Freiberg 09596 (Germany); Dinnebier, Robert E. [Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart 70569 (Germany); Röder, Christian [TU Bergakademie Freiberg, Institute of Theoretical Physics, Leipziger Strasse 23, Freiberg 09596 (Germany); Freyer, Daniela, E-mail: daniela.freyer@chemie.tu-freiberg.de [TU Bergakademie Freiberg, Institute of Inorganic Chemistry, Leipziger Strasse 29, Freiberg 09596 (Germany)

2015-08-15

For the first time a complete solid solution series Ni{sub 2x}Mg{sub 2−2x}Cl(OH){sub 3} of an atacamite type alkaline main group metal chloride, Mg{sub 2}Cl(OH){sub 3}, and a transition group metal chloride, Ni{sub 2}Cl(OH){sub 3}, was prepared and characterized by chemical and thermal analysis as well as by Raman and IR spectroscopy, and high resolution laboratory X-ray powder diffraction. All members of the solid solution series crystallize in space group Pnam (62). The main building units of these crystal structures are distorted, edge-linked Ni/MgO{sub 4}Cl{sub 2} and Ni/MgO{sub 5}Cl octahedra. The distribution of Ni{sup 2+}- and Mg{sup 2+}-ions among these two metal-sites within the solid solution series is discussed in detail. The crystallization of the solid solution phases occurs via an intermediate solid solution series, (Ni/Mg)Cl{sub 2x}(OH){sub 2−2x}, with variable Cl: OH ratio up to the 1:3 ratio according to the formula Ni{sub 2x}Mg{sub 2−2x} Cl(OH){sub 3}. For one isolated intermediate solid solution member, Ni{sub 0.70}Mg{sub 0.30}Cl{sub 0.58}(OH){sub 1.42}, the formation and crystal structure is presented as well. - Graphical abstract: For the first time a complete solid solution series, Ni{sub 2x}Mg{sub 2−2x} Cl(OH){sub 3}, was synthesized and characterized. Structure solution by revealed that Ni{sup 2+} prefers to occupy the Jahn–Teller-like distorted hole, out of two available cation sites. Substitution of Ni{sup 2+} by Mg{sup 2+} in atacamite type Ni{sub 2}Cl(OH){sub 3} results in systematic band shifts in Raman and IR spectra as well as in systematic changes in thermal properties. The α-polymorphs M{sub 2}Cl(OH){sub 3} with M=Mg{sup 2+}, Ni{sup 2+} and other divalent transition metal ions, as described in literature, were identified as separate compounds. - Highlights: • First synthesis of solid solution series between main and transition metal chloride. • Ni{sup 2+} prefers to occupy Jahn–Teller-like distorted octahedral holes

Oberbeck–Boussinesq free convection of water based nanoliquids in a vertical channel using Dirichlet, Neumann and Robin boundary conditions on temperature

Directory of Open Access Journals (Sweden)

Nur Asiah Mohd Makhatar

2016-09-01

Full Text Available A numerical investigation is carried out into the flow and heat transfer within a fully-developed mixed convection flow of water–alumina (Al2O3–water, water–titania (TiO2–water and water–copperoxide (CuO–water in a vertical channel by considering Dirichlet, Neumann and Robin boundary conditions. Actual values of thermophysical quantities are used in arriving at conclusions on the three nanoliquids. The Biot number influences on velocity and temperature distributions are opposite in regions close to the left wall and the right wall. Robin condition is seen to favour symmetry in the flow velocity whereas Dirichlet and Neumann conditions skew the flow distribution and push the point of maximum velocity to the right of the channel. A reversal of role is seen between them in their influence on the flow in the left-half and the right-half of the channel. This leads to related consequences in heat transport. Viscous dissipation is shown to aid flow and heat transport. The present findings reiterate the observation on heat transfer in other configurations that only low concentrations of nanoparticles facilitate enhanced heat transport for all three temperature conditions. Significant change was observed in Neumann condition, whereas the changes are too extreme in Dirichlet condition. It is found that Robin condition is the most stable condition. Further, it is also found that all three nanoliquids have enhanced heat transport compared to that by base liquid, with CuO–water nanoliquid shows higher enhancement in its Nusselt number, compared to Al2O3 and TiO2.

Calorimetric measurements on plutonium rich (U,Pu)O2 solid solutions

International Nuclear Information System (INIS)

Kandan, R.; Babu, R.; Nagarajan, K.; Vasudeva Rao, P.R.

2008-01-01

Enthalpy increments of U (1-y) Pu y O 2 solid solutions with y = 0.45, 0.55 and 0.65 were measured using a high-temperature differential calorimeter by employing the method of inverse drop calorimetry in the temperature range 956-1803 K. From the fit equations for the enthalpy increments, other thermodynamic functions such as heat capacity, entropy and Gibbs energy function have been computed in the temperature range 298-1800 K. The results are presented and compared with the data available in the literature. The results indicate that the enthalpies of U (1-y) Pu y O 2 solid solutions with y = 0.45, 0.55 and 0.65 obey the Neumann-Kopp's molar additivity rule

Proof of Polyakov conjecture on supercomplex plane

International Nuclear Information System (INIS)

Kachkachi, M.; Kouadik, S.

1994-10-01

Using Neumann series, we solve iteratively SBE to arbitrary order. Then applying this, we compute the energy momentum tensor and n points functions for generic n starting from WZP action on the supercomplex plane. We solve the superconformal Ward identity and we show that the iterative solution to arbitrary order is resumed by WZP action. This proves the Polyakov conjecture on supercomplex plane. (author). 8 refs

On the Application of the Fourier Series Solution to the Hydromagnetic Buoyant Two-Dimensional Laminar Vertical Jet

Directory of Open Access Journals (Sweden)

Marco Rosales-Vera

2012-01-01

Full Text Available The problem of a hydromagnetic hot two-dimensional laminar jet issuing vertically into an otherwise quiescent fluid of a lower temperature is studied. We propose solutions to the boundary layer equations using the classical Fourier series. The method is essentiall to transform the boundary layer equations to a coupled set of nonlinear first-order ordinary differential equations through the Fourier series. The accuracy of the results has been tested by the comparison of the velocity distributions obtained by the Fourier series with those calculated by finite difference method. The results show that the present method, based on the Fourier series, is an efficient method, suitable to solve boundary layer equations applied to plane jet flows with high accuracy.

Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators

DEFF Research Database (Denmark)

Gimperlein, Heiko; Grubb, Gerd

2014-01-01

The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained for perturbat......The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained...... for perturbations of fractional powers of the Laplacian. In the selfadjoint case, extensions to t∈C+  are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup....

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

Science.gov (United States)

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Coupling Neumann development and component mode synthesis methods for stochastic analysis of random structures

Directory of Open Access Journals (Sweden)

Driss Sarsri

2014-05-01

Full Text Available In this paper, we propose a method to calculate the first two moments (mean and variance of the structural dynamics response of a structure with uncertain variables and subjected to random excitation. For this, Newmark method is used to transform the equation of motion of the structure into a quasistatic equilibrium equation in the time domain. The Neumann development method was coupled with Monte Carlo simulations to calculate the statistical values of the random response. The use of modal synthesis methods can reduce the dimensions of the model before integration of the equation of motion. Numerical applications have been developed to highlight effectiveness of the method developed to analyze the stochastic response of large structures.

The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

Energy Technology Data Exchange (ETDEWEB)

Ganapol, B.; Picca, P. [Dept. of Aerospace and Mechanical Engineering, Univ. of Arizona (United States); Previti, A.; Mostacci, D. [Laboratorio di Montecuccolino, Alma Mater Studiorum - Universita di Bologna (Italy)

2012-07-01

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

Effect of background dielectric on TE-polarized photonic bandgap of metallodielectric photonic crystals using Dirichlet-to-Neumann map method.

Science.gov (United States)

Sedghi, Aliasghar; Rezaei, Behrooz

2016-11-20

Using the Dirichlet-to-Neumann map method, we have calculated the photonic band structure of two-dimensional metallodielectric photonic crystals having the square and triangular lattices of circular metal rods in a dielectric background. We have selected the transverse electric mode of electromagnetic waves, and the resulting band structures showed the existence of photonic bandgap in these structures. We theoretically study the effect of background dielectric on the photonic bandgap.

Non-parametric characterization of long-term rainfall time series

Science.gov (United States)

Tiwari, Harinarayan; Pandey, Brij Kishor

2018-03-01

The statistical study of rainfall time series is one of the approaches for efficient hydrological system design. Identifying, and characterizing long-term rainfall time series could aid in improving hydrological systems forecasting. In the present study, eventual statistics was applied for the long-term (1851-2006) rainfall time series under seven meteorological regions of India. Linear trend analysis was carried out using Mann-Kendall test for the observed rainfall series. The observed trend using the above-mentioned approach has been ascertained using the innovative trend analysis method. Innovative trend analysis has been found to be a strong tool to detect the general trend of rainfall time series. Sequential Mann-Kendall test has also been carried out to examine nonlinear trends of the series. The partial sum of cumulative deviation test is also found to be suitable to detect the nonlinear trend. Innovative trend analysis, sequential Mann-Kendall test and partial cumulative deviation test have potential to detect the general as well as nonlinear trend for the rainfall time series. Annual rainfall analysis suggests that the maximum changes in mean rainfall is 11.53% for West Peninsular India, whereas the maximum fall in mean rainfall is 7.8% for the North Mountainous Indian region. The innovative trend analysis method is also capable of finding the number of change point available in the time series. Additionally, we have performed von Neumann ratio test and cumulative deviation test to estimate the departure from homogeneity. Singular spectrum analysis has been applied in this study to evaluate the order of departure from homogeneity in the rainfall time series. Monsoon season (JS) of North Mountainous India and West Peninsular India zones has higher departure from homogeneity and singular spectrum analysis shows the results to be in coherence with the same.

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

Science.gov (United States)

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(0divergent series appear when the concentration or survival probabilities are evaluated via the method of separation of variables. While the solution for normal diffusion problems is, at most, divergent as t-->0 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models

Science.gov (United States)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2018-05-01

In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.

Intertwining solutions for magnetic relativistic Hartree type equations

Science.gov (United States)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

Auto-validating von Neumann rejection sampling from small phylogenetic tree spaces

Directory of Open Access Journals (Sweden)

York Thomas

2009-01-01

Full Text Available Abstract Background In phylogenetic inference one is interested in obtaining samples from the posterior distribution over the tree space on the basis of some observed DNA sequence data. One of the simplest sampling methods is the rejection sampler due to von Neumann. Here we introduce an auto-validating version of the rejection sampler, via interval analysis, to rigorously draw samples from posterior distributions over small phylogenetic tree spaces. Results The posterior samples from the auto-validating sampler are used to rigorously (i estimate posterior probabilities for different rooted topologies based on mitochondrial DNA from human, chimpanzee and gorilla, (ii conduct a non-parametric test of rate variation between protein-coding and tRNA-coding sites from three primates and (iii obtain a posterior estimate of the human-neanderthal divergence time. Conclusion This solves the open problem of rigorously drawing independent and identically distributed samples from the posterior distribution over rooted and unrooted small tree spaces (3 or 4 taxa based on any multiply-aligned sequence data.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

Science.gov (United States)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

Directory of Open Access Journals (Sweden)

Luisa Toscano

2016-01-01

Full Text Available A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.

Logo and Von Neumann Ideas [and] Towards a Humanistic Use of Computers in Education = Hacia una insercion humanista de las computadoras en la educacion.

Science.gov (United States)

Reggini, Horacio C.

The first article, "LOGO and von Neumann Ideas," deals with the creation of new procedures based on procedures defined and stored in memory as LOGO lists of lists. This representation, which enables LOGO procedures to construct, modify, and run other LOGO procedures, is compared with basic computer concepts first formulated by John von…

Non-von Neumann computing using plasmon particles interacting with phase change materials (Conference Presentation)

Science.gov (United States)

Saiki, Toshiharu

2016-09-01

Control of localized surface plasmon resonance (LSPR) excited on metal nanostructures has drawn attention for applications in dynamic switching of plasmonic devices. As a reversible active media for LSPR control, chalcogenide phase-change materials (PCMs) such as GeSbTe (GST) are promising for high-contrast robust plasmonic switching. Owing to the plasticity and the threshold behavior during both amorphization and crystallization of PCMs, PCM-based LSPR switching elements possess a dual functionality of memory and processing. Integration of LSPR switching elements so that they interact with each other will allow us to build non-von-Neumann computing devices. As a specific demonstration, we discuss the implementation of a cellular automata (CA) algorithm into interacting LSPR switching elements. In the model we propose, PCM cells, which can be in one of two states (amorphous and crystalline), interact with each other by being linked by a AuNR, whose LSPR peak wavelength is determined by the phase of PCM cells on the both sides. The CA program proceeds by irradiating with a light pulse train. The local rule set is defined by the temperature rise in the PCM cells induced by the LSPR of the AuNR, which is subject to the intensity and wavelength of the irradiating pulse. We also investigate the possibility of solving a problem analogous to the spin-glass problem by using a coupled dipole system, in which the individual coupling strengths can be modified to optimize the system so that the exact solution can be easily reached. For this algorithm, we propose an implementation based on an idea that coupled plasmon particles can create long-range spatial correlations, and the interaction of this with a phase-change material allows the coupling strength to be modified.

Investigation into isomolar series of Al(NO3)3, Na3VO4 solution mixture and composition of solid phases

International Nuclear Information System (INIS)

Chernysh, L.F.; Nakhodnova, A.P.; Makarova, R.A.

1979-01-01

Conducted is investigation of properties of isomolar series of aluminium nitrate and sodiUm vanadate solutions at pH of the latter 12.5; 10.0; 7.0 and the temperature of 25 deg C using the methods of pH-metry, conductometry, ''seeming'' volume of precipitations, residual concentration of aluminium and vanadium. It is shown, that the composition property diagram of the system investigated does not reflect the true composition of solid-phase products of the reaction, which depends on the component ratio in solution. Bottom phases of isomolar series are mainly heterogeneous. At the excess of sodium vanadate solution and its high pH values conditions for the basic salt formation are created. At pH of the Na 3 VO 4 solution of 12.5 and 10.0 and Al(NO 3 ) 3 : Na 3 VO 4 ratios 4:6 and 3:7 respectively obtained are the basic aluminium vanadates of the (AlOH) 3 (VO 4 ) 2 x 7.5H 2 O and (AlOH) 2 V 2 O 7 x5H 2 O composition, some of their physicochemical properties being investigated

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid

OpenAIRE

Mitri, F. G.

2015-01-01

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\\theta = \\pi) in the near-field an...

Phase separation phenomena in solutions of poly(2,6-dimethyl-1,4-phenylene oxide). IV. Thermodynamic parameters for solutions in a series of homologous solvents: Toluene to hexylbenzene

NARCIS (Netherlands)

Koenhen, D.M.; Bakker, A.; Broens, L.; van den Berg, J.W.A.; Smolders, C.A.

1984-01-01

Melting-point curves for solutions of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) in a series of homologous solvents (toluene to n-hexylbenzene) have been obtained from visual and differential scanning calorimetry measurements. The measured melting points were used to calculate thermodynamic

Von-Neumann and Beyond: Memristor Architectures

KAUST Repository

Naous, Rawan

2017-05-01

An extensive reliance on technology, an abundance of data, and increasing processing requirements have imposed severe challenges on computing and data processing. Moreover, the roadmap for scaling electronic components faces physical and reliability limits that hinder the utilization of the transistors in conventional systems and promotes the need for faster, energy-efficient, and compact nano-devices. This work thus capitalizes on emerging non-volatile memory technologies, particularly the memristor for steering novel design directives. Moreover, aside from the conventional deterministic operation, a temporal variability is encountered in the devices functioning. This inherent stochasticity is addressed as an enabler for endorsing the stochastic electronics field of study. We tackle this approach of design by proposing and verifying a statistical approach to modelling the stochastic memristors behaviour. This mode of operation allows for innovative computing designs within the approximate computing and beyond Von-Neumann domains. In the context of approximate computing, sacrificing functional accuracy for the sake of energy savings is proposed based on inherently stochastic electronic components. We introduce mathematical formulation and probabilistic analysis for Boolean logic operators and correspondingly incorporate them into arithmetic blocks. Gate- and system-level accuracy of operation is presented to convey configurability and the different effects that the unreliability of the underlying memristive components has on the intermediary and overall output. An image compression application is presented to reflect the efficiency attained along with the impact on the output caused by the relative precision quantification. In contrast, in neuromorphic structures the memristors variability is mapped onto abstract models of the noisy and unreliable brain components. In one approach, we propose using the stochastic memristor as an inherent source of variability in

Atomic switch: atom/ion movement controlled devices for beyond von-neumann computers.

Science.gov (United States)

Hasegawa, Tsuyoshi; Terabe, Kazuya; Tsuruoka, Tohru; Aono, Masakazu

2012-01-10

An atomic switch is a nanoionic device that controls the diffusion of metal ions/atoms and their reduction/oxidation processes in the switching operation to form/annihilate a conductive path. Since metal atoms can provide a highly conductive channel even if their cluster size is in the nanometer scale, atomic switches may enable downscaling to smaller than the 11 nm technology node, which is a great challenge for semiconductor devices. Atomic switches also possess novel characteristics, such as high on/off ratios, very low power consumption and non-volatility. The unique operating mechanisms of these devices have enabled the development of various types of atomic switch, such as gap-type and gapless-type two-terminal atomic switches and three-terminal atomic switches. Novel functions, such as selective volatile/nonvolatile, synaptic, memristive, and photo-assisted operations have been demonstrated. Such atomic switch characteristics can not only improve the performance of present-day electronic systems, but also enable development of new types of electronic systems, such as beyond von- Neumann computers. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On the connection between quantum fields and von Neumann algebras of local operators

International Nuclear Information System (INIS)

Driessler, W.; Summers, S.J.; Wichmann, E.H.

1986-01-01

The relationship between a standard local quantum field and a net of local von Neumann algebras is discussed. Two natural possibilities for such an association are identified, and conditions for these to obtain are found. It is shown that the local net can naturally be so chosen that it satisfies the Special Condition of Duality. The notion of an intrinsically local field operator is introduced, and it is shown that such an operator defines a local net with which the field is locally associated. A regularity condition on the field is formulated, and it is shown that if this condition holds, then there exists a unique local net with which the field is locally associated if and only if the field algebra contains at least one intrinsically local operator. Conditions under which a field and other fields in its Borchers class are associated with the same local net are found, in terms of the regularity condition mentioned. (orig.)

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

Science.gov (United States)

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

An analytic solution to the homogeneous EIT problem on the 2D disk and its application to estimation of electrode contact impedances

International Nuclear Information System (INIS)

Demidenko, Eugene

2011-01-01

An analytic solution of the potential distribution on a 2D homogeneous disk for electrical impedance tomography under the complete electrode model is expressed via an infinite system of linear equations. For the shunt electrode model with two electrodes, our solution coincides with the previously derived solution expressed via elliptic integral (Pidcock et al 1995 Physiol. Meas. 16 77–90). The Dirichlet-to-Neumann map is derived for statistical estimation via nonlinear least squares. The solution is validated in phantom experiments and applied for breast contact impedance estimation in vivo. Statistical hypothesis testing is used to test whether the contact impedances are the same across electrodes or all equal zero. Our solution can be especially useful for a rapid real-time test for bad surface contact in clinical setting

Tensor categories and endomorphisms of von Neumann algebras with applications to quantum field theory

CERN Document Server

Bischoff, Marcel; Longo, Roberto; Rehren, Karl-Henning

2015-01-01

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).

Investigation of Noises in GPS Time Series: Case Study on Epn Weekly Solutions

Science.gov (United States)

Klos, Anna; Bogusz, Janusz; Figurski, Mariusz; Kosek, Wieslaw; Gruszczynski, Maciej

2014-05-01

The noises in GPS time series are stated to be described the best by the combination of white (Gaussian) and power-law processes. They are mainly the effect of mismodelled satellite orbits, Earth orientation parameters, atmospheric effects, antennae phase centre effects, or of monument instability. Due to the fact, that velocities of permanent stations define the kinematic reference frame, they have to fulfil the requirement of being stable at 0.1 mm/yr. The previously performed researches showed, that the wrong assumption of noise model leads to the underestimation of velocities and their uncertainties from 2 up to even 11, especially in the Up direction. This presentation focuses on more than 200 EPN (EUREF Permanent Network) stations from the area of Europe with various monument types (concrete pillars, buildings, metal masts, with or without domes, placed on the ground or on the rock) and coordinates of weekly changes (GPS weeks 0834-1459). The topocentric components (North, East, Up) in ITRF2005 which come from the EPN Re-Processing made by the Military University of Technology Local Analysis Centre (MUT LAC) were processed with Maximum Likelihood Estimation (MLE) using CATS software. We have assumed the existence of few combinations of noise models (these are: white, flicker and random walk noise with integer spectral indices and power-law noise models with fractional spectral indices) and investigated which of them EPN weekly time series are likely to follow. The results show, that noises in GPS time series are described the best by the combination of white and flicker noise model. It is strictly related to the so-called common mode error (CME) that is spatially correlated error being one of the dominant error source in GPS solutions. We have assumed CME as spatially uniform, what was a good approximation for stations located hundreds of kilometres one to another. Its removal with spatial filtering reduces the amplitudes of white and flicker noise by a

Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...

Unstable Mode Solutions to the Klein-Gordon Equation in Kerr-anti-de Sitter Spacetimes

Science.gov (United States)

Dold, Dominic

2017-03-01

For any cosmological constant {Λ = -3/ℓ2 r+2 > |a|ℓ}. We obtain an analogous result for Neumann boundary conditions if {5/4 < α < 9/4}. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses {α} such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result adopts methods of Shlapentokh-Rothman developed in (Commun. Math. Phys. 329:859-891, 2014) and provides the first rigorous construction of a superradiant instability for negative cosmological constant.

Series Solution for Steady Three-Dimensional Flow due to Spraying on Inclined Spinning Disk by Homotopy Perturbation Method

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Saeed Dinarvand

2012-01-01

Full Text Available The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM. The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.

Contribution of Lattice Distortion to Solid Solution Strengthening in a Series of Refractory High Entropy Alloys

Science.gov (United States)

Chen, H.; Kauffmann, A.; Laube, S.; Choi, I.-C.; Schwaiger, R.; Huang, Y.; Lichtenberg, K.; Müller, F.; Gorr, B.; Christ, H.-J.; Heilmaier, M.

2018-03-01

We present an experimental approach for revealing the impact of lattice distortion on solid solution strengthening in a series of body-centered-cubic (bcc) Al-containing, refractory high entropy alloys (HEAs) from the Nb-Mo-Cr-Ti-Al system. By systematically varying the Nb and Cr content, a wide range of atomic size difference as a common measure for the lattice distortion was obtained. Single-phase, bcc solid solutions were achieved by arc melting and homogenization as well as verified by means of scanning electron microscopy and X-ray diffraction. The atomic radii of the alloying elements for determination of atomic size difference were recalculated on the basis of the mean atomic radii in and the chemical compositions of the solid solutions. Microhardness (μH) at room temperature correlates well with the deduced atomic size difference. Nevertheless, the mechanisms of microscopic slip lead to pronounced temperature dependence of mechanical strength. In order to account for this particular feature, we present a combined approach, using μH, nanoindentation, and compression tests. The athermal proportion to the yield stress of the investigated equimolar alloys is revealed. These parameters support the universality of this aforementioned correlation. Hence, the pertinence of lattice distortion for solid solution strengthening in bcc HEAs is proven.

The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

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H. O. Bakodah

2013-01-01

Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Proof of existence of global solutions for m-component reaction-diffusion systems with mixed boundary conditions via the Lyapunov functional method

International Nuclear Information System (INIS)

Abdelmalek, Salem; Kouachi, Said

2007-01-01

To prove global existence for solutions of m-component reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions and nonhomogeneous Robin boundary conditions. The purpose of this paper is to prove the existence of a global solution using a single inequality for the polynomial growth condition of the reaction terms. Our technique is based on the construction of polynomial functionals. This result generalizes those obtained recently by Kouachi et al (at press), Kouachi (2002 Electron. J. Diff. Eqns 2002 1), Kouachi (2001 Electron. J. Diff. Eqns 2001 1) and independently by Malham and Xin (1998 Commun. Math. Phys. 193 287)

Accurate and efficient implementation of the von Neumann representation for laser pulses with discrete and finite spectra

International Nuclear Information System (INIS)

Dimler, Frank; Fechner, Susanne; Rodenberg, Alexander; Brixner, Tobias; Tannor, David J

2009-01-01

We recently introduced the von Neumann picture, a joint time-frequency representation, for describing ultrashort laser pulses. The method exploits a discrete phase-space lattice of nonorthogonal Gaussians to represent the pulses; an arbitrary pulse shape can be represented on this lattice in a one-to-one manner. Although the representation was originally defined for signals with an infinite continuous spectrum, it can be adapted to signals with discrete and finite spectrum with great computational savings, provided that discretization and truncation effects are handled with care. In this paper, we present three methods that avoid loss of accuracy due to these effects. The approach has immediate application to the representation and manipulation of femtosecond laser pulses produced by a liquid-crystal mask with a discrete and finite number of pixels.

A novel method for the measurement of the von Neumann spike in detonating high explosives

Science.gov (United States)

Sollier, A.; Bouyer, V.; Hébert, P.; Doucet, M.

2016-06-01

We present detonation wave profiles measured in T2 (97 wt. % TATB) and TX1 (52 wt. % TATB and 45 wt. % HMX) high explosives. The experiments consisted in initiating a detonation wave in a 15 mm diameter cylinder of explosive using an explosive wire detonator and an explosive booster. Free surface velocity wave profiles were measured at the explosive/air interface using a Photon Doppler Velocimetry system. We demonstrate that a comparison of these free surface wave profiles with those measured at explosive/window interfaces in similar conditions allows to bracket the von Neumann spike in a narrow range. For T2, our measurements show that the spike pressure lies between 35.9 and 40.1 GPa, whereas for TX1, it lies between 42.3 and 47.0 GPa. The numerical simulations performed in support to these measurements show that they can be used to calibrate reactive burn models and also to check the accuracy of the detonation products equation of state at low pressure.

Geometric Series: A New Solution to the Dog Problem

Science.gov (United States)

Dion, Peter; Ho, Anthony

2013-01-01

This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…

[Award of the Salomon-Neumann-Medal 2017 - Speech of the Laureate Prof. Bernt-Peter Robra, 5 September 2017, St. Peter´s Church Lübeck].

Science.gov (United States)

Robra, Bernt-Peter

2018-02-19

The Salomon-Neumann-Medal 2017 of the German Society for Social Medicine and Prevention (DGSMP) was awarded to Bernt-Peter Robra, Institute for Social Medicine and Health Economics (ISMG) of the Otto von Guericke University Magdeburg. The person and scientific merits of Manfred Pflanz are valued and topics of the masterplan2020-process are highlighted, that offer chances for developments in medicine and public health. © Georg Thieme Verlag KG Stuttgart · New York.

Bridge flap technique as a single-step solution to mucogingival problems: A case series

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Vivek Gupta

2011-01-01

Full Text Available Shallow vestibule, gingival recession, inadequate width of attached gingiva (AG and aberrant frenum pull are an array of mucogingival problems for which several independent and effective surgical solutions are reported in the literature. This case series reports the effectiveness of the bridge flap technique as a single-step surgical entity for increasing the depth of the vestibule, root coverage, increasing the width of the AG and solving the problem of abnormal frenum pull. Eight patients with 18 teeth altogether having Millers class I, II or III recession along with problems of shallow vestibule, inadequate width of AG and with or without frenum pull underwent this surgical procedure and were followed-up till 9 months post-operatively. The mean root coverage obtained was 55% and the mean average gain in width of the AG was 3.5 mm. The mean percentage gain in clinical attachment level was 41%. The bridge flap technique can be an effective single-step solution for the aforementioned mucogingival problems if present simultaneously in any case, and offers considerable advantages over other mucogingival surgical techniques in terms of simplicity, limited chair-time for the patient and the operator, single surgical intervention for manifold mucogingival problems and low morbidity because of the absence of palatal donor tissue.

From divergent power series to analytic functions theory and application of multisummable power series

CERN Document Server

Balser, Werner

1994-01-01

Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

Existence, regularity and representation of solutions of time fractional wave equations

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Valentin Keyantuo

2017-09-01

Full Text Available We study the solvability of the fractional order inhomogeneous Cauchy problem $$ \\mathbb{D}_t^\\alpha u(t=Au(t+f(t, \\quad t>0,\\;1<\\alpha\\le 2, $$ where A is a closed linear operator in some Banach space X and $f:[0,\\infty\\to X$ a given function. Operator families associated with this problem are defined and their regularity properties are investigated. In the case where A is a generator of a $\\beta$-times integrated cosine family $(C_\\beta(t$, we derive explicit representations of mild and classical solutions of the above problem in terms of the integrated cosine family. We include applications to elliptic operators with Dirichlet, Neumann or Robin type boundary conditions on $L^p$-spaces and on the space of continuous functions.

Convergent Power Series of sech⁡(x and Solutions to Nonlinear Differential Equations

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U. Al Khawaja

2018-01-01

Full Text Available It is known that power series expansion of certain functions such as sech⁡(x diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS to obtain a power series representation of sech⁡(x that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2. A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.

Investigation into isomolar series of Al(NO/sub 3/)/sub 3/, Na/sub 3/VO/sub 4/ solution mixture and composition of solid phases

Energy Technology Data Exchange (ETDEWEB)

Chernysh, L F; Nakhodnova, A P; Makarova, R A [Donetskij Gosudarstvennyj Univ. (Ukrainian SSR)

1979-11-01

Conducted is investigation of properties of isomolar series of aluminium nitrate and sodium vanadate solutions at pH of the latter 12.5; 10.0; 7.0 and the temperature of 25 deg C using the methods of pH-metry, conductometry, ''seeming'' volume of precipitations, residual concentration of aluminium and vanadium. It is shown, that the composition property diagram of the system investigated does not reflect the true composition of solid-phase products of the reaction, which depends on the component ratio in solution. Bottom phases of isomolar series are mainly heterogeneous. At the excess of sodium vanadate solution and its high pH values conditions for the basic salt formation are created. At pH of the Na/sub 3/VO/sub 4/ solution of 12.5 and 10.0 and Al(NO/sub 3/)/sub 3/: Na/sub 3/VO/sub 4/ ratios 4:6 and 3:7 respectively obtained are the basic aluminium vanadates of the (AlOH)/sub 3/(VO/sub 4/)/sub 2/x 7.5H/sub 2/O and (AlOH)/sub 2/V/sub 2/O/sub 7/x5H/sub 2/O composition, some of their physicochemical properties being investigated.

Case series and descriptive cohort studies in neurosurgery: the confusion and solution.

Science.gov (United States)

Esene, Ignatius N; Ngu, Julius; El Zoghby, Mohamed; Solaroglu, Ihsan; Sikod, Anna M; Kotb, Ali; Dechambenoit, Gilbert; El Husseiny, Hossam

2014-08-01

Case series (CS) are well-known designs in contemporary use in neurosurgery but are sometimes used in contexts that are incompatible with their true meaning as defined by epidemiologists. This inconsistent, inappropriate and incorrect use, and mislabeling impairs the appropriate indexing and sorting of evidence. Using PubMed, we systematically identified published articles that had "case series" in the "title" in 15 top-ranked neurosurgical journals from January 2008 to December 2012. The abstracts and/or full articles were scanned to identify those with descriptions of the principal method as being "case series" and then classified as "true case series" or "non-case series" by two independent investigators with 100 % inter-rater agreement. Sixty-four articles had the label "case series" in their "titles." Based on the definition of "case series" and our appraisal of the articles using Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines, 18 articles (28.13 %) were true case series, while 46 (71.87 %) were mislabeled. Thirty-five articles (54.69 %) mistook retrospective (descriptive) cohorts for CS. CS are descriptive with an outcome-based sampling, while "descriptive cohorts" have an exposure-based sampling of patients, followed over time to assess outcome(s). A comparison group is not a defining feature of a cohort study and distinguishes descriptive from analytic cohorts. A distinction between a case report, case series, and descriptive cohorts is absolutely necessary to enable the appropriate indexing, sorting, and application of evidence. Researchers need better training in methods and terminology, and editors and reviewers should scrutinize more carefully manuscripts claiming to be "case series" studies.

Evidence of nonuniqueness and oscillatory solutions in computational fluid mechanics

International Nuclear Information System (INIS)

Nunziato, J.W.; Gartling, D.K.; Kipp, M.E.

1985-01-01

We will review some of our recent experiences in computing solutions for nonlinear fluids in relatively simple, two-dimensional geometries. The purpose of this discussion will be to display by example some of the interesting but difficult questions that arise when ill-behaved solutions are obtained numerically. We will consider two examples. As the first example, we will consider a nonlinear elastic (compressible) fluid with chemical reactions and discuss solutions for detonation and detonation failure in a two-dimensional cylinder. In this case, the numerical algorithm utilizes a finite-difference method with artificial viscosity (von Neumann-Richtmyer method) and leads to two, distinctly different, stable solutions depending on the time step criterion used. The second example to be considered involves the convection of a viscous fluid in a rectangular container as a result of an exothermic polymerization reaction. A solidification front develops near the top of the container and propagates down through the fluid, changing the aspect ratio of the region ahead of the front. Using a Galerkin-based finite element method, a numerical solution of the partial differential equations is obtained which tracks the front and correctly predicts the fluid temperatures near the walls. However, the solution also exhibits oscillatory behavior with regard to the number of cells in the fluid ahead of the front and in the strength of the cells. More definitive experiments and analysis are required to determine whether this oscillatory phenomena is a numerical artifact or a physical reality. 20 refs., 14 figs

Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Sigmund, Ole

2009-01-01

The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology...... information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential...... equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimisation problems in linear elasticity, solved on sequential and parallel computers....

Equi-frequency contour of photonic crystals with the extended Dirichlet-to-Neumann wave vector eigenvalue equation method

International Nuclear Information System (INIS)

Jiang Bin; Zhang Yejing; Wang Yufei; Liu Anjin; Zheng Wanhua

2012-01-01

We present the extended Dirichlet-to-Neumann wave vector eigenvalue equation (DtN-WVEE) method to calculate the equi-frequency contour (EFC) of square lattice photonic crystals (PhCs). With the extended DtN-WVEE method and Snell's law, the effective refractive index of the mode with a circular EFC can be obtained, which is further validated with the refractive index weighted by the electric field or magnetic field. To further verify the EFC calculated by the DtN-WVEE method, the finite-difference time-domain method is also used. Compared with other wave vector eigenvalue equation methods that calculate EFC directly, the size of the eigenmatrix used in the DtN-WVEE method is much smaller, and the computation time is significantly reduced. Since the DtN-WVEE method solves wave vectors for given arbitrary frequencies, it can also find applications in studying the optical properties of a PhC with dispersive, lossy and magnetic materials. (paper)

A Power Series Expansion and Its Applications

Science.gov (United States)

Chen, Hongwei

2006-01-01

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

Bandgap calculation of two-dimensional mixed solid-fluid phononic crystals by Dirichlet-to-Neumann maps

International Nuclear Information System (INIS)

Li Fenglian; Wang Yuesheng; Zhang Chuanzeng

2011-01-01

A numerical method based on the Dirichlet-to-Neumann (DtN) map is presented to compute the bandgaps of two-dimensional phononic crystals, which are composed of square or triangular lattices of circular solid cylinders in a fluid matrix. The DtN map is constructed using the cylindrical wave expansion in a unit cell. A linear eigenvalue problem, which depends on the Bloch wave vector and involves relatively small matrices, is formulated. Numerical calculations are performed for typical systems with various acoustic impedance ratios of the solid inclusions and the fluid matrix. The results indicate that the DtN-map based method can provide accurate results for various systems efficiently. In particular it takes into account the fluid-solid interface conditions and the transverse wave mode in the solid component, which has been proven to be significant when the acoustic impedance of the solid inclusions is close to or smaller than that of the fluid matrix. For systems with an acoustic impedance of the inclusion much less than that of the matrix, physical flat bands appear in the band structures, which will be missed if the transverse wave mode in the solid inclusions is neglected.

Divergent Perturbation Series

International Nuclear Information System (INIS)

Suslov, I.M.

2005-01-01

Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed

Solution of a Two-Dimensionel Problem on the Motion of a Heat Wave Front with the use of Power Series and the Boundary Element Method

Directory of Open Access Journals (Sweden)

A. Kazakov

2016-12-01

Full Text Available The paper discusses a nonlinear parabolic equation describing the process of heat conduction for the case of the power dependence of the heat conductivity factor on temperature. Besides heat distribution in space, it describes filtration of a polytropic gas in a porous medium, whereupon, in the English-language literature, this equation is generally referred to as the porous medium equation. A distinctive feature of this equation is the degeneration of its parabolic type when the required function becomes zero, whereupon the equation acquires some properties typical of first-order equations. Particularly, in some cases, it proves possible to substantiate theorems of the existence and uniqueness of heat-wave (filtration-wave type solutions for it. This paper proves a theorem of the existence and uniqueness of the solution to the problem of the motion of a heat wave with a specified front in the instance of two independent variables. At that, since the front has the form of a closed plane curve, a transition t o the polar coordinate system is performed. The solution is constructed in the form of a series, a constructible recurrent procedure for calculating its coefficients being proposed. The series convergence is proved by the majorant method. A boundary-element-based computation algorithm in the form of a computer program has been developed and implemented to solve the problem under study. Test examples are considered, the calculations made by a program designed by the authors being compared with the truncated series. A good agreement of the obtained results has been established.

Rheological and micro-Raman time-series characterization of enzyme sol–gel solution toward morphological control of electrospun fibers

International Nuclear Information System (INIS)

Oriero, Dennis A; Weakley, Andrew T; Aston, D Eric

2012-01-01

Rheological and micro-Raman time-series characterizations were used to investigate the chemical evolutionary changes of silica sol–gel mixtures for electrospinning fibers to immobilize an enzyme (tyrosinase). Results of dynamic rheological measurements agreed with the expected structural transitions associated with reacting sol–gel systems. The electrospinning sols exhibited shear-thinning behavior typical of a power law model. Ultrafine (200–300 nm diameter) fibers were produced at early and late times within the reaction window of approximately one hour from initial mixing of sol solutions with and without enzyme; diameter distributions of these fibers showed much smaller deviations than expected. The enzyme markedly increased magnitudes of both elastic and viscous moduli but had no significant impact on final fiber diameters, suggesting that the shear-thinning behavior of both sol–gel mixtures is dominant in the fiber elongation process. The time course and scale for the electrospinning batch fabrication show strong correlations between the magnitudes in rheological property changes over time and the chemical functional group evolution obtained from micro-Raman time-series analysis of the reacting sol–gel systems.

Rheological and micro-Raman time-series characterization of enzyme sol–gel solution toward morphological control of electrospun fibers

Science.gov (United States)

Oriero, Dennis A; Weakley, Andrew T; Aston, D Eric

2012-01-01

Rheological and micro-Raman time-series characterizations were used to investigate the chemical evolutionary changes of silica sol–gel mixtures for electrospinning fibers to immobilize an enzyme (tyrosinase). Results of dynamic rheological measurements agreed with the expected structural transitions associated with reacting sol–gel systems. The electrospinning sols exhibited shear-thinning behavior typical of a power law model. Ultrafine (200–300 nm diameter) fibers were produced at early and late times within the reaction window of approximately one hour from initial mixing of sol solutions with and without enzyme; diameter distributions of these fibers showed much smaller deviations than expected. The enzyme markedly increased magnitudes of both elastic and viscous moduli but had no significant impact on final fiber diameters, suggesting that the shear-thinning behavior of both sol–gel mixtures is dominant in the fiber elongation process. The time course and scale for the electrospinning batch fabrication show strong correlations between the magnitudes in rheological property changes over time and the chemical functional group evolution obtained from micro-Raman time-series analysis of the reacting sol–gel systems. PMID:27877486

Well-posedness and exact controllability of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation

Directory of Open Access Journals (Sweden)

Ruili Wen

2016-08-01

Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.

Analytical solutions for systems of partial differential-algebraic equations.

Science.gov (United States)

Benhammouda, Brahim; Vazquez-Leal, Hector

2014-01-01

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

A diagrammatic description of the equations of motion, current and noise within the second-order von Neumann approach

International Nuclear Information System (INIS)

Karlström, O; Pedersen, J N; Bergenfeldt, C; Samuelsson, P; Wacker, A; Emary, C; Zedler, P; Brandes, T

2013-01-01

We investigate the second-order von Neumann approach from a diagrammatic point of view and demonstrate its equivalence with the resonant tunneling approximation. The investigation of higher order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough comparison sheds light on the validity of all these self-consistent second-order approaches. We analyze the discrepancy between the noise calculated by our method and the exact Levitov formula for a simple non-interacting quantum dot model. Furthermore, we study the noise of the canyon of current suppression in a two-level dot, a phenomenon that requires the inclusion of electron–electron interaction as well as higher order tunneling processes. (paper)

Exact boundary controllability for a series of membranes elastically connected

Directory of Open Access Journals (Sweden)

Waldemar D. Bastos

2017-01-01

Full Text Available In this article we study the exact controllability with Neumann boundary controls for a system of linear wave equations coupled in parallel by lower order terms on piecewise smooth domains of the plane. We obtain square integrable controls for initial state with finite energy and time of controllability near the optimal value.

Effect of Hofmeister series salts on Absorptivity of aqueous solutions on Sodium polyacrylate

Science.gov (United States)

Korrapati, Swathi; Pullela, Phani Kumar; Vijayalakshmi, U.

2017-11-01

Sodium polyacrylate (SPA) is a popular super absorbent commonly used in children diapers, sanitary pads, adult diapers etc. The use of SPA is in force from past 30 years and the newer applications like as food preservant are evolving. SPA is recently discovered by our group for improvement of sensitivity of colorimetric agents. Though the discovery of improvement in sensitivity is phenomenal, the mechanism still remains a puzzle. A typical assay reagent contains colorimetric/fluorescent reagents, buffers, salts, stabilizers etc. These chemicals are known to influence the water absorptivity of SPA. If we were to perform chemical/biochemical assays on SPA absorbed reagents effect of salts and other excipients on colorimetric/fluorescence compounds absorbed on SPA is very important. The hofmeister series are standard for studying effect of salts on permeability, stability, aggregation, fluorescence quenching etc. We recently studied affect of urea, sodium chloride, ammonium sulfate, guanidine thiocayanate on fluorescence characteristics of fluorescence compounds and noted that except urea all other reagents have resulted in fluorescence quenching and urea had an opposite effect and increased the fluorescence intensity. This result was attributed to the different water structure around fluorescent in urea solution versus other chaotropic agents.

Homogenization of Portuguese long-term temperature data series: Lisbon, Coimbra and Porto

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A. L. Morozova

2012-12-01

Full Text Available Three long-term temperature data series measured in Portugal were studied to detect and correct non-climatic homogeneity breaks and are now available for future studies of climate variability.

Series of monthly minimum (T_min and maximum (T_max temperatures measured in the three Portuguese meteorological stations of Lisbon (from 1856 to 2008, Coimbra (from 1865 to 2005 and Porto (from 1888 to 2001 were studied to detect and correct non-climatic breaks. These series, together with monthly series of average temperature (T_aver and temperature range (DTR derived from them, were tested in order to detect breaks, using firstly metadata, secondly a visual analysis, and thirdly four widely used homogeneity tests: von Neumann ratio test, Buishand test, standard normal homogeneity test, and Pettitt test. The homogeneity tests were used in absolute (using temperature series themselves and relative (using sea-surface temperature anomalies series obtained from HadISST2.0.0.0 close to the Portuguese coast or already corrected temperature series as reference series modes. We considered the T_min, T_max and DTR series as most informative for the detection of breaks due to the fact that T_min and T_max could respond differently to changes in position of a thermometer or other changes in the instrument's environment; T_aver series have been used mainly as control.

The homogeneity tests showed strong inhomogeneity of the original data series, which could have both internal climatic and non-climatic origins. Breaks that were identified by the last three mentioned homogeneity tests were compared with available metadata containing data such as instrument changes, changes in station location and environment, observation procedures, etc. Significant breaks (significance 95% or more that coincided with known dates of

The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation

KAUST Repository

Aguareles, M.

2014-06-01

In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.

The Peano-series solution for modeling shear horizontal waves in piezoelectric plates

Directory of Open Access Journals (Sweden)

Ben Ghozlen M.H.

2012-06-01

Full Text Available The shear horizontal (SH wave devices have been widely used in electroacoustic. To improve their performance, the phase velocity dispersion and the electromechanical coupling coefficient of the Lamb wave should be calculated exactly in the design. Therefore, this work is to analyze exactly the Lamb waves polarized in the SH direction in homogeneous plate pie.zoelectric material (PZT-5H. An alternative method is proposed to solve the wave equation in such a structure without using the standard method based on the electromechanical partial waves. This method is based on an analytical solution, the matricant explicitly expressed under the Peano series expansion form. Two types of configuration have been addressed, namely the open circuited and the short circuited. Results confirm that the SH wave provides a number of attractive properties for use in sensing and signal processing applications. It has been found that the phase velocity remains nearly constant for all values of h/λ (h is the plate thickness, λ the acoustic wavelength. Secondly the SH0 wave mode can provide very high electromechanical coupling. Graphical representations of electrical and mechanical amounts function of depth are made, they are in agreement with the continuity rules. The developed Peano technique is in agreement with the classical approach, and can be suitable with cylindrical geometry.

Neumann aitab rahvuskaaslased maailma turule / Kati Murutar

Index Scriptorium Estoniae

Murutar, Kati, 1967-

2009-01-01

Norras elava rahvusvahelise äri spetsialisti Indrek Michael Neumanni firma Progate Trade International Business Consulting and Solution annab Eesti ettevõtjatele nõuandeid rahvusvahelisele turule sisenemiseks

LABOUR TAXATION: FORMAL AND INFORMAL SOLUTIONS

Directory of Open Access Journals (Sweden)

Ioana Maria Costea

2012-11-01

Full Text Available The present study aims to create a panorama of doctrinal, legal and jurisprudential solutions, which determine the heterogeneity of labour market’s fiscal hypotheses’. The study identifies a progressive series of interactions between economic and social factors, which generate at the juridical level a specific series of fiscal solutions, both traditional and innovating for the qualification and taxation of labour revenues. Heterogeneity of working forms is presently a complex, main direction in business with effects both at economic and legal level. This study provides an overview of statutory and case-law solutions for the legal classification and therefore tax classification of personal income.

Data completion problems solved as Nash games

International Nuclear Information System (INIS)

Habbal, A; Kallel, M

2012-01-01

The Cauchy problem for an elliptic operator is formulated as a two-player Nash game. Player (1) is given the known Dirichlet data, and uses as strategy variable the Neumann condition prescribed over the inaccessible part of the boundary. Player (2) is given the known Neumann data, and plays with the Dirichlet condition prescribed over the inaccessible boundary. The two players solve in parallel the associated Boundary Value Problems. Their respective objectives involve the gap between the non used Neumann/Dirichlet known data and the traces of the BVP's solutions over the accessible boundary, and are coupled through a difference term. We prove the existence of a unique Nash equilibrium, which turns out to be the reconstructed data when the Cauchy problem has a solution. We also prove that the completion algorithm is stable with respect to noise, and present two 3D experiments which illustrate the efficiency and stability of our algorithm.

Expansion of Sobolev functions in series in Laguerre polynomials

International Nuclear Information System (INIS)

Selyakov, K.I.

1985-01-01

The solution of the integral equation for the Sobolev functions is represented in the form of series in Laguerre polynomials. The coefficients of these series are simultaneously the coefficients of the power series for the Ambartsumyan-Chandrasekhar H functions. Infinite systems of linear algebraic equations with Toeplitz matrices are given for the coefficients of the series. Numerical results and approximate expressions are given for the case of isotropic scattering

Combinatorial algebra syntax and semantics

CERN Document Server

Sapir, Mark V

2014-01-01

Combinatorial Algebra: Syntax and Semantics provides a comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of  more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about the growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata.   With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified...

Extending "the Rubber Rope": Convergent Series, Divergent Series and the Integrating Factor

Science.gov (United States)

McCartney, Mark

2013-01-01

A well-known mathematical puzzle regarding a worm crawling along an elastic rope is considered. The resulting generalizations provide examples for use in a teaching context including applications of series summation, the use of the integrating factor for the solution of differential equations, and the evaluation of definite integrals. A number of…

Nonlinear reflection of shock shear waves in soft elastic media.

Science.gov (United States)

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

The use of synthetic input sequences in time series modeling

International Nuclear Information System (INIS)

Oliveira, Dair Jose de; Letellier, Christophe; Gomes, Murilo E.D.; Aguirre, Luis A.

2008-01-01

In many situations time series models obtained from noise-like data settle to trivial solutions under iteration. This Letter proposes a way of producing a synthetic (dummy) input, that is included to prevent the model from settling down to a trivial solution, while maintaining features of the original signal. Simulated benchmark models and a real time series of RR intervals from an ECG are used to illustrate the procedure

A parallel implementation of the ghost-cell immersed boundary ...

Indian Academy of Sciences (India)

S Peter

cylinder. Keywords. Taylor series; inverse distance weighting; Neumann boundary condition; ... Kim et al [4], for controlling the production of spurious force ..... continuously increases with a because of the Magnus effect. 7. Conclusions.

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

Directory of Open Access Journals (Sweden)

U. Filobello-Nino

2015-01-01

Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

Science.gov (United States)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

Modeling Taylor series approximations for prompt neutron kinetics with lab view simulations

International Nuclear Information System (INIS)

Adzri, E. P.

2012-09-01

The reactor point kinetics equations have been subjected to intense research in an effort to find simple yet accurate numerical solutions methods. The equations are very stiff numerically, meaning that there is a wide variation in the decay constants, so that using a particular time step in the numerical solution may provide sufficient accuracy for the group, but not for another. Several solutions techniques have been presented on the point kinetics equations with varying degrees of complexity. These include Power Series Solutions, CORE, PCA, Genapol and Taylor series methods. In this research, algorithms were developed based on the first and second order Taylor series expansion and simulated in LabVIEW to solve the Reactor Point Kinetics equations using block diagram nodes implemented within stacked sequences. The algorithms developed were fast,accurate and simple to code. Several reactivity insertions were used to simulate the change in neutron population with time. The LabVIEW- Taylor series solutions were compared with other solution techniques such as Power Series Solutions, CORE, PCA, Genapol and McMahon and Pierson's Taylor series approximation. The results of LabVIEW-Taylor series technique used by McMahon and Pearson The LabVIEW-implemented techniques were found to agree very well with these other methods. At 1x10 -8 s the neutron population was 1.000220 neutrons / cm 3 , at 1 x 10 -2 s it was 2.007681 neutrons / cm 3 and at 1x10 -1 s it was 2.075317 neutrons / cm 3 ; same results reported by Genapol for a fast reactor, it produced good and accurate results and compared very favorably with other methods found in the literature. Using much smaller time steps to the order or 10 -8 s commensurate with fast reactor parameters also produced very satisfactory results, indicating that the LabVIEW-based Taylor series technique is suitable for simulating the kinetics of fast reactors as well as thermal reactors. Algorithms developed that included second order terms

Computation of solar perturbations with Poisson series

Science.gov (United States)

Broucke, R.

1974-01-01

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

On a novel matrix method for three-dimensional photoelasticity

International Nuclear Information System (INIS)

Theocaris, P.S.; Gdoutos, E.E.

1978-01-01

A non-destructive method for the photoelastic determination of three-dimensional stress distributions, based on the Mueller and Jones calculi, is developed. The differential equations satisfied by the Stokes and Jones vectors, when a polarized light beam passes through a photoelastic model, presenting rotation of the secondary principal stress directions, are established in matrix form. The Peano-Baker method is used for the solution of these differential equations in a matrix series form, establishing the elements of the Mueller and Jones matrices of the photoelastic model. These matrices are experimentally determined by using different wavelengths in conjunction with Jones' 'equivalence theorem'. The Neumann equations are immediately deduced from the above-mentioned differential equations. (orig.) [de

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Residual power series method for fractional Sharma-Tasso-Olever equation

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Amit Kumar

2016-02-01

Full Text Available In this paper, we introduce a modified analytical approximate technique to obtain solution of time fractional Sharma-Tasso-Olever equation. First, we present an alternative framework of the Residual power series method (RPSM which can be used simply and effectively to handle nonlinear fractional differential equations arising in several physical phenomena. This method is basically based on the generalized Taylor series formula and residual error function. A good result is found between our solution and the given solution. It is shown that the proposed method is reliable, efficient and easy to implement on all kinds of fractional nonlinear problems arising in science and technology.

Hydration patterns and salting effects in sodium chloride solution.

Science.gov (United States)

Li, Weifeng; Mu, Yuguang

2011-10-07

The salting effects of 2M sodium chloride electrolyte are studied based on a series of model solutes with properties ranging from hydrophobic to hydrophilic. Generally, hydrophobic solutes will be salted out and hydrophilic solutes will be salted in by NaCl solution. The solvation free energy changes are highly correlated with Kirkwood-Buff integrals. The underlying mechanism resorts to the preferential binding of ions and water to solutes. Our results demonstrate that the salting effect not only depends on the salt's position in Hofmeister series, but also on the solutes' specifics. Taking the hydration free energies of solutes and ions as independent variables, a schematic diagram of salting effects is suggested. The resolved multifaceted salting effects rely on the sensitive balance of the tripartite interaction among solutes, ions, and water. © 2011 American Institute of Physics

Une méthode de calcul par éléments finis de la résistence de vague des corps flottants ou immergés en théorie linéaire A Finite Elements Method for Computing the Resistance of Floating Or Submerged Bodies to Wave Action Using a Linear Theory

Directory of Open Access Journals (Sweden)

Cariou A.

2006-11-01

Full Text Available Pour calculer le potentiel de l'écoulement autour d'un corps en mouvement rectiligne uniforme, soit en fluide illimité (engin sous-marin, soit sur une mer infinie (corps flottant ou voisin de la surface libre, on se place dans le cadre du problème de Neumann extérieur ou du problème de Neumann Kelvin. Pour résoudre ces problèmes on se propose de délimiter autour de la carène un domaine fluide fini (,ri dont les frontières sont : la carène (SC, une surface (SE entourant la carène et éventuellement la portion de surface libre (SI. limitée par les lignes de flottaison de SC et SE. La solution à l'intérieur de (,ri est déterminée à l'aide d'une méthode d'éléments finis et elle est raccordée à la solution en domaine infini elle-même calculée grâce aux fonctions de Green du problème (ou solutions élémentaires. For computing the flow potential around a body in uniform rectilinear movement, either in an unlimited fluid (subsea croft or on an infinite sea (body floating near the free surface, consideration must be given ta the outside Neumann problem or ta the Neumann Kelvin problem. Ta solve these problems, this article proposes ta delimit a finite fluid realm (T: around the body. The limits of this realm are: I the body (SC, 2 a surface (SE surrounding the body, and eventually 3 the portion of free surface (SU bounded by the waterlines of SC and SE. The solution within iri is determined by a finite elements method, and it is related ta the solution in on infinite realm which in turn is computed by the Green functions of the problem (or elementary solutions.

Bernstein Series Solution of a Class of Lane-Emden Type Equations

Directory of Open Access Journals (Sweden)

Osman Rasit Isik

2013-01-01

Full Text Available The purpose of this study is to present an approximate solution that depends on collocation points and Bernstein polynomials for a class of Lane-Emden type equations with mixed conditions. The method is given with some priori error estimate. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit n which gives a better result in any norm. Finally, the effectiveness of the method is illustrated by some numerical experiments. Numerical results are consistent with the theoretical results.

Series expansion solution of the Wegner-Houghton renormalisation group equation

International Nuclear Information System (INIS)

Margaritis, A.; Odor, G.; Patkos, A.

1987-11-01

The momentum independent projection of the Wegner-Houghton renormalisation group equation is solved with power series expansion. Convergence rate is analyzed for the n-vector model. Further evidence is presented for the first order nature of the chiral symmetry restoration at finite temperature in QCD with 3 light flavors. (author) 16 refs

Early-Time Solution of the Horizontal Unconfined Aquifer in the Buildup Phase

Science.gov (United States)

Gravanis, Elias; Akylas, Evangelos

2017-10-01

We derive the early-time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

Transition from Endothermic to Exothermic Dissolution of Hydroxyapatite Ca5(PO43OH–Johnbaumite Ca5(AsO43OH Solid Solution Series at Temperatures Ranging from 5 to 65 °C

Directory of Open Access Journals (Sweden)

Bartosz Puzio

2018-06-01

Full Text Available Five crystalline members of the hydroxyapatite (HAP; Ca5(PO43OH–johnbaumite (JBM; Ca5(AsO43OH series were crystallized at alkaline pH from aqueous solutions and used in dissolution experiments at 5, 25, 45, and 65 °C. Equilibrium was established within three months. Dissolution was slightly incongruent, particularly at the high-P end of the series. For the first time, the Gibbs free energy of formation ΔGf0, enthalpy of formation ΔHf0, entropy of formation Sf0, and specific heat of formation Copf were determined for HAP–JBM solid solution series. Based on the dissolution reaction, Ca5(AsO4m(PO43−mOH = 5Ca2+(aq + mAsO43−(aq + (3 − mPO43−(aq + OH−(aq, their solubility product Ksp,298.15 was determined. Substitution of arsenic (As for phosphorus (P in the structure of apatite resulted in a linear increase in the value of Ksp: from HAP logKsp,298.15 = −57.90 ± 1.57 to JBM logKsp,298.15 = −39.22 ± 0.56. The temperature dependence of dissolution in this solid solution series is very specific; in the temperature range of 5 °C to 65 °C, the enthalpy of dissolution ΔHr varied around 0. For HAP, the dissolution reaction at 5 °C and 25 °C was endothermic, which transitioned at around 40 °C and became exothermic at 45 °C and 65 °C.

A new analytical solution to the diffusion problem: Fourier series ...

African Journals Online (AJOL)

This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.

Rayleigh-Schrödinger series and Birkhoff decomposition

Science.gov (United States)

Novelli, Jean-Christophe; Paul, Thierry; Sauzin, David; Thibon, Jean-Yves

2018-01-01

We derive new expressions for the Rayleigh-Schrödinger series describing the perturbation of eigenvalues of quantum Hamiltonians. The method, somehow close to the so-called dimensional renormalization in quantum field theory, involves the Birkhoff decomposition of some Laurent series built up out of explicit fully non-resonant terms present in the usual expression of the Rayleigh-Schrödinger series. Our results provide new combinatorial formulae and a new way of deriving perturbation series in quantum mechanics. More generally we prove that such a decomposition provides solutions of general normal form problems in Lie algebras.

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

OpenAIRE

Elsaid, A.; Abdel Latif, M. S.; Maneea, M.

2016-01-01

Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on ...

On polynomial solutions of the Heun equation

International Nuclear Information System (INIS)

Gurappa, N; Panigrahi, Prasanta K

2004-01-01

By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)

Solving eigenvalue problems on curved surfaces using the Closest Point Method

KAUST Repository

Macdonald, Colin B.; Brandman, Jeremy; Ruuth, Steven J.

2011-01-01

defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples

An introduction to Fourier series and integrals

CERN Document Server

Seeley, Robert T

2006-01-01

This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.

Stability of twisted rods, helices and buckling solutions in three dimensions

KAUST Repository

Majumdar, Apala; Raisch, Alexander

2014-01-01

© 2014 IOP Publishing Ltd & London Mathematical Society. We study stability problems for equilibria of a naturally straight, inextensible, unshearable Kirchhoff rod allowed to deform in three dimensions (3D), subject to terminal loads. We investigate the stability of the twisted, straight state in 3D for three different boundary-value problems, cast in terms of Dirichlet and Neumann boundary conditions for the Euler angles, with and without isoperimetric constraints. In all cases, we obtain explicit stability estimates in terms of the twist, external load and elastic constants and in the Dirichlet case, we compute bifurcation diagrams for the Euler angles as a function of the external load. In the same vein, we obtain explicit stability estimates for a family of prototypical helical equilibria in 3D and demonstrate that they are stable for a range of tensile and compressive forces. We propose a numerical L2-gradient flow model to study the stability and dynamical evolution (in viscous model situations) of Kirchhoff rod equilibria. In Nizette and Goriely 1999 J. Math. Phys. 40 2830-66, the authors construct a family of localized buckling solutions. We apply our L2-gradient flow model to these localized buckling solutions, demonstrate that they are unstable, study their evolution and the simulations demonstrate rich spatio oral patterns that strongly depend on the boundary conditions and imposed isoperimetric constraints.

Stability of twisted rods, helices and buckling solutions in three dimensions

KAUST Repository

Majumdar, Apala

2014-11-03

© 2014 IOP Publishing Ltd & London Mathematical Society. We study stability problems for equilibria of a naturally straight, inextensible, unshearable Kirchhoff rod allowed to deform in three dimensions (3D), subject to terminal loads. We investigate the stability of the twisted, straight state in 3D for three different boundary-value problems, cast in terms of Dirichlet and Neumann boundary conditions for the Euler angles, with and without isoperimetric constraints. In all cases, we obtain explicit stability estimates in terms of the twist, external load and elastic constants and in the Dirichlet case, we compute bifurcation diagrams for the Euler angles as a function of the external load. In the same vein, we obtain explicit stability estimates for a family of prototypical helical equilibria in 3D and demonstrate that they are stable for a range of tensile and compressive forces. We propose a numerical L2-gradient flow model to study the stability and dynamical evolution (in viscous model situations) of Kirchhoff rod equilibria. In Nizette and Goriely 1999 J. Math. Phys. 40 2830-66, the authors construct a family of localized buckling solutions. We apply our L2-gradient flow model to these localized buckling solutions, demonstrate that they are unstable, study their evolution and the simulations demonstrate rich spatio oral patterns that strongly depend on the boundary conditions and imposed isoperimetric constraints.

Transmission Line Series Compensation for Wind Energy Transmission

International Nuclear Information System (INIS)

Palanichamy, C; Wong, Y C

2015-01-01

Wind energy has demonstrated to be a clean, copious and absolutely renewable source of energy, and the large penetration of it into the power grid indicates that wind energy is considered an effective means of power generation, Transmission of wind energy from remote locations to load centers necessitates long transmission lines. Series compensation is a proven and economical transmission solution to address system power transfer strength, grid stability, and voltage profile issues of long transmission lines. In this paper, a programmable approach to determine the capacitive reactance of series capacitor and optimum location for its placement to achieve maximum power transfer gas been presented. The respective program with sample solutions has been provided for real-time applications. (paper)

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

Science.gov (United States)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Efficient two-level preconditionined conjugate gradient method on the GPU

NARCIS (Netherlands)

Gupta, R.; Van Gijzen, M.B.; Vuik, K.

2011-01-01

We present an implementation of Two-Level Preconditioned Conjugate Gradient Method for the GPU. We investigate a Truncated Neumann Series based preconditioner in combination with deflation and compare it with Block Incomplete Cholesky schemes. This combination exhibits fine-grain parallelism and

A multiple-scale power series method for solving nonlinear ordinary differential equations

Directory of Open Access Journals (Sweden)

Chein-Shan Liu

2016-02-01

Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

Convergent WKB Series--How Can It be ?

International Nuclear Information System (INIS)

Ezawa, Hiroshi; Nakamura, Toru; Watanabe, Keiji

2008-01-01

Schroedinger equation for a polynomial potential with the highest order term having an even power and a positive coefficient is solved for high eigenvalues E n in two different ways after Liouville transformation, (a) converting the differential equation into integral equation and solving it iteratively and (b) by the WKB method. While the series solution in powers of 1/√(E n ) from (b) is known to diverge, we show that the one from (a) converges. We show then that asymptotic re-expansion of the convergent series from (a) agrees with the divergent series from (b). Actually, we have been able to show the agreement only up to order (1/√(E n )) 5 , but we believe that it holds to all orders. If this is true, the divergent WKB series can be reorganized into a convergent series, which is in fact obtained by the method of iteration (a)

General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere

Energy Technology Data Exchange (ETDEWEB)

Bayat, Yahya; EkhteraeiToussi, THamid [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of)

2015-06-15

A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.

Patchy proteins, anions and the Hofmeister series

Energy Technology Data Exchange (ETDEWEB)

Lund, Mikael; Jungwirth, Pavel [Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo namesti 2, 16610 Prague 6 (Czech Republic); Center for Complex Molecular Systems and Biomolecules, Flemingovo namesti 2, 16610 Prague 6 (Czech Republic)], E-mail: mikael.lund@uochb.cas.cz

2008-12-10

We investigate specific anion binding to a range of patchy protein models and use our results to probe protein-protein interactions for aqueous lysozyme solutions. Our molecular simulation studies show that the ion-protein interaction mechanism and strength largely depend on the nature of the interfacial amino acid residues. Via direct ion pairing, small anions interact with charged side-chains while larger anions are attracted to non-polar residues due to several solvent assisted mechanisms. Incorporating ion and surface specificity into a mesoscopic model for protein-protein interactions we calculate the free energy of interaction between lysozyme molecules in aqueous solutions of sodium chloride and sodium iodide. In agreement with experiment, our finding is that 'salting out' follows the reverse Hofmeister series for pH below the iso-electric point and the direct series for pH above pI.

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

Science.gov (United States)

Scott, James R.; Martini, Michael C.

2010-01-01

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body

Approximate variational solutions of the Grad-Shafranov equation

International Nuclear Information System (INIS)

Ludwig, G.O.

2001-01-01

Approximate solutions of the Grad-Schlueter-Shafranov equation based on variational methods are developed. The power series solutions of the Euler-Lagrange equations for equilibrium are compared with direct variational results for a low aspect ratio tokamak equilibrium. (author)

Computer local construction of a general solution for the Chew-Low equations

International Nuclear Information System (INIS)

Gerdt, V.P.

1980-01-01

General solution of the dynamic form of the Chew-Low equations in the vicinity of the restpoint is considered. A method for calculating coefficients of series being members of such solution is suggested. The results of calculations, coefficients of power series and expansions carried out by means of the SCHOONSCHIP and SYMBAL systems are given. It is noted that the suggested procedure of the Chew-Low equation solutions basing on using an electronic computer as an instrument for analytical calculations permits to obtain detail information on the local structure of general solution

Characterization of the LAWB99-series and ORLEC-series Glasses

Energy Technology Data Exchange (ETDEWEB)

Fox, K. M. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Edwards, T. B. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Riley, W. T. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

2017-12-01

In this report, the Savannah River National Laboratory provides chemical analysis results for a series of simulated low activity waste (LAW) glass compositions. These data will be used in the development of improved sulfur solubility models for LAW glass. A procedure developed at the Pacific Northwest National Laboratory for producing sulfur saturated melts (SSMs) was used to fabricate the glasses characterized in this report. This method includes triplicate melting steps with excess sodium sulfate, followed by grinding and washing to remove unincorporated sulfur salts. The wash solutions were also analyzed as part of this study.

New solutions of Heun's general equation

International Nuclear Information System (INIS)

Ishkhanyan, Artur; Suominen, Kalle-Antti

2003-01-01

We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.

Thermal boundary condition effects on forced convection heat transfer. Application of a numerical solution of an adjoint problem; Kyosei tairyu netsudentatsu mondai ni okeru netsuteki kyokai joken no eikyo. Zuihan mondai no suchi kai wo mochiita kosatsu

Energy Technology Data Exchange (ETDEWEB)

Momose, K.; Saso, K.; Kimoto, H. [Osaka University, Osaka (Japan). Faculty of Engineering Science

1997-11-25

We propose a numerical solution for the adjoint operator of a forced convection heat transfer problem to evaluate mean heat transfer characteristics under arbitrary thermal conditions. Using the numerical solutions of the adjoint problems under Dirichlet and Neumann conditions, both of which can be computed using a conventional CFD code, the influence function of the local surface temperature on the total heat transfer and that of the local surface heat flux on the mean surface temperature are obtained. As a result, the total heat fluxes for arbitrary surface temperature distributions and the mean surface temperatures for arbitrary surface heat flux distributions can be calculated using these influence functions. The influence functions for a circular cylinder and for an in-line square rod array are presented. 14 refs., 9 figs., 1 tab.

Vibrational spectra of solid solution series with ordered perovskite structure

NARCIS (Netherlands)

Blasse, G.

I.R. and Raman spectra are reported for the following three systems: Ba2CaMo1−xTexO6, Ba2−xSrxMgWO6 and Ba2Ca1−xMgxWO6. In the first series the internal vibrations of the M6+O6 octahedra do not influence each other. The intensity of ν1 (MoO6) is five times that of ν1 (TeO6). In the second system

Inhomogeneities detection in annual precipitation time series in Portugal using direct sequential simulation

Science.gov (United States)

Caineta, Júlio; Ribeiro, Sara; Costa, Ana Cristina; Henriques, Roberto; Soares, Amílcar

2014-05-01

Climate data homogenisation is of major importance in monitoring climate change, the validation of weather forecasting, general circulation and regional atmospheric models, modelling of erosion, drought monitoring, among other studies of hydrological and environmental impacts. This happens because non-climate factors can cause time series discontinuities which may hide the true climatic signal and patterns, thus potentially bias the conclusions of those studies. In the last two decades, many methods have been developed to identify and remove these inhomogeneities. One of those is based on geostatistical simulation (DSS - direct sequential simulation), where local probability density functions (pdf) are calculated at candidate monitoring stations, using spatial and temporal neighbouring observations, and then are used for detection of inhomogeneities. This approach has been previously applied to detect inhomogeneities in four precipitation series (wet day count) from a network with 66 monitoring stations located in the southern region of Portugal (1980-2001). This study revealed promising results and the potential advantages of geostatistical techniques for inhomogeneities detection in climate time series. This work extends the case study presented before and investigates the application of the geostatistical stochastic approach to ten precipitation series that were previously classified as inhomogeneous by one of six absolute homogeneity tests (Mann-Kendall test, Wald-Wolfowitz runs test, Von Neumann ratio test, Standard normal homogeneity test (SNHT) for a single break, Pettit test, and Buishand range test). Moreover, a sensibility analysis is implemented to investigate the number of simulated realisations that should be used to accurately infer the local pdfs. Accordingly, the number of simulations per iteration is increased from 50 to 500, which resulted in a more representative local pdf. A set of default and recommended settings is provided, which will help

Comparative acid-base properties of the surface of components of the CdTe-ZnS system in series of substitutional solid solutions and their analogs

Science.gov (United States)

Kirovskaya, I. A.; Kasatova, I. Yu.

2011-07-01

The acid-base properties of the surface of solid solutions and binary components of the CdTe-ZnS system are studied by hydrolytic adsorption, nonaqueous conductometric titration, mechanochemistry, IR spectroscopy, and Raman scattering spectroscopy. The strength, nature, and concentration of acid centers on the original surface and that exposed to CO are determined. The changes in acid-base properties in dependence on the composition of the system under investigation in the series of CdB6, ZnB6 analogs are studied.

Double Fourier Series Solution of Poisson’s Equation on a Sphere.

Science.gov (United States)

1980-10-29

algebraic systems, the solution of these systems, and the inverse transform of the solution in Fourier space back to physi- cal space. 6. Yee, S. Y. K...Multiply each count in steps (2) through (5) by K] 7. Inverse transform um(0j j = 1, J - 1, to obtain u k; set u(P) = u 0 (P). [K(J - 1) log 2 K

Comparison of three Stark problem solution techniques for the bounded case

Science.gov (United States)

Hatten, Noble; Russell, Ryan P.

2015-01-01

Three methods of obtaining solutions to the Stark problem—one developed by Lantoine and Russell using Jacobi elliptic and related functions, one developed by Biscani and Izzo using Weierstrass elliptic and related functions, and one developed by Pellegrini, Russell, and Vittaldev using and Taylor series extended to the Stark problem—are compared qualitatively and quantitatively for the bounded motion case. For consistency with existing available code for the series solution, Fortran routines of the Lantoine method and Biscani method are newly implemented and made available. For these implementations, the Lantoine formulation is found to be more efficient than the Biscani formulation in the propagation of a single trajectory segment. However, for applications for which acceptable accuracy may be achieved by orders up to 16, the Pellegrini series solution is shown to be more efficient than either analytical method. The three methods are also compared in the propagation of sequentially connected trajectory segments in a low-thrust orbital transfer maneuver. Separate tests are conducted for discretizations between 8 and 96 segments per orbit. For the series solution, the interaction between order and step size leads to computation times that are nearly invariable to discretization for a given truncation error tolerance over the tested range of discretizations. This finding makes the series solution particularly attractive for mission design applications where problems may require both coarse and fine discretizations. Example applications include the modeling of low-thrust propulsion and time-varying perturbations—problems for which the efficient propagation of relatively short Stark segments is paramount because the disturbing acceleration generally varies continuously.

Optimal separable bases and series expansions

International Nuclear Information System (INIS)

Poirier, B.

1997-01-01

A method is proposed for the efficient calculation of the Green close-quote s functions and eigenstates for quantum systems of two or more dimensions. For a given Hamiltonian, the best possible separable approximation is obtained from the set of all Hilbert-space operators. It is shown that this determination itself, as well as the solution of the resultant approximation, is a problem of reduced dimensionality. Moreover, the approximate eigenstates constitute the optimal separable basis, in the sense of self-consistent field theory. The full solution is obtained from the approximation via iterative expansion. In the time-independent perturbation expansion for instance, all of the first-order energy corrections are zero. In the Green close-quote s function case, we have a distorted-wave Born series with optimized convergence properties. This series may converge even when the usual Born series diverges. Analytical results are presented for an application of the method to the two-dimensional shifted harmonic-oscillator system, in the course of which the quantum tanh 2 potential problem is solved exactly. The universal presence of bound states in the latter is shown to imply long-lived resonances in the former. In a comparison with other theoretical methods, we find that the reaction path Hamiltonian fails to predict such resonances. copyright 1997 The American Physical Society

Irradiation effects on electrical properties of DNA solution/Al Schottky diodes

Science.gov (United States)

Al-Ta'ii, Hassan Maktuff Jaber; Periasamy, Vengadesh; Iwamoto, Mitsumasa

2018-04-01

Deoxyribonucleic acid (DNA) has emerged as one of the most exciting organic material and as such extensively studied as a smart electronic material since the last few decades. DNA molecules have been reported to be utilized in the fabrication of small-scaled sensors and devices. In this current work, the effect of alpha radiation on the electrical properties of an Al/DNA/Al device using DNA solution was studied. It was observed that the carrier transport was governed by electrical interface properties at the Al-DNA interface. Current ( I)-voltage ( V) curves were analyzed by employing the interface limited Schottky current equations, i.e., conventional and Cheung and Cheung's models. Schottky parameters such as ideality factor, barrier height and series resistance were also determined. The extracted barrier height of the Schottky contact before and after radiation was calculated as 0.7845, 0.7877, 0.7948 and 0.7874 eV for the non-radiated, 12, 24 and 36 mGy, respectively. Series resistance of the structure was found to decline with the increase in the irradiation, which was due to the increase in the free radical root effects in charge carriers in the DNA solution. Results pertaining to the electronic profiles obtained in this work may provide a better understanding for the development of precise and rapid radiation sensors using DNA solution.

Exact Solutions of the Harry-Dym Equation

International Nuclear Information System (INIS)

Mokhtari, Reza

2011-01-01

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation. (general)

Application of polynomial preconditioners to conservation laws

NARCIS (Netherlands)

Geurts, Bernardus J.; van Buuren, R.; Lu, H.

2000-01-01

Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of

Wave scattering theory a series approach based on the Fourier transformation

CERN Document Server

Eom, Hyo J

2001-01-01

The book provides a unified technique of Fourier transform to solve the wave scattering, diffraction, penetration, and radiation problems where the technique of separation of variables is applicable. The book discusses wave scattering from waveguide discontinuities, various apertures, and coupling structures, often encountered in electromagnetic, electrostatic, magnetostatic, and acoustic problems. A system of simultaneous equations for the modal coefficients is formulated and the rapidly-convergent series solutions amenable to numerical computation are presented. The series solutions find practical applications in the design of microwave/acoustic transmission lines, waveguide filters, antennas, and electromagnetic interference/compatibilty-related problems.

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

Science.gov (United States)

2015-07-09

227 (2008): 8820–8840. [13] Jerison, David S., and Carlos E. Kenig. “The Neumann Problem on Lipschitz Do- mains.” B. Am. Math. Soc. 4.2 (1981): 203–207...J. Numer. Anal. 33.3 (1996): 971–996. [17] Markushevich, A. I. Complex analysis. 2nd ed. Trans. Richard A. Silverman . New York: Chelsea Publishing

Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

CSIR Research Space (South Africa)

Fedotov, I

2006-07-01

Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...

Divergent series, summability and resurgence II simple and multiple summability

CERN Document Server

Loday-Richaud, Michèle

2016-01-01

Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and res...

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

Science.gov (United States)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

Semianalytic Solution of Space-Time Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

SPLINE-FUNCTIONS IN THE TASK OF THE FLOW AIRFOIL PROFILE

Directory of Open Access Journals (Sweden)

Mikhail Lopatjuk

2013-12-01

Full Text Available The method and the algorithm of solving the problem of streamlining are presented. Neumann boundary problem is reduced to the solution of integral equations with given boundary conditions using the cubic spline-functions

Exploration of polyelectrolytes as draw solutes in forward osmosis processes

KAUST Repository

Ge, Qingchun

2012-03-01

The development of the forward osmosis (FO) process has been constrained by the slow development of appropriate draw solutions. Two significant concerns related to draw solutions are the draw solute leakage and intensiveenergy requirement in recycling draw solutes after the FO process. FO would be much attractive if there is no draw solute leakage and the recycle of draw solutes is easy and economic. In this study, polyelectrolytes of a series of polyacrylic acid sodium salts (PAA-Na), were explored as draw solutes in the FO process. The characteristics of high solubility in water and flexibility in structural configuration ensure the suitability of PAA-Na as draw solutes and their relative ease in recycle through pressure-driven membrane processes. The high water flux with insignificant salt leakage in the FO process and the high salt rejection in recycle processes reveal the superiority of PAA-Na to conventional ionic salts, such as NaCl, when comparing their FO performance via the same membranes. The repeatable performance of PAA-Na after recycle indicates the absence of any aggregation problems. The overall performance demonstrates that polyelectrolytes of PAA-Na series are promising as draw solutes, and the new concept of using polyelectrolytes as draw solutes in FO processes is applicable. © 2011 Elsevier Ltd.

An introduction to Laplace transforms and Fourier series

CERN Document Server

Dyke, Phil

2014-01-01

Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...

The kinematical AdS{sub 5}×S{sup 5} Neumann coefficient

Energy Technology Data Exchange (ETDEWEB)

Bajnok, Zoltan [MTA Lendület Holographic QFT Group, Wigner Research Centre,P.O.B. 49, Budapest 114, H-1525 (Hungary); Janik, Romuald A. [Institute of Physics, Jagiellonian University,ul. Łojasiewicza 11, Kraków, 30-348 (Poland)

2016-02-22

For the case of two particles a solution of the string field theory vertex axioms can be factorized into a standard form factor and a kinematical piece which includes the dependence on the size of the third string. In this paper we construct an exact solution of the kinematical axioms for AdS{sub 5}×S{sup 5} which includes all order wrapping corrections w.r.t. the size of the third string. This solution is expressed in terms of elliptic Gamma functions and ordinary elliptic functions. The solution is valid at any coupling and we analyze its weak coupling, pp-wave and large L limit.

PhilDB: the time series database with built-in change logging

Directory of Open Access Journals (Sweden)

Andrew MacDonald

2016-03-01

Full Text Available PhilDB is an open-source time series database that supports storage of time series datasets that are dynamic; that is, it records updates to existing values in a log as they occur. PhilDB eases loading of data for the user by utilising an intelligent data write method. It preserves existing values during updates and abstracts the update complexity required to achieve logging of data value changes. It implements fast reads to make it practical to select data for analysis. Recent open-source systems have been developed to indefinitely store long-period high-resolution time series data without change logging. Unfortunately, such systems generally require a large initial installation investment before use because they are designed to operate over a cluster of servers to achieve high-performance writing of static data in real time. In essence, they have a ‘big data’ approach to storage and access. Other open-source projects for handling time series data that avoid the ‘big data’ approach are also relatively new and are complex or incomplete. None of these systems gracefully handle revision of existing data while tracking values that change. Unlike ‘big data’ solutions, PhilDB has been designed for single machine deployment on commodity hardware, reducing the barrier to deployment. PhilDB takes a unique approach to meta-data tracking; optional attribute attachment. This facilitates scaling the complexities of storing a wide variety of data. That is, it allows time series data to be loaded as time series instances with minimal initial meta-data, yet additional attributes can be created and attached to differentiate the time series instances when a wider variety of data is needed. PhilDB was written in Python, leveraging existing libraries. While some existing systems come close to meeting the needs PhilDB addresses, none cover all the needs at once. PhilDB was written to fill this gap in existing solutions. This paper explores existing time

Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method

Directory of Open Access Journals (Sweden)

Shaheed N. Huseen

2013-01-01

Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

International Nuclear Information System (INIS)

Darmani, G.; Setayeshi, S.; Ramezanpour, H.

2012-01-01

In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

Distributions of traces of metals on sorption from solutions of vanadium(V)

International Nuclear Information System (INIS)

Evseeva, N.K.; Turnaov, A.N.; Telegin, G.F.; Kremenskaya, I.N.

1983-01-01

A study is made of the distributions of traces of metals between aqueous solutions of vanadium(V) and a solid reagent made by introducing di-2-ethylhexylphosphoric acid into an inert matrix: a nonionic macroporous copolymer of polystyrene with divinyl benzene (wofatit Y 29). As regards degree of extraction, the trace components fall in the series zinc > cadmium > manganese > copper > cobalt, which resemble the extractability series. The vanadium content of the solution and the concentrations of the trace components have virtually no effect on the sorption. The process is effective in concentrating trace components from solutions containing vanadium(V)

Distribution of microimpurities of metals at their sorption from vanadium (5) solutions

International Nuclear Information System (INIS)

Evseeva, N.K.; Turanov, A.N.; Telegin, G.F.; Kremenskaya, I.N.

1983-01-01

Distribution of metal microimpurities (Zn, Mn, Cu, Co, Fe) between aqueous solutions of vanadium (5) and solid extracting agent, prepared by means of introduction of di-2-ethylhexylphosphoric acid into inert matrix-nonionogeneous macropore copolymer of polystyrene with divinylbenzene (vofatit Y-29), has been studied. Accroding to the degree of extraction the microimpurities are arranged in the series: zinc > cadmium > manganese > copper > cobalt, which is similar to the series of extractability. Vanadium content in solution and concentration of microimpurities practically does not affect the sorption. It has been established that the process is effective for microimpurities concentration from solutions containing vanadium (5)

Distribution of microimpurities of metals at their sorption from vanadium (5) solutions

Energy Technology Data Exchange (ETDEWEB)

Evseeva, N.K.; Turanov, A.N.; Telegin, G.F.; Kremenskaya, I.N.

1983-01-01

Distribution of metal microimpurities (Zn, Mn, Cu, Co, Fe) between aqueous solutions of vanadium (5) and solid extracting agent, prepared by means of introduction of di-2-ethylhexylphosphoric acid into inert matrix-nonionogeneous macropore copolymer of polystyrene with divinylbenzene (vofatit Y-29), has been studied. According to the degree of extraction the microimpurities are arranged in the series: zinc > cadmium > manganese > copper > cobalt, which is similar to the series of extractability. Vanadium content in solution and concentration of microimpurities practically does not affect the sorption. It has been established that the process is effective for microimpurities concentration from solutions containing vanadium (5).

Neoclassical Solution of Transient Interaction of Plane Acoustic Waves with a Spherical Elastic Shell

Directory of Open Access Journals (Sweden)

Hanson Huang

1996-01-01

Full Text Available A detailed solution to the transient interaction of plane acoustic waves with a spherical elastic shell was obtained more than a quarter of a century ago based on the classical separation of variables, series expansion, and Laplace transform techniques. An eight-term summation of the time history series was sufficient for the convergence of the shell deflection and strain, and to a lesser degree, the shell velocity. Since then, the results have been used routinely for validation of solution techniques and computer methods for the evaluation of underwater explosion response of submerged structures. By utilizing modern algorithms and exploiting recent advances of computer capacities and floating point mathematics, sufficient terms of the inverse Laplace transform series solution can now be accurately computed. Together with the application of the Cesaro summation using up to 70 terms of the series, two primary deficiencies of the previous solution are now remedied: meaningful time histories of higher time derivative data such as acceleration and pressure are now generated using a sufficient number of terms in the series; and uniform convergence around the discontinuous step wave front is now obtained, completely eradicating spurious oscillations due to the Gibbs' phenomenon. New results of time histories of response items of interest are presented.

Efficient Approximate OLAP Querying Over Time Series

DEFF Research Database (Denmark)

Perera, Kasun Baruhupolage Don Kasun Sanjeewa; Hahmann, Martin; Lehner, Wolfgang

2016-01-01

The ongoing trend for data gathering not only produces larger volumes of data, but also increases the variety of recorded data types. Out of these, especially time series, e.g. various sensor readings, have attracted attention in the domains of business intelligence and decision making. As OLAP...... queries play a major role in these domains, it is desirable to also execute them on time series data. While this is not a problem on the conceptual level, it can become a bottleneck with regards to query run-time. In general, processing OLAP queries gets more computationally intensive as the volume...... of data grows. This is a particular problem when querying time series data, which generally contains multiple measures recorded at fine time granularities. Usually, this issue is addressed either by scaling up hardware or by employing workload based query optimization techniques. However, these solutions...

New two- and three-parameter solutions of the MPST equation

International Nuclear Information System (INIS)

Krori, K.D.; Chaudhury, T.; Bhattacharjee, R.

1981-01-01

Some new two- and three-parameter solutions of the MPST (Misra et al. Phys. Rev.; D7:1587 (1973)) equation are presented. All the three-parameter solutions are physical in the sense of asymptotic flatness. The simplest member of the three-parameter series of solutions is identical with a three-parameter solution of the static Einstein-Maxwell equations recently discovered by Bonnor (J. Phys. A.; 12:853 (1979)). (author)

Browse Title Index

African Journals Online (AJOL)

Items 601 - 650 of 985 ... Vol 10 (2006), On a differential subordination of some certain ... Vol 10 (2006), On iterative solution of non-linear equation ... Vol 12 (2008), On non-commutative L, spaces over quasilocal von neumann algebra, Abstract.

The ATOMFT integrator - Using Taylor series to solve ordinary differential equations

Science.gov (United States)

Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.

1988-01-01

This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.

Recurrent Neural Network Applications for Astronomical Time Series

Science.gov (United States)

Protopapas, Pavlos

2017-06-01

The benefits of good predictive models in astronomy lie in early event prediction systems and effective resource allocation. Current time series methods applicable to regular time series have not evolved to generalize for irregular time series. In this talk, I will describe two Recurrent Neural Network methods, Long Short-Term Memory (LSTM) and Echo State Networks (ESNs) for predicting irregular time series. Feature engineering along with a non-linear modeling proved to be an effective predictor. For noisy time series, the prediction is improved by training the network on error realizations using the error estimates from astronomical light curves. In addition to this, we propose a new neural network architecture to remove correlation from the residuals in order to improve prediction and compensate for the noisy data. Finally, I show how to set hyperparameters for a stable and performant solution correctly. In this work, we circumvent this obstacle by optimizing ESN hyperparameters using Bayesian optimization with Gaussian Process priors. This automates the tuning procedure, enabling users to employ the power of RNN without needing an in-depth understanding of the tuning procedure.

Stochastic B-series and order conditions for exponential integrators

DEFF Research Database (Denmark)

Arara, Alemayehu Adugna; Debrabant, Kristian; Kværnø, Anne

2018-01-01

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential integrators. The resulting...

Calculation of Volterra kernels for solutions of nonlinear differential equations

NARCIS (Netherlands)

van Hemmen, JL; Kistler, WM; Thomas, EGF

2000-01-01

We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of

On a Functional Equation for the Generating Function of the Logarithmic Series Distribution

OpenAIRE

Panaretos, John

1987-01-01

This note deals with finding the solution of a functional equation, where the function involved has the additional property of being a probability generating function. It turns out that the unique solution of this particular functional equation is the probability generating function of the logarithmic series distribution

A Hierarchical Approach to Persistent Scatterer Network Construction and Deformation Time Series Estimation

Directory of Open Access Journals (Sweden)

Rui Zhang

2014-12-01

Full Text Available This paper presents a hierarchical approach to network construction and time series estimation in persistent scatterer interferometry (PSI for deformation analysis using the time series of high-resolution satellite SAR images. To balance between computational efficiency and solution accuracy, a dividing and conquering algorithm (i.e., two levels of PS networking and solution is proposed for extracting deformation rates of a study area. The algorithm has been tested using 40 high-resolution TerraSAR-X images collected between 2009 and 2010 over Tianjin in China for subsidence analysis, and validated by using the ground-based leveling measurements. The experimental results indicate that the hierarchical approach can remarkably reduce computing time and memory requirements, and the subsidence measurements derived from the hierarchical solution are in good agreement with the leveling data.

Divergent series, summability and resurgence I monodromy and resurgence

CERN Document Server

Mitschi, Claude

2016-01-01

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solution...

Detecting Anisotropic Inclusions Through EIT

Science.gov (United States)

Cristina, Jan; Päivärinta, Lassi

2017-12-01

We study the evolution equation {partialtu=-Λtu} where {Λt} is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary {Σt}. We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the restriction of harmonic functions on M}=Σ_{0 to the boundaries of {partialΣt}. Consequently we are able to derive a lower bound for the difference of the Dirichlet-Neumann maps in terms of the difference of a background metrics g and an inclusion metric {g+χ_{Σ}(h-g)} on a manifold M.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution

Science.gov (United States)

D'Ariano, Giacomo Mauro

2018-04-01

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.

Properties of subentropy

International Nuclear Information System (INIS)

Datta, Nilanjana; Dorlas, Tony; Jozsa, Richard; Benatti, Fabio

2014-01-01

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's theorem. Here we establish a series of properties of subentropy, paralleling the well-developed analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for min-entropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classical-quantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally, we give an operational interpretation of subentropy within classical information theory

Two-dimensional analytical solutions for chemical transport in aquifers. Part 1. Simplified solutions for sources with constant concentration. Part 2. Exact solutions for sources with constant flux rate

International Nuclear Information System (INIS)

Shan, C.; Javandel, I.

1996-05-01

Analytical solutions are developed for modeling solute transport in a vertical section of a homogeneous aquifer. Part 1 of the series presents a simplified analytical solution for cases in which a constant-concentration source is located at the top (or the bottom) of the aquifer. The following transport mechanisms have been considered: advection (in the horizontal direction), transverse dispersion (in the vertical direction), adsorption, and biodegradation. In the simplified solution, however, longitudinal dispersion is assumed to be relatively insignificant with respect to advection, and has been neglected. Example calculations are given to show the movement of the contamination front, the development of concentration profiles, the mass transfer rate, and an application to determine the vertical dispersivity. The analytical solution developed in this study can be a useful tool in designing an appropriate monitoring system and an effective groundwater remediation method

Rogue wave solutions of the nonlinear Schrödinger equation with ...

Indian Academy of Sciences (India)

In this paper, a unified formula of a series of rogue wave solutions for the standard ... rating a noise-sensitive nonlinear process in which extremely broadband radiations are ..... Based on [21,24], the higher-order rational solution of eq. (15) are.

Time series models for prediction the total and dissolved heavy metals concentration in road runoff and soil solution of roadside embankments

Science.gov (United States)

Aljoumani, Basem; Kluge, Björn; sanchez, Josep; Wessolek, Gerd

2017-04-01

Highways and main roads are potential sources of contamination for the surrounding environment. High traffic rates result in elevated heavy metal concentrations in road runoff, soil and water seepage, which has attracted much attention in the recent past. Prediction of heavy metals transfer near the roadside into deeper soil layers are very important to prevent the groundwater pollution. This study was carried out on data of a number of lysimeters which were installed along the A115 highway (Germany) with a mean daily traffic of 90.000 vehicles per day. Three polyethylene (PE) lysimeters were installed at the A115 highway. They have the following dimensions: length 150 cm, width 100 cm, height 60 cm. The lysimeters were filled with different soil materials, which were recently used for embankment construction in Germany. With the obtained data, we will develop a time series analysis model to predict total and dissolved metal concentration in road runoff and in soil solution of the roadside embankments. The time series consisted of monthly measurements of heavy metals and was transformed to a stationary situation. Subsequently, the transformed data will be used to conduct analyses in the time domain in order to obtain the parameters of a seasonal autoregressive integrated moving average (ARIMA) model. Four phase approaches for identifying and fitting ARIMA models will be used: identification, parameter estimation, diagnostic checking, and forecasting. An automatic selection criterion, such as the Akaike information criterion, will use to enhance this flexible approach to model building

Maximin equilibrium

NARCIS (Netherlands)

Ismail, M.S.

2014-01-01

We introduce a new concept which extends von Neumann and Morgenstern's maximin strategy solution by incorporating `individual rationality' of the players. Maximin equilibrium, extending Nash's value approach, is based on the evaluation of the strategic uncertainty of the whole game. We show that

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

Science.gov (United States)

Xie, Dexuan; Volkmer, Hans W.; Ying, Jinyong

2016-04-01

The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism

Science.gov (United States)

Lyashko, A. D.

2017-11-01

A new analytical presentation of the solution for steady-state oscillations of orthotopic rectangular prism is found. The corresponding infinite system of linear algebraic equations has been deduced by the superposition method. A countable set of precise eigenfrequencies and elementary eigenforms is found. The identities are found which make it possible to improve the convergence of all the infinite series in the solution of the problem. All the infinite series in presentation of solution are analytically summed up. Numerical calculations of stresses in the rectangular orthotropic prism with a uniform along the border and harmonic in time load on two opposite faces have been performed.

New solutions of Heun's general equation

Energy Technology Data Exchange (ETDEWEB)

Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak (Armenia); Suominen, Kalle-Antti [Helsinki Institute of Physics, PL 64, Helsinki (Finland)

2003-02-07

We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

Effectiveness of Multivariate Time Series Classification Using Shapelets

Directory of Open Access Journals (Sweden)

A. P. Karpenko

2015-01-01

Full Text Available Typically, time series classifiers require signal pre-processing (filtering signals from noise and artifact removal, etc., enhancement of signal features (amplitude, frequency, spectrum, etc., classification of signal features in space using the classical techniques and classification algorithms of multivariate data. We consider a method of classifying time series, which does not require enhancement of the signal features. The method uses the shapelets of time series (time series shapelets i.e. small fragments of this series, which reflect properties of one of its classes most of all.Despite the significant number of publications on the theory and shapelet applications for classification of time series, the task to evaluate the effectiveness of this technique remains relevant. An objective of this publication is to study the effectiveness of a number of modifications of the original shapelet method as applied to the multivariate series classification that is a littlestudied problem. The paper presents the problem statement of multivariate time series classification using the shapelets and describes the shapelet–based basic method of binary classification, as well as various generalizations and proposed modification of the method. It also offers the software that implements a modified method and results of computational experiments confirming the effectiveness of the algorithmic and software solutions.The paper shows that the modified method and the software to use it allow us to reach the classification accuracy of about 85%, at best. The shapelet search time increases in proportion to input data dimension.

On a hierarchical construction of the anisotropic LTSN solution from the isotropic LTSN solution

International Nuclear Information System (INIS)

Foletto, Taline; Segatto, Cynthia F.; Bodmann, Bardo E.; Vilhena, Marco T.

2015-01-01

In this work, we present a recursive scheme targeting the hierarchical construction of anisotropic LTS N solution from the isotropic LTS N solution. The main idea relies in the decomposition of the associated LTS N anisotropic matrix as a sum of two matrices in which one matrix contains the isotropic and the other anisotropic part of the problem. The matrix containing the anisotropic part is considered as the source of the isotropic problem. The solution of this problem is made by the decomposition of the angular flux as a truncated series of intermediate functions and replace in the isotropic equation. After the replacement of these into the split isotropic equation, we construct a set of isotropic recursive problems, that are readily solved by the classic LTS N isotropic method. We apply this methodology to solve problems considering homogeneous and heterogeneous anisotropic regions. Numerical results are presented and compared with the classical LTS N anisotropic solution. (author)

Analytical solution of the toroidal constant tension solenoid

International Nuclear Information System (INIS)

Gralnick, S.L.; Tenney, F.H.

1975-01-01

The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 percent

MTU underfloor rail drives based on Series 1600 engines

Energy Technology Data Exchange (ETDEWEB)

Bamberger, Norbert; Lieb, Martin; Reich, Christian [MTU Friedrichshafen GmbH, Friedrichshafen (Germany)

2013-05-15

With the heavy demands now being placed on railcar drive systems, ever more powerful solutions are needed. For the new high-speed trains in Britain's Intercity Express Programme (IEP), Hitachi udorses the use of MTU's underfloor drives based on Series 1600 engines.

Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case

International Nuclear Information System (INIS)

Inglis, S M; Jarvis, P D

2012-01-01

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell–Dirac equations, we set up the formalism for non-Abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-Abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-Abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series. (paper)

An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

DEFF Research Database (Denmark)

Larsen, Niels Vesterdal; Breinbjerg, Olav

2004-01-01

Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems

Directory of Open Access Journals (Sweden)

Shuang Wang

2012-01-01

Full Text Available As an efficient tool, radial basis function (RBF has been widely used for the multivariate approximation, interpolating continuous, and the solution of the particle differential equations. However, ill-conditioned interpolation matrix may be encountered when the interpolation points are very dense or irregularly arranged. To avert this problem, RBFs with variable shape parameters are introduced, and several new variation strategies are proposed. Comparison with the RBF with constant shape parameters are made, and the results show that the condition number of the interpolation matrix grows much slower with our strategies. As an application, an improved collocation meshless method is formulated by employing the new RBF. In addition, the Hermite-type interpolation is implemented to handle the Neumann boundary conditions and an additional sine/cosine basis is introduced for the Helmlholtz equation. Then, two interior acoustic problems are solved with the presented method; the results demonstrate the robustness and effectiveness of the method.

Formal solutions of inverse scattering problems. III

International Nuclear Information System (INIS)

Prosser, R.T.

1980-01-01

The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions

Relative Utilitarianism

OpenAIRE

DHILLON, Amrita; MERTENS, Jean-François

1993-01-01

In a framework of preferences over lotteries, we show that an axiom system consisting of weakned versions of Arrow’s axioms has a unique solution. “Relative Utilitarianism” consists of first normalizing individual von Neumann-Morgenstern utilities between 0 and 1 and then summing them.

Solution of two group neutron diffusion equation by using homotopy analysis method

International Nuclear Information System (INIS)

Cavdar, S.

2010-01-01

The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.

Dealing with Multiple Solutions in Structural Vector Autoregressive Models.

Science.gov (United States)

Beltz, Adriene M; Molenaar, Peter C M

2016-01-01

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.

Kundt spacetimes as solutions of topologically massive gravity

Energy Technology Data Exchange (ETDEWEB)

Chow, David D K; Pope, C N; Sezgin, Ergin [George P and Cynthia W Mitchell Institute for Fundamental Physics and Astronomy, Texas A and M University, College Station, TX 77843-4242 (United States)

2010-05-21

We obtain new solutions of topologically massive gravity. We find the general Kundt solutions, which in three dimensions are spacetimes admitting an expansion-free null geodesic congruence. The solutions are generically of algebraic type II, but special cases are types III, N or D. Those of type D are the known spacelike-squashed AdS{sub 3} solutions and of type N are the known AdS pp-waves or new solutions. Those of types II and III are the first known solutions of these algebraic types. We present explicitly the Kundt solutions that are constant scalar invariant (CSI) spacetimes, for which all scalar polynomial curvature invariants are constant, whereas for the general case, we reduce the field equations to a series of ordinary differential equations. The CSI solutions of types II and III are deformations of spacelike-squashed AdS{sub 3} and the round AdS{sub 3}, respectively.

Structure of water and the thermodynamics of aqueous solutions

Energy Technology Data Exchange (ETDEWEB)

Nemethy, G.

1970-10-26

This report represents the summary of a series of lectures held at the Istituto Superiore di Sanita, Laboratori di Fisica, from 18 September to 26 October 1970. The topics discussed were: Intermolecular forces, the individual water molecule and the hydrogen bond, the structures of the solid phases of water, experimental information on the strucuture of liquid water, theoretical models of water structure, experimental properties and theoretical models of aqueous solutions of nonpolar solutes, polar solutes, and electrolytes, the conformational stability of biological macromolecules.

False-nearest-neighbors algorithm and noise-corrupted time series

International Nuclear Information System (INIS)

Rhodes, C.; Morari, M.

1997-01-01

The false-nearest-neighbors (FNN) algorithm was originally developed to determine the embedding dimension for autonomous time series. For noise-free computer-generated time series, the algorithm does a good job in predicting the embedding dimension. However, the problem of predicting the embedding dimension when the time-series data are corrupted by noise was not fully examined in the original studies of the FNN algorithm. Here it is shown that with large data sets, even small amounts of noise can lead to incorrect prediction of the embedding dimension. Surprisingly, as the length of the time series analyzed by FNN grows larger, the cause of incorrect prediction becomes more pronounced. An analysis of the effect of noise on the FNN algorithm and a solution for dealing with the effects of noise are given here. Some results on the theoretically correct choice of the FNN threshold are also presented. copyright 1997 The American Physical Society

Characteristics of official and experimental GRACE time series by GFZ and CSR - with applications to polar signals

Science.gov (United States)

Horvath, Alexander; Horwath, Martin; Pail, Roland

2014-05-01

The Release-05 monthly solutions by the three centers of the GRACE Science and Data System are a significant improvement with respect to the previous Release 4. Meanwhile, previous assessments have revealed different noise levels between the solutions by CSR, GFZ and JPL, and also different amplitudes of interannual signal in the solutions by GFZ as compared to the two other centers. Encouraged by the science community, GFZ and CSR have kindly provided additional sets of time series. GFZ has reprocessed the RL05 monthly solutions (up to degree and order 90) with revised processing. CSR has made available monthly solutions with standard processing up to degree and order 96, in addition to their solutions up to degree and order 60. We compare these different time series with respect to their signal and noise content and analyze them on global and regional scale. For the regional scale our special interest is paid on Antarctica and on revealing polar signals such as ice mass trends and GIA. Following the necessity of destriping, an optimal choice for the setup of the Swenson & Wahr filter approach is evaluated to adapt to the specific signal and noise level in Antarctica. Furthermore we analyze the potential benefit of mixed time series solutions in order to combine the strengths of the solutions available. Concerning the question for an optimal maximum degree we suggest that for resolving large polar ice mass changes, it would be beneficial to provide gravity field variations even beyond degree 90.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

Science.gov (United States)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

2017-11-01

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

Thermodynamic Mixing Behavior Of F-OH Apatite Crystalline Solutions

Science.gov (United States)

Hovis, G. L.

2011-12-01

It is important to establish a thermodynamic data base for accessory minerals and mineral series that are useful in determining fluid composition during petrologic processes. As a starting point for apatite-system thermodynamics, Hovis and Harlov (2010, American Mineralogist 95, 946-952) reported enthalpies of mixing for a F-Cl apatite series. Harlov synthesized all such crystalline solutions at the GFZ-Potsdam using a slow-cooled molten-flux method. In order to expand thermodynamic characterization of the F-Cl-OH apatite system, a new study has been initiated along the F-OH apatite binary. Synthesis of this new series made use of National Institute of Standards and Technology (NIST) 2910a hydroxylapatite, a standard reference material made at NIST "by solution reaction of calcium hydroxide with phosphoric acid." Synthesis efforts at Lafayette College have been successful in producing fluorapatite through ion exchange between hydroxylapatite 2910a and fluorite. In these experiments, a thin layer of hydroxylapatite powder was placed on a polished CaF2 disc (obtained from a supplier of high-purity crystals for spectroscopy), pressed firmly against the disc, then annealed at 750 °C (1 bar) for three days. Longer annealing times did not produce further change in unit-cell dimensions of the resulting fluorapatite, but it is uncertain at this time whether this procedure produces a pure-F end member (chemical analyses to be performed in the near future). It is clear from the unit-cell dimensions, however, that the newly synthesized apatite contains a high percentage of fluorine, probably greater than 90 mol % F. Intermediate compositions for a F-OH apatite series were made by combining 2910a hydroxylapatite powder with the newly synthesized fluorapatite in various proportions, then conducting chemical homogenization experiments at 750 °C on each mixture. X-ray powder diffraction data indicated that these experiments were successful in producing chemically homogeneous

Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

DEFF Research Database (Denmark)

Garde, Henrik

2018-01-01

. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...

Strong coupling analogue of the Born series

International Nuclear Information System (INIS)

Dolinszky, T.

1989-10-01

In a given partial wave, the strength of the centrifugal term to be incorporated into the WKBA solutions in different spatial regions can be adjusted so as to make the first order wave functions everywhere smooth and, in strong coupling, exactly reproduce Quantum Mechanics throughout the space. The relevant higher order approximations supply an absolute convergent series expansion of the exact scattering state. (author) 4 refs.; 2 figs.; 2 tabs

New exact solutions of the (2 + 1)-dimensional breaking soliton system via an extended mapping method

International Nuclear Information System (INIS)

Ma Songhua; Fang Jianping; Zheng Chunlong

2009-01-01

By means of an extended mapping method and a variable separation method, a series of solitary wave solutions, periodic wave solutions and variable separation solutions to the (2 + 1)-dimensional breaking soliton system is derived.

Mo-99 production on a LEU solution reactor

International Nuclear Information System (INIS)

Brown, R.W.; Thome, L.A.; Khvostionov, V.Y.

2005-01-01

A pilot homogenous reactor utilizing LEU has been developed by the Kurchatov Institute in Moscow along with their commercial partner TCI Medical. This solution reactor operates at levels up to 50 kilowatts and has successfully produced high quality Mo-99 and Sr-89. Radiochemical extraction of medical radionuclides from the reactor solution is performed by passing the solution across a series of inorganic sorbents. This reactor has commercial potential for medical radionuclide production using LEU UO 2 SO 4 fuel. Additional development work is needed to optimize multiple 50 kilowatt cores while at the same time, optimizing production efficiency and capital expenditure. (author)

Non-perturbative analytical solutions of the space- and time-fractional Burgers equations

International Nuclear Information System (INIS)

Momani, Shaher

2006-01-01

Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0 < α, β ≤ 1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed

Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions

Directory of Open Access Journals (Sweden)

Vladimir V. Varlamov

1999-01-01

classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.

The adsorption of molybdenum(VI) onto activated carbon from acid solution

International Nuclear Information System (INIS)

De Wet, H.F.

1985-11-01

The adsorption of molybdenum(VI) onto activated carbon is dependent on which nuclides are present in the solution. In this study the adsorption of Mo(VI) onto activated carbon is examined as a function of two variables, namely: the total molybdenum concentration and the pH. The equilibration time, the influence of ionic strength and the reversibility of the system was also examined. A series of solutions of a specified molybdenum concentration were equilibrated with activated carbon. In these experiments the pH varied from 5,5 to 0,9 while the temperature and ionic strength remained constant. The solutions were analysed colorimetrically and the pH equilibrium of each was measured. The molybdenum concentration for the series of experiments varied from 5x10 -4 M to 2x10 -2 M. 61 refs., 39 figs., 38 tabs

Time series analysis and its applications with R examples

CERN Document Server

Shumway, Robert H

2017-01-01

The fourth edition of this popular graduate textbook, like its predecessors, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonli...

Solubility of uranovanadates of the series A2+(VUO6)2 · nH2O (A2+ = Mg, Ca, Sr, Ba, Co, Ni, Cu, Pb) in water or aqueous solutions

International Nuclear Information System (INIS)

Chernorukov, N.G.; Sulejmanov, E.V.; Nipruk, O.V.; Lizunova, G.M.

2001-01-01

Solubility of uranovanadates of the series A 2+ (VUO 6 ) 2 · nH 2 O (A 2+ - Mg, Ca, Sr, Ba, Co, Ni, Cu, Pb) in water and aqueous solutions of inorganic acids at 25 deg C and different pH values was determined experimentally. The data obtained permitted calculation the Gibbs standard functions of formation and consideration of their state under conditions that were not studied experimentally, in the presence of carbon dioxide, in particular [ru

On the solvability of initial boundary value problems for nonlinear ...

African Journals Online (AJOL)

In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...

Self-organising mixture autoregressive model for non-stationary time series modelling.

Science.gov (United States)

Ni, He; Yin, Hujun

2008-12-01

Modelling non-stationary time series has been a difficult task for both parametric and nonparametric methods. One promising solution is to combine the flexibility of nonparametric models with the simplicity of parametric models. In this paper, the self-organising mixture autoregressive (SOMAR) network is adopted as a such mixture model. It breaks time series into underlying segments and at the same time fits local linear regressive models to the clusters of segments. In such a way, a global non-stationary time series is represented by a dynamic set of local linear regressive models. Neural gas is used for a more flexible structure of the mixture model. Furthermore, a new similarity measure has been introduced in the self-organising network to better quantify the similarity of time series segments. The network can be used naturally in modelling and forecasting non-stationary time series. Experiments on artificial, benchmark time series (e.g. Mackey-Glass) and real-world data (e.g. numbers of sunspots and Forex rates) are presented and the results show that the proposed SOMAR network is effective and superior to other similar approaches.

A series of Zn/Cd coordination polymers constructed from 1,4-naphthalenedicarboxylate and N-donor ligands: Syntheses, structures and luminescence sensing of Cr{sup 3+} in aqueous solutions

Energy Technology Data Exchange (ETDEWEB)

Hu, Dong-Cheng [College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou 730070 (China); Key Laboratory for Preparation and Application of Ordered Structural Materials of Guangdong Province, Shantou University, Shantou 515063 (China); Fan, Yan; Si, Chang-Dai; Wu, Ya-Jun; Dong, Xiu-Yan; Yang, Yun-Xia; Yao, Xiao-Qiang [College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou 730070 (China); Liu, Jia-Cheng, E-mail: jcliu8@nwnu.edu.cn [College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou 730070 (China)

2016-09-15

A novel series of Zn/Cd coordination polymers based on H{sub 3}L, namely, [Zn{sub 2}(HL){sub 2}(bipy){sub 2}(H{sub 2}O){sub 6}]{sub n} (1), [Zn(HL)(phen)]{sub n} (2), [Cd{sub 3}L{sub 2}(bbi){sub 3}]{sub n} (3), [Zn{sub 3}L{sub 2}(bbi){sub 3}]{sub n} (4) [(H{sub 3}L =4-[(1-carboxynaphthalen-2-yl)oxy]phthalic acid, bipy =4,4′-bipyridine, phen =1,10-phenanthroline, bbi =1,1′-(1,4-butanediyl)bis(imidazole] have been successfully synthesized by solvothermal reaction. Compound 1 possesses two diverse 1D chains constructed by different bipy coligands, which were further connected to form a 3D supramolecular architecture by hydrogen bonding interactions. Compound 2 possesses a complicated 1D chain based on secondary building unit (SBU) with binuclear Zn cluster. Compounds 3 and 4 exhibit similar 2D→3D framework, which can be rationalized as (3,4,4)-connected 3D net with a Schläfli symbol of (6{sup 3}.8.10{sup 2}){sub 2}(6{sup 3}){sub 2}(6{sup 4}.8.10). In particular, compound 3 exhibited a high sensitivity for Cr{sup 3+} in aqueous solutions, which suggest that compound 3 is a promising luminescent probe for selectively sensing Cr{sup 3+}. - Graphical abstract: A series of novel Zn/Cd coordination polymers have been successfully synthesized by solvothermal reaction. The unique 3D Cd{sup 2+} polymer containing bbi as second ligand demonstrates high sensitivity for detection of toxic Cr{sup 3+} in aqueous solutions. Display Omitted - Highlights: • π-conjugated semirigid tricarboxylate ligands with naphthalene rings(H{sub 3}L) were rationally designed. • Four Zn/Cd coordination polymers based on H{sub 3}L have been successfully synthesized by solvothermal reaction. • Compound 3 is a promising luminescent probe for selectively sensing Cr{sup 3+} with high sensitivity in aqueous solutions.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

Science.gov (United States)

D'Ariano, Giacomo Mauro

2018-04-28

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Investigation of complexing in solutions of salt mixture In(NO3)3-NaVO3

International Nuclear Information System (INIS)

Nakhodnova, A.N.; Listratenko, I.V.

1987-01-01

Spectrophotometry, conductometry and pH-metry are used to investigate properties and composition of the solid phases of isomolar series of In(NO 3 ) 3 -NaVO 3 salt mixture solutions and series of solutions having constant concentration of one of the components and varied of the other. Results of investigation are presented. It is stated that in the investigated solution series in weakly acid media HPA with the ratios [In 3+ ]:[V 5+ ] being equal to 11:1, 6:1, and 1:9, are formed. Composition of the complexes is mainly defined by the ratio of the components in In(NO 3 ) 3 and NaVO 3 salt mixture solutions and the medium acidity. Compounds of Na 2 OxIn 2 O 3 x2.5V 2 O 5 x8.5H 2 O and Cs 2 OxIn 2 O 3 x6V 2 O 5 x6.5H 2 O empirical formulae are separated. Results of IR spectroscopy, derivatography and X-ray phase analysis of the corresponding salts are presented

Explicit solution for a wave equation with nonlocal condition

Science.gov (United States)

Bazhlekova, Emilia; Dimovski, Ivan

2012-11-01

An initial-boundary value problem with a nonlocal boundary condition for one-dimensional wave equation is studied. Applying spectral projections, we find a series solution of the problem. The character of the solution found shows that the oscillation amplitude of the system described by this equation increases with time at any fixed x in absence of external forces. To find a representation of the solution more convenient for numerical calculation we develop a two-dimensional operational calculus for the problem. The solution is expressed as a sum of non-classical convolution products of particular solutions and the arbitrary initial functions. This result is an extension of the classical Duhamel principle for the space variable. The representation is used successfully for numerical computation and visualization of the solution. Numerical results obtained for specific test problems with known exact solutions indicate that the present technique provides accurate numerical solutions.

An Optimal Lower Eigenvalue System

Directory of Open Access Journals (Sweden)

Yingfan Liu

2011-01-01

Full Text Available An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and suffcient conditions concerning existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.

On the Borel summability of divergent solutions of the heat equation

OpenAIRE

Lutz, D. A.; Miyake, M.; Schäfke, R.

1999-01-01

In recent years, the theory of Borel summability or multisummability of divergent power series of one variable has been established and it has been proved that every formal solution of an ordinary differential equation with irregular singular point is multisummable. For partial differential equations the summability problem for divergent solutions has not been studied so well, and in this paper we shall try to develop the Borel summability of divergent solutions of the Cauch...

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

Science.gov (United States)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Genetic evaluation of seeds of highly endangered Pinus uliginosa Neumann from Węgliniec reserve for ex-situ conservation program

Directory of Open Access Journals (Sweden)

Andrzej Lewandowski

2011-01-01

Full Text Available Peat-bog pine Pinus uliginosa Neumann has become extinct or rare in many parts of Europe. We have investigated the levels of genetic variation and inbreeding in seeds collected from a highly endangered reserve of this species in Poland, using allozymes as genetic markers. Generally, a high level of genetic variation was observed. The mean expected heterozygosity was 0.376, while average (Na and effective (Ne numbers of alleles per locus were 2.45 and 1.67, respectively. Nevertheless, we have detected relatively low levels of outcrossing, and potential biparental inbreeding. The population-wide multilocus outcrossing rate was estimated to be 0.706 (±0.091, while the minimum variance mean of single-locus estimates was distinctly lower (ts=0.611. The estimates of outcrossing calculated for individual trees ranged widely from 0.051 to 1.017, indicating the complexity of outcrossing patterns. The investigated population of P. uliginasa from Węgliniec is small and surrounded by extensive forest stands of P. sylvestris. Our three-year records of phenological observations demonstrated that flowering periods for P. uliginosa and P. sylvestris overlap, allowing for cross-pollination. The possibility of P. uliginosa pollination by P. sylvestris creates a potential danger of genetic erosion of the P. uliginosa gene pool. Nonetheless, based on a species specific cpDNA marker we have found that among 533 seedlings of P. uliginosa there were only six seedlings carrying cpDNA marker specific for P. sylvestris, indicating that such hybridization seems to be rare.

Fourier series

CERN Document Server

Tolstov, Georgi P

1962-01-01

Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

Fourier Magnitude-Based Privacy-Preserving Clustering on Time-Series Data

Science.gov (United States)

Kim, Hea-Suk; Moon, Yang-Sae

Privacy-preserving clustering (PPC in short) is important in publishing sensitive time-series data. Previous PPC solutions, however, have a problem of not preserving distance orders or incurring privacy breach. To solve this problem, we propose a new PPC approach that exploits Fourier magnitudes of time-series. Our magnitude-based method does not cause privacy breach even though its techniques or related parameters are publicly revealed. Using magnitudes only, however, incurs the distance order problem, and we thus present magnitude selection strategies to preserve as many Euclidean distance orders as possible. Through extensive experiments, we showcase the superiority of our magnitude-based approach.

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

2015-01-01

Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

Coarse-Grained Modeling of Polyelectrolyte Solutions

Science.gov (United States)

Denton, Alan R.; May, Sylvio

2014-03-01

Ionic mixtures, such as electrolyte and polyelectrolyte solutions, have attracted much attention recently for their rich and challenging combination of electrostatic and non-electrostatic interparticle forces and their practical importance, from battery technologies to biological systems. Hydration of ions in aqueous solutions is known to entail ion-specific effects, including variable solubility of organic molecules, as manifested in the classic Hofmeister series for salting-in and salting-out of proteins. The physical mechanism by which the solvent (water) mediates effective interactions between ions, however, is still poorly understood. Starting from a microscopic model of a polyelectrolyte solution, we apply a perturbation theory to derive a coarse-grained model of ions interacting through both long-range electrostatic and short-range solvent-induced pair potentials. Taking these effective interactions as input to molecular dynamics simulations, we calculate structural and thermodynamic properties of aqueous ionic solutions. This work was supported by the National Science Foundation under Grant No. DMR-1106331.

Photochemical decomposition of Formaldehyde in solution

International Nuclear Information System (INIS)

Garrido Z, G.

1995-01-01

In this work was studied the effect of ultraviolet radiation produced by a mercury low pressure lamp in solutions of formaldehyde. These solutions were exposed to ultraviolet rays at different times. In some of these series of solutions was added a photosensibilizer in order to obtain a high photodecomposition of formaldehyde. The techniques used for determine the products of the decomposition were the following: 1. In order to measure the residual formaldehyde and glioxal, the Hantzsch and 2,4-dinitrophenylhydrazine methods were used. 2. pH's measurements of the solutions, before and after exposition. 3. Paper's chromatography for determine presence of formed acids. 4. Acid-base tritiations for measure total acidification. We observed that when the time of exposition to UV rays was increased, a high photodecomposition of formaldehyde was formed and, besides, a greater quantity of another products. Of the reagents used like photosensibilizers, with the ruthenium reagent, the best results were obtained. (Author)

Analytical Solution of Pantograph Equation with Incommensurate Delay

Science.gov (United States)

Patade, Jayvant; Bhalekar, Sachin

2017-08-01

Pantograph equation is a delay differential equation (DDE) arising in electrodynamics. This paper studies the pantograph equation with two delays. The existence, uniqueness, stability and convergence results for DDEs are presented. The series solution of the proposed equation is obtained by using Daftardar-Gejji and Jafari method and given in terms of a special function. This new special function has several properties and relations with other functions. Further, we generalize the proposed equation to fractional-order case and obtain its solution.

Wedges I

International Nuclear Information System (INIS)

DeWitt-Morette, C.; Low, S.G.; Schulman, L.S.; Shiekh, A.Y.

1986-01-01

The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results - hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value problem of differential equations; solutions defined on multiply connected spaces. Section 3: geometrical theory of diffraction; identification of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a /sigma phi/-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function

Tide Gauge Records Reveal Improved Processing of Gravity Recovery and Climate Experiment Time-Variable Mass Solutions over the Coastal Ocean

Science.gov (United States)

Piecuch, Christopher G.; Landerer, Felix W.; Ponte, Rui M.

2018-05-01

Monthly ocean bottom pressure solutions from the Gravity Recovery and Climate Experiment (GRACE), derived using surface spherical cap mass concentration (MC) blocks and spherical harmonics (SH) basis functions, are compared to tide gauge (TG) monthly averaged sea level data over 2003-2015 to evaluate improved gravimetric data processing methods near the coast. MC solutions can explain ≳ 42% of the monthly variance in TG time series over broad shelf regions and in semi-enclosed marginal seas. MC solutions also generally explain ˜5-32 % more TG data variance than SH estimates. Applying a coastline resolution improvement algorithm in the GRACE data processing leads to ˜ 31% more variance in TG records explained by the MC solution on average compared to not using this algorithm. Synthetic observations sampled from an ocean general circulation model exhibit similar patterns of correspondence between modeled TG and MC time series and differences between MC and SH time series in terms of their relationship with TG time series, suggesting that observational results here are generally consistent with expectations from ocean dynamics. This work demonstrates the improved quality of recent MC solutions compared to earlier SH estimates over the coastal ocean, and suggests that the MC solutions could be a useful tool for understanding contemporary coastal sea level variability and change.

New solutions to the Vortex Anisotropic Electron Hydrodynamic equations for a Weibel plasma

International Nuclear Information System (INIS)

Bychenkov, V.Yu.; Kovalev, V.F.; Pustovalov, V.V.

1996-01-01

On the basis of the group analysis, new nonlinear solutions to the equations of Vortex Anisotropic Electron Hydrodynamics (VAEH) describing large-scale magnetic structures in a plasm with an anisotropic pressure are obtained. Unlike familiar particular nonlinear solutions to the VAEH equations, new solutions, which are found in the form of an infinite series, are invariant or partially invariant with respect to the permissible Lie and Lie-Baecklund symmetry groups. Examples of finite regular solutions and solutions in the form of magnetic explosion are presented to illustrate the new solutions obtained

Adsorption kinetics of diblock copolymers from a micellar solution on silica and titania.

NARCIS (Netherlands)

Bijsterbosch, H.D.; Cohen Stuart, M.A.; Fleer, G.J.

1998-01-01

The solution and adsorption behavior of a series of diblock copolymers of hydrophobic poly(dimethyl siloxane) and hydrophilic poly(2-ethyl-2-oxazoline) was studied. These block copolymers formed large polydisperse micelles in an aqueous solution. The critical micelle concentration was lower than 2

Building Chaotic Model From Incomplete Time Series

Science.gov (United States)

Siek, Michael; Solomatine, Dimitri

2010-05-01

This paper presents a number of novel techniques for building a predictive chaotic model from incomplete time series. A predictive chaotic model is built by reconstructing the time-delayed phase space from observed time series and the prediction is made by a global model or adaptive local models based on the dynamical neighbors found in the reconstructed phase space. In general, the building of any data-driven models depends on the completeness and quality of the data itself. However, the completeness of the data availability can not always be guaranteed since the measurement or data transmission is intermittently not working properly due to some reasons. We propose two main solutions dealing with incomplete time series: using imputing and non-imputing methods. For imputing methods, we utilized the interpolation methods (weighted sum of linear interpolations, Bayesian principle component analysis and cubic spline interpolation) and predictive models (neural network, kernel machine, chaotic model) for estimating the missing values. After imputing the missing values, the phase space reconstruction and chaotic model prediction are executed as a standard procedure. For non-imputing methods, we reconstructed the time-delayed phase space from observed time series with missing values. This reconstruction results in non-continuous trajectories. However, the local model prediction can still be made from the other dynamical neighbors reconstructed from non-missing values. We implemented and tested these methods to construct a chaotic model for predicting storm surges at Hoek van Holland as the entrance of Rotterdam Port. The hourly surge time series is available for duration of 1990-1996. For measuring the performance of the proposed methods, a synthetic time series with missing values generated by a particular random variable to the original (complete) time series is utilized. There exist two main performance measures used in this work: (1) error measures between the actual

A Systematic Comparison of Vertical GPS Time Series Calculated by Five Processing Centers for Detecting Climatic-Induced Crustal Movements

Science.gov (United States)

Setti Junior, P. D. T.; Wdowinski, S.

2016-12-01

Vertical crustal movements, as observed by continuous GPS measurements, are sensitive to load changes induced by atmospheric and hydrological processes, as lake level fluctuations, ice melt, groundwater depletion, or drought. These movements are often dominated by a seasonal signal but also by year-to-year changes, which reflect a long-term climatic signal. Recently, we developed a new technique that extracts the climatic signal by removing the seasonal signal from vertical GPS time series (Wdowinski et al., 2016). However, the method's results, which are the climatic signals, are very sensitive to the quality of the time series and the choice of reference frame (RF). In this study, we conduct a systematic comparison between eight vertical GPS time series calculated by five processing centers and evaluate their suitability to extract the climatic signal. We use the solutions produced by Central Washington University (CWU), New Mexico Institute of Technology (NMT), Nevada Geodetic Laboratory (NGL), Scripps Orbit and Permanent Array Center (SOPAC) and Jet Propulsion Laboratory (JPL), as well as combined solution calculated by the Plate Boundary Observatory (PBO) and GPS Explorer. We use the solutions constrained in the IGS08 RF and in the case of NGL, we also use the NA12 solutions. Three of the processing centers, CWU, NGL and JPL use the GIPSY software, whereas the other two, NMT and SOPAC, use GAMIT. Both combined solutions integrate between GIPSY and GAMIT solutions. We conducted our comparative analysis in two study areas, one in western US taking advantage of the two decades long time series of the Basin and Range network, and the other in eastern U.S. and Canada (Washington DC area, Newfoundland, and Ottawa area). Preliminary results suggest that the three GIPSY solutions (CWU, NGL and JPL) are more consistent between one another compared with the GAMIT solutions. The GIPSY solutions also yield climatic signal that is more consistent with regional climatic

`Indoor` series vending machines; `Indoor` series jido hanbaiki

Energy Technology Data Exchange (ETDEWEB)

Gensui, T.; Kida, A. [Fuji Electric Co. Ltd., Tokyo (Japan); Okumura, H. [Fuji Denki Reiki Co. Ltd., Tokyo (Japan)

1996-07-10

This paper introduces three series of vending machines that were designed to match the interior of an office building. The three series are vending machines for cups, paper packs, cans, and tobacco. Among the three series, `Interior` series has a symmetric design that was coated in a grain pattern. The inside of the `Interior` series is coated by laser satin to ensure a sense of superior quality and a refined style. The push-button used for product selection is hot-stamped on the plastic surface to ensure the hair-line luster. `Interior Phase II` series has a bay window design with a sense of superior quality and lightness. The inside of the `Interior Phase II` series is coated by laser satin. `Interior 21` series is integrated with the wall except the sales operation panel. The upper and lower dress panels can be detached and attached. The door lock is a wire-type structure with high operativity. The operation block is coated by titanium color. The dimensions of three series are standardized. 6 figs., 1 tab.

Pretreatment of americium/curium solutions for vitrification

International Nuclear Information System (INIS)

Rudisill, T.S.

1996-01-01

Vitrification will be used to stabilize an americium/curium (Am/Cm) solution presently stored in F-Canyon for eventual transport to the heavy isotope programs at Oak Ridge National Laboratory. Prior to vitrification, an in-tank oxalate precipitation and a series of oxalic/nitric acid washes will be used to separate these elements and lanthanide fission products from the bulk of the uranium and metal impurities present in the solution. Pretreatment development experiments were performed to understand the behavior of the lanthanides and the metal impurities during the oxalate precipitation and properties of the precipitate slurry. The results of these experiments will be used to refine the target glass composition allowing optimization of the primary processing parameters and design of the solution transfer equipment

A generalized exp-function method for multiwave solutions of sine ...

Indian Academy of Sciences (India)

With the development of soliton theory, finding multiwave solutions has ... transmission, self-transparency due to nonlinear effects of optical pulses, ..... Secondly, expanding each new dependent variable in infinite series of a formal expansion.

Buoyancy-driven chaotic regimes during solute dispersion in pore networks

International Nuclear Information System (INIS)

Tsakiroglou, C.D.; Theodoropoulou, M.A.; Karoutsos, V.

2005-01-01

In an attempt to investigate gravity effects on solute dispersion at the scale of a pore network, single source-solute transport visualization experiments are performed on glass-etched pore networks of varying morphology and degree of pore-scale heterogeneities. The (lighter) low solute concentration aqueous solution flows steadily through the porous medium and the (heavier) high solute concentration solution is injected at a very low and constant flow rate through an inner port. The transient evolution of the solute concentration distribution over various regions of the pore network is determined at different scales by capturing and video-recording snapshots of the dispersion on PC, measuring automatically the spatial variation of the color intensity of the solution, and transforming the color intensities to solute concentrations. Without the action of gravity, the steady-state dispersion regime changes with Peclet (Pe) number, and the longitudinal and transverse dispersivities are estimated by fitting the experimental datasets to approximate analytic solutions of the advection-dispersion equation. Under the action of gravity, multiple of steady-state solute dispersion regimes is developed at each Pe value, and lobe-shaped instabilities of the solute concentration are observed across the pore network, as the downward flow of the denser (higher solute concentration) fluid is counterbalanced by the upward flow of the less dense (lower solute concentration) fluid. The steady-state dispersion regimes may be periodic, quasi-periodic or chaotic depending on the system parameters. The nature of the transient fluctuations of the average solute concentration is analyzed by identifying the periodicity of the fluctuations, determining the autocorrelation function and the statistical moments of the time series, and inspecting the FFT (fast Fourier transform) power spectra. It is found that the mixing zone tends to be stabilized at higher values of the Peclet (Pe) number

Solutions for confluent and double-confluent Heun equations and some applications

Energy Technology Data Exchange (ETDEWEB)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2008-07-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Solutions for confluent and double-confluent Heun equations and some applications

International Nuclear Information System (INIS)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B.

2008-01-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Reducing errors in the GRACE gravity solutions using regularization

Science.gov (United States)

Save, Himanshu; Bettadpur, Srinivas; Tapley, Byron D.

2012-09-01

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth's monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003-Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4

BBGKY hierarchy and dynamics of correlations

International Nuclear Information System (INIS)

Polishchuk, D.O.

2010-01-01

We derive the BBGKY hierarchy for the Fermi and Bose many-particle systems, using the von Neumann hierarchy for the correlation operators. The solution of the Cauchy problem of the formulated hierarchy in the case of an n-body interaction potential is constructed in the space of sequences of trace-class operators.

Answers to selected problems in multivariable calculus with linear algebra and series

CERN Document Server

Trench, William F

1972-01-01

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples.The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eig

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

Science.gov (United States)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Collegiate Aviation Research and Education Solutions to Critical Safety Issues. UNO Aviation Monograph Series. UNOAI Report.

Science.gov (United States)

Bowen, Brent, Ed.

This document contains four papers concerning collegiate aviation research and education solutions to critical safety issues. "Panel Proposal Titled Collegiate Aviation Research and Education Solutions to Critical Safety Issues for the Tim Forte Collegiate Aviation Safety Symposium" (Brent Bowen) presents proposals for panels on the…

The Astringency of the GP Algorithm for Forecasting Software Failure Data Series

Directory of Open Access Journals (Sweden)

Yong-qiang Zhang

2007-05-01

Full Text Available The forecasting of software failure data series by Genetic Programming (GP can be realized without any assumptions before modeling. This discovery has transformed traditional statistical modeling methods as well as improved consistency for model applicability. The individuals' different characteristics during the evolution of generations, which are randomly changeable, are treated as Markov random processes. This paper also proposes that a GP algorithm with "optimal individuals reserved strategy" is the best solution to this problem, and therefore the adaptive individuals finally will be evolved. This will allow practical applications in software reliability modeling analysis and forecasting for failure behaviors. Moreover it can verify the feasibility and availability of the GP algorithm, which is applied to software failure data series forecasting on a theoretical basis. The results show that the GP algorithm is the best solution for software failure behaviors in a variety of disciplines.

Neumann's Tumor

African Journals Online (AJOL)

GB

2017-03-01

://dx.doi.org/10.4314/ejhs.v27i2.11. Received: November 21, 2016. Accepted: December 8 ... normal tooth development (9).This case report intends to .... leave a notch in the alveolus that may result in an incomplete dental ...

Remote system of data acquisition and equipment maintenance with communication door Series; Sistema remoto de aquisicao de dados e manutencao de equipamentos com portas de comunicacao Serie

Energy Technology Data Exchange (ETDEWEB)

Marques, Ailton; Cabrera, Fernando [TRANSIERRA S.A., Santa Cruz (Bolivia)

2005-07-01

The present work has for objective to present the Remote System of Data Acquisition and Equipment Maintenance with Communication door Series - GASYRG. The solution is based on a converter of protocol (Serial -Ethernet) and a panel that the function of commutator (switch) managed by control system assumes (SCADA). (author)

The Analytic Solution of Schroedinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

International Nuclear Information System (INIS)

Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu

2009-01-01

The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)

A Study for Obtaining New and More General Solutions of Special-Type Nonlinear Equation

International Nuclear Information System (INIS)

Zhao Hong

2007-01-01

The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

Homotopy analysis solutions of point kinetics equations with one delayed precursor group

International Nuclear Information System (INIS)

Zhu Qian; Luo Lei; Chen Zhiyun; Li Haofeng

2010-01-01

Homotopy analysis method is proposed to obtain series solutions of nonlinear differential equations. Homotopy analysis method was applied for the point kinetics equations with one delayed precursor group. Analytic solutions were obtained using homotopy analysis method, and the algorithm was analysed. The results show that the algorithm computation time and precision agree with the engineering requirements. (authors)

Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions

Directory of Open Access Journals (Sweden)

Qingkai Kong

2012-02-01

Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with  Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.

Fourth-order poisson solver for the simulation of bounded plasmas

International Nuclear Information System (INIS)

Knorr, G.; Joyce, G.; Marcus, A.J.

1980-01-01

The solution of the two-dimensional Poisson equation in a rectangle with periodic boundaries in one direction and Dirichlet or Neumann boundaries in the other can be handled by a Fast Fourier Transform in one dimension and a fast nonperiodic procedure such as splines in the other. Such a solution is necessary for the simulation of semiperiodic plasma systems. A method is presented which is direct and of fourth order in both the electric potential and the electric fields

Analytic solution to variance optimization with no short positions

Science.gov (United States)

Kondor, Imre; Papp, Gábor; Caccioli, Fabio

2017-12-01

We consider the variance portfolio optimization problem with a ban on short selling. We provide an analytical solution by means of the replica method for the case of a portfolio of independent, but not identically distributed, assets. We study the behavior of the solution as a function of the ratio r between the number N of assets and the length T of the time series of returns used to estimate risk. The no-short-selling constraint acts as an asymmetric \

Simulations of water and solute movement in the buried waste repository at Vaalputs

International Nuclear Information System (INIS)

Hutson, J.L.

1987-01-01

A previous series of simulations examined the movement of water through trench cap configurations of several types. The objectives of this series are i) to extent the simulations from the surface to the bottom of the repository, accounting for the placement of drums, ii) to examine the magnitude and direction of water fluxes throughout this depth and iii) to simulate the movement of solutes, using various assumptions regarding solute adsorption. Two models were used. The first was an adaptation of a solute transport model which incorporates the transient water flow model used in previous simulations. This was used primarily to estimate the likely water fluxes in the drum placement region. Since it requires large amounts of computer time this model was used to simulate periods of one or two years only. The second model was a very simple steady state solute transport model which was used to simulate Cs distribution after a 100 year period, using flux data obtained from the transient model simulations. The most important conclusion reached from this series of simulations is that the movement of Cs in the soil under the likely water regime is extremely slow. 'Worst case' situations were simulated. Some of these situations are unlikely in reality but provide a useful indication of the rates of movement of solute under various conditions. For this reason it was assumed that plants were absent in cases when maximum percolation was simulated and present when maximum upward flow was simulated. In no case was a 'wick' (a textural barrier to unsaturated water flow) assumed to be present

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Rapid Airplane Parametric Input Design(RAPID)

Science.gov (United States)

Smith, Robert E.; Bloor, Malcolm I. G.; Wilson, Michael J.; Thomas, Almuttil M.

2004-01-01

An efficient methodology is presented for defining a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. A small set of design parameters and grid control parameters govern the process. The general airplane configuration has wing, fuselage, vertical tail, horizontal tail, and canard components. The wing, tail, and canard components are manifested by solving a fourth-order partial differential equation subject to Dirichlet and Neumann boundary conditions. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. Grid sensitivity is obtained by applying the automatic differentiation precompiler ADIFOR to software for the grid generation. The computed surface grids, volume grids, and sensitivity derivatives are suitable for a wide range of Computational Fluid Dynamics simulation and configuration optimizations.

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

Science.gov (United States)

Kaul, Upender K.; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Separation of hafnium from zirconium in their tetrachloride solution in molten alkali metal chlorides

Energy Technology Data Exchange (ETDEWEB)

Salyulev, A B; Kudyakov, V Ya; Smirnov, M V; Moskalenko, N I [AN SSSR, Sverdlovsk. Inst. Ehlektrokhimii

1984-08-01

The coefficient of HfCl/sub 4/ and ZrCl/sub 4/ separation in the process of vapour sublimation from their solutions in molten NaCl, KCl, CsCl, NaCl-KCl and NaCl-CsCl equimolar mixtures is found to vary in the series from approximately 1.10 to approximately 1.22 and practically not to depend on the temperature (in the 600-910 deg) range and concentration (2-25 mol.% ZrCl/sub 4/+HfCl/sub 4/). HfCl/sub 4/ and ZrCl/sub 4/ are shown to form almost perfect solutions with each other, which in their turn form imperfect solutions with molten alkali metal chlorides, with the strength of hafnium complex chloride anions increasing higher than that of zirconium in the series from NaCl to CsCl.

Separation of hafnium from zirconium in their tetrachloride solution in molten alkali metal chlorides

International Nuclear Information System (INIS)

Salyulev, A.B.; Kudyakov, V.Ya.; Smirnov, M.V.; Moskalenko, N.I.

1984-01-01

The coefficient of HfCl 4 and ZrCl 4 separation in the process of vapour sublimation from their solutions in molten NaCl, KCl, CsCl, NaCl-KCl and NaCl-CsCl equimolar mixtures is found to vary in the series from approximately 1.10 to approximately 1.22 and practically not to depend on the temperature (in the 600-910 deg) range and concentration (2-25 mol.% ZrCl 4 +HfCl 4 ). HfCl 4 and ZrCl 4 are shown to form almost perfect solutions with each other, which in their turn form imperfect solutions with molten alkali metal chlorides, with the strength of hafnium complex chloride anions increasing higher than that of zirconium in the series from NaCl to CsCl

Stilbazolium Merocyanine Dye Determination in Different Solutions, Concentrations and Colloids Using SERS

DEFF Research Database (Denmark)

Pajchrowski, Grzegorz; Abdali, Salim; Nørbygaard, Thomas

2006-01-01

Surface Enhanced Raman Scattering (SERS) measurements were carried out on stilbazolium merocyanine dye in methanol and pyridine solvents. Both solutions were measured in series of concentrations, covering a range of 5·10-5 M to 5·10-8 M. In these measurements Ag and Au colloids were used and the ......Surface Enhanced Raman Scattering (SERS) measurements were carried out on stilbazolium merocyanine dye in methanol and pyridine solvents. Both solutions were measured in series of concentrations, covering a range of 5·10-5 M to 5·10-8 M. In these measurements Ag and Au colloids were used...... report here on the success of using SERS to obtain Raman spectra of merocyanine dye at very low concentration in an attempt of new approach, which can be used for further investigations of the dye. The SERS spectra will here be reported and the results from different solutions, colloids, concentrations...

Consistent two-dimensional visualization of protein-ligand complex series

Directory of Open Access Journals (Sweden)

Stierand Katrin

2011-06-01

Full Text Available Abstract Background The comparative two-dimensional graphical representation of protein-ligand complex series featuring different ligands bound to the same active site offers a quick insight in their binding mode differences. In comparison to arbitrary orientations of the residue molecules in the individual complex depictions a consistent placement improves the legibility and comparability within the series. The automatic generation of such consistent layouts offers the possibility to apply it to large data sets originating from computer-aided drug design methods. Results We developed a new approach, which automatically generates a consistent layout of interacting residues for a given series of complexes. Based on the structural three-dimensional input information, a global two-dimensional layout for all residues of the complex ensemble is computed. The algorithm incorporates the three-dimensional adjacencies of the active site residues in order to find an universally valid circular arrangement of the residues around the ligand. Subsequent to a two-dimensional ligand superimposition step, a global placement for each residue is derived from the set of already placed ligands. The method generates high-quality layouts, showing mostly overlap-free solutions with molecules which are displayed as structure diagrams providing interaction information in atomic detail. Application examples document an improved legibility compared to series of diagrams whose layouts are calculated independently from each other. Conclusions The presented method extends the field of complex series visualizations. A series of molecules binding to the same protein active site is drawn in a graphically consistent way. Compared to existing approaches these drawings substantially simplify the visual analysis of large compound series.

The power series method in the effectiveness factor calculations

OpenAIRE

Filipich, C. P.; Villa, L. T.; Grossi, Ricardo Oscar

2017-01-01

In the present paper, exact analytical solutions are obtained for nonlinear ordinary differential equations which appear in complex diffusionreaction processes. A technique based on the power series method is used. Numerical results were computed for a number of cases which correspond to boundary value problems available in the literature. Additionally, new numerical results were generated for several important cases. Fil: Filipich, C. P.. Universidad Tecnológica Nacional. Facultad Regiona...

Aqueous solutions that model the cytosol : studies on polarity, chemical reactivity and enzyme kinetics

NARCIS (Netherlands)

Asaad, N.; den Otter, M.J.; Engberts, J.B.F.N.

2004-01-01

Concentrated solutions of a series of organic compounds have been prepared and the effects of these solutes on the properties of the solvent system assessed as a function of their concentration and nature. Polarity, as measured by Reichardt's E-T(30) probe, exhibits a linear variation with both

On Sums of Numerical Series and Fourier Series

Science.gov (United States)

Pavao, H. Germano; de Oliveira, E. Capelas

2008-01-01

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)

A quasilinear model for solute transport under unsaturated flow

International Nuclear Information System (INIS)

Houseworth, J.E.; Leem, J.

2009-01-01

We developed an analytical solution for solute transport under steady-state, two-dimensional, unsaturated flow and transport conditions for the investigation of high-level radioactive waste disposal. The two-dimensional, unsaturated flow problem is treated using the quasilinear flow method for a system with homogeneous material properties. Dispersion is modeled as isotropic and is proportional to the effective hydraulic conductivity. This leads to a quasilinear form for the transport problem in terms of a scalar potential that is analogous to the Kirchhoff potential for quasilinear flow. The solutions for both flow and transport scalar potentials take the form of Fourier series. The particular solution given here is for two sources of flow, with one source containing a dissolved solute. The solution method may easily be extended, however, for any combination of flow and solute sources under steady-state conditions. The analytical results for multidimensional solute transport problems, which previously could only be solved numerically, also offer an additional way to benchmark numerical solutions. An analytical solution for two-dimensional, steady-state solute transport under unsaturated flow conditions is presented. A specific case with two sources is solved but may be generalized to any combination of sources. The analytical results complement numerical solutions, which were previously required to solve this class of problems.

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

International Nuclear Information System (INIS)

Li Nianhua; Li Yuqi

2011-01-01

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable. (general)

Time-domain analytic Solutions of two-wire transmission line excited by a plane-wave field

Institute of Scientific and Technical Information of China (English)

Ni Gu-Yan; Yan Li; Yuan Nai-Chang

2008-01-01

This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain.By the frequency-domain Baum-Liu-Tesche(BLT)equation,the time-domain analytic solutions are obtained and expressed in an infinite geometric series.Moreover,it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval.In other word.the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval.The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform,and the agreement is excellent.

Three-Dimensional Nanobiocomputing Architectures With Neuronal Hypercells

Science.gov (United States)

2007-06-01

Neumann architectures, and CMOS fabrication. Novel solutions of massive parallel distributed computing and processing (pipelined due to systolic... and processing platforms utilizing molecular hardware within an enabling organization and architecture. The design technology is based on utilizing a...Microsystems and Nanotechnologies investigated a novel 3D3 (Hardware Software Nanotechnology) technology to design super-high performance computing

A device for uranium series leaching from glass fiber in HEPA filter

International Nuclear Information System (INIS)

Gye-Nam Kim; Hye-Min Park; Wang-Kyu Choi; Jei-Kwon Moon

2012-01-01

For the disposal of a high efficiency particulate air (HEPA) glass filter into the environment, the glass fiber should be leached to lower its radioactive concentration to the clearance level. To derive an optimum method for the removal of uranium series from a HEPA glass fiber, five methods were applied in this study. That is, chemical leaching by a 4.0 M HNO 3 -0.1 M Ce(IV) solution, chemical leaching by a 5 wt% NaOH solution, chemical leaching by a 0.5 M H 2 O 2 -1.0 M Na 2 CO 3 solution, chemical consecutive chemical leaching by a 4.0 M HNO 3 solution, and repeated chemical leaching by a 4.0 M HNO 3 solution were used to remove the uranium series. The residual radioactivity concentrations of 238 U, 235 U, 226 Ra, and 234 Th in glass after leaching for 5 h by the 4.0 M HNO 3 -0.1 M Ce(IV) solution were 2.1, 0.3, 1.1, and 1.2 Bq/g. The residual radioactivity concentrations of 238 U, 235 U, 226 Ra, and 234 Th in glass after leaching for 36 h by 4.0 M HNO 3 -0.1 M Ce(IV) solution were 76.9, 3.4, 63.7, and 71.9 Bq/g. The residual radioactivity concentrations of 238 U, 235 U, 226 Ra, and 234 Th in glass after leaching for 8 h by a 0.5 M H 2 O 2 -1.0 M Na 2 CO 3 solution were 8.9, 0.0, 1.91, and 6.4 Bq/g. The residual radioactivity concentrations of 238 U, 235 U, 226 Ra, and 234 Th in glass after consecutive leaching for 8 h by the 4.0 M HNO 3 solution were 2.08, 0.12, 1.55, and 2.0 Bq/g. The residual radioactivity concentrations of 238 U, 235 U, 226 Ra, and 234 Th in glass after three repetitions of leaching for 3 h by the 4.0 M HNO 3 solution were 0.02, 0.02, 0.29, and 0.26 Bq/g. Meanwhile, the removal efficiencies of 238 U, 235 U, 226 Ra, and 234 Th from the waste solution after its precipitation-filtration treatment with NaOH and alum for reuse of the 4.0 M HNO 3 waste solution were 100, 100, 93.3, and 100%. (author)

Infinite series

CERN Document Server

Hirschman, Isidore Isaac

2014-01-01

This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the app

A Solution to the Fundamental Linear Fractional Order Differential Equation

Science.gov (United States)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model

Directory of Open Access Journals (Sweden)

Nikola V. Georgiev

2003-01-01

Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.

Robust Force Control of Series Elastic Actuators

Directory of Open Access Journals (Sweden)

Andrea Calanca

2014-07-01

Full Text Available Force-controlled series elastic actuators (SEA are widely used in novel human-robot interaction (HRI applications, such as assistive and rehabilitation robotics. These systems are characterized by the presence of the “human in the loop”, so that control response and stability depend on uncertain human dynamics, including reflexes and voluntary forces. This paper proposes a force control approach that guarantees the stability and robustness of the coupled human-robot system, based on sliding-mode control (SMC, considering the human dynamics as a disturbance to reject. We propose a chattering free solution that employs simple task models to obtain high performance, comparable with second order solutions. Theoretical stability is proven within the sliding mode framework, and predictability is reached by avoiding the reaching phase by design. Furthermore, safety is introduced by a proper design of the sliding surface. The practical feasibility of the approach is shown using an SEA prototype coupled with a human impedance in severe stress tests. To show the quality of the approach, we report a comparison with state-of-the-art second order SMC, passivity-based control and adaptive control solutions.

Error compensation for hybrid-computer solution of linear differential equations

Science.gov (United States)

Kemp, N. H.

1970-01-01

Z-transform technique compensates for digital transport delay and digital-to-analog hold. Method determines best values for compensation constants in multi-step and Taylor series projections. Technique also provides hybrid-calculation error compared to continuous exact solution, plus system stability properties.

SaaS Platform for Time Series Data Handling

Science.gov (United States)

Oplachko, Ekaterina; Rykunov, Stanislav; Ustinin, Mikhail

2018-02-01

The paper is devoted to the description of MathBrain, a cloud-based resource, which works as a "Software as a Service" model. It is designed to maximize the efficiency of the current technology and to provide a tool for time series data handling. The resource provides access to the following analysis methods: direct and inverse Fourier transforms, Principal component analysis and Independent component analysis decompositions, quantitative analysis, magnetoencephalography inverse problem solution in a single dipole model based on multichannel spectral data.

Apparent and partial molal heat capacities of aqueous rare earth nitrate solutions at 250C

International Nuclear Information System (INIS)

Spedding, F.H.; Baker, J.L.; Walters, J.P.

1979-01-01

Specific heats of aqueous solutions of the trinitrates of La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu were measured from 0.1 m to saturation at 25 0 C. Apparent molal heat capacities, phi/sub cp/, were calculated for these solutions, and empirical polynomial equations were obtained which expressed phi/sub cp/ as a function of m/sup 1/2/ for each salt. The partial molal heat capacities of the solvent, anti C 1 /sub p/, and solute, anti C 2 /sub p/, were calculated from these equations. Unlike chloride and perchlorate data reported earlier, values of anti C 1 /sub p/ for nitrate solutions across the rare earth series did not show a two series effect. Instead, anti C 1 /sub p/ values at lower concentrations (0.5 and 1.0 m) appear correlated with reported first formation constants for rare earth-nitrate complexes. 31 references, 9 figures, 2 tables

Critical experiment study on uranyl nitrate solution experiment facility

International Nuclear Information System (INIS)

Zhu Qingfu; Shi Yongqian; Wang Jinrong

2005-01-01

The Uranyl Nitrate Solution Experiment Facility was constructed for the research on nuclear criticality safety. In this paper, the configuration of the facility is introduced; a series of critical experiments on uranyl nitrate solution is described later, which were performed for various uranium concentrations under different conditions, i.e. with or without neutron absorbers in the core and with or without water-reflector outside the core. Critical volume and the minimum 235U critical mass for different uranium concentrations are presented. Finally, theoretical analysis is made on the experimental results. (authors)

Approximate solution fuzzy pantograph equation by using homotopy perturbation method

Science.gov (United States)

Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.

2017-09-01

In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.

Comparing numerical methods for the solutions of the Chen system

International Nuclear Information System (INIS)

Noorani, M.S.M.; Hashim, I.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.

2007-01-01

In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given

Synthesis of side-chain polystyrenes for all organic solution processed OLEDs

OpenAIRE

Lorente Sánchez, Alejandro Jose (Dr.)

2017-01-01

In the present work side-chain polystyrenes were synthesized and characterized, in order to be applied in multilayer OLEDs fabricated by solution process techniques. Manufacture of optoelectronic devices by solution process techniques is meant to decrease significantly fabrication cost and allow large scale production of such devices. This dissertation focusses in three series, enveloped in two material classes. The two classes differ to each other in the type of charge transport exhibited...

Some Characteristics Of the Financial Data Series

Directory of Open Access Journals (Sweden)

Gheorghe Săvoiu

2013-05-01

Full Text Available This paper attempts to delineate from a theoretical of view the financial data series relative to other statistical data, starting from the financial econometrics’ models and from the resulting features of the specific descriptive statistics’ analysis of these characteristic series. From the analysis of these financial data during either very short and short or medium periods of time or from the information provided by the website of the Bucharest Stock Exchange (BVB, the trend of great values of kurtosis or eccentricity and skewness or asymmetry of series appears as a characteristic tendency. During a long period of time, between 1920 and 2008, this tendency seems to be more relevant, being confirmed by an excerpt from the author’s earlier paper written in 2009, concerning the statistical Dow Jones Industrial Average Index (DJIA Index. The skewness, kurtosis and normality of data distribution analysis, using Jarque Bera test, along with the identification of residual autocorrelation or serial correlation in the presence of significant residual values and heteroskedasticity are the major evaluated aspects. Finally, the author investigates the optimal way to ensure statistical comparability inflationary and deflationary method for financial series of data, and offers a solution to the selection of the appropriate indicator from the categories of the absolute values, absolute variation of the absolute values and the relative variation of the absolute values, expressed by percentages, with the finding of the latter alternative as the best alternative in the world of financial modelling of the economic and financial processes and phenomena.

The Numerical Solution of an Abelian Ordinary Differential Equation ...

African Journals Online (AJOL)

In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...

Cosmological Solutions of Tensor–Vector Theories of Gravity by ...

Indian Academy of Sciences (India)

We consider tensor–vector theories by varying the space- time–matter coupling ... solutions by considering the character of critical points of the theory and their stability .... light (Magueijo 2003) that has arisen from the possibility of varying fine structure constant. ... Vector-like dark energy displays a series of properties that.

Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field

International Nuclear Information System (INIS)

Ni Guyan; Yan Li; Yuan Naichang

2008-01-01

This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum–Liu–Tesche (BLT) equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent. (the physics of elementary particles and fields)

Solution of Differential Equations with Polynomial Coefficients with the Aid of an Analytic Continuation of Laplace Transform

Directory of Open Access Journals (Sweden)

Tohru Morita

2016-03-01

Full Text Available In a series of papers, we discussed the solution of Laplace’s differential equation (DE by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC of Riemann–Liouville fractional derivative (fD and the distribution theory in the space D′R or the AC of Laplace transform. We now obtain the solutions of the hypergeometric DE, which are expressed by the hypergeometric functions, with the aid of the AC of Riemann–Liouville fD, and the distribution theory in the space D′r,R, which is introduced in this paper, or by the term-by-term inverse Laplace transform of AC of Laplace transform of the solution expressed by a series.

Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

KAUST Repository

El-Amin, Mohamed; Radwan, Ahmed G.; Sun, Shuyu

2017-01-01

In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

KAUST Repository

El-Amin, Mohamed

2017-07-06

In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

Science.gov (United States)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

International Nuclear Information System (INIS)

Dai Chaoqing; Zhang Jiefang

2006-01-01

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation

Science.gov (United States)

Pashkevich, V. V.

2017-03-01

The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.

Using trees to compute approximate solutions to ordinary differential equations exactly

Science.gov (United States)

Grossman, Robert

1991-01-01

Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

Multiple (Two) Met Bel 601 In Series Ultimate Vacuum Testing

Energy Technology Data Exchange (ETDEWEB)

Restivo, M. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

2016-09-30

SRNL Environmental and Chemical Process Technology (E&CPT) was requested to perform testing of vacuum pumps per a verbal request from the Customer, SRNL Hydrogen Processing Technology. Tritium Operations is currently having difficulties procuring the Normetex™® Model 15 m³/hr (9 CFM) vacuum pump (formerly Normetex Pompes, now Eumeca_SARL). One possible solution proposed by Hydrogen Processing Technology personnel is to use two Senior Aerospace Metal Bellows MB-601 vacuum pumps piped with the heads in series, and the pumps in series (Figure 1 below). This memorandum documents the ultimate vacuum testing that was performed to determine if this concept was a viable alternate vacuum pump strategy. This testing dovetails with previous pump evaluations documented in references 1 and 2.

Heating of leads casks. An analytical solution to the heat equation made up of a series of Laguerre functions; Echauffement des chateaux de plomb. Une solution analytique a l'equation de la chaleur constituee par une serie de fonctions de Laguerre

Energy Technology Data Exchange (ETDEWEB)

Formery, Ph; Gilles, A [Commissariat a l' Energie Atomique, Dir. des Productions, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1968-07-01

The packing used for the transport of highly radioactive materials such as in-pile irradiated rods; have to comply to fairly strict safety standards. They should in particular resist to fire without the radioactive protection being seriously affected. The heating of a transport cask placed in a fire has been calculated by normal automatic computation methods assuming that only thermal radiation is responsible for the heating and that this obeys STEFAN'S law. Simultaneously, a purely analytical treatment has been attempted as follows. The existence of a simple solution, of the Laguerre function type, to the heat equation has been demonstrated. By superposing an infinite number of simple solutions, it is possible to produce a fairly general solution, depending on parameters, which satisfies the initial state and the limiting conditions. The parameters can be adjusted so that the temperature and the flux produced on the shell by this solution satisfy approximately STEFAN'S relationship. (authors) [French] Les emballages qui servent au transport de produits fortement radioactifs, tels que des barreaux irradies dans les piles, doivent satisfaire a des normes de securite assez strictes. Ils doivent, en particulier, resister au feu sans que la protection contre le rayonnement soit sensiblement entamee. L'echauffement, par seul rayonnement thermique suppose obeir a la loi de STEFAN, d'un chateau de transport plonge dans un feu a ete calcule par les methodes habituelles du calcul automatique. Parallelement a ete tentee l'approche purement analytique que voici: Une solution simple, du type fonction de LAGUERRE, a l'equation de la chaleur est mise en evidence. La superposition, en nombre infini, de solutions simples, permet de fabriquer une solution assez generale dependant de parametres, satisfaisant a l'etat initial et aux conditions aux limites. Les parametres peuvent etre ajustes de facon que la temperature et le flux engendres sur la coque par cette solution

Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

OpenAIRE

Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

2017-01-01

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

KAUST Repository

Domínguez, Luis F.

2012-06-25

An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).

The dynamics of discrete populations and series of events

CERN Document Server

Hopcraft, Keith Iain; Ridley, Kevin D

2014-01-01

IntroductionReferencesStatistical PreliminariesIntroductionProbability DistributionsMoment-Generating FunctionsDiscrete ProcessesSeries of EventsSummaryFurther ReadingMarkovian Population ProcessesIntroductionBirths and DeathsImmigration and the Poisson ProcessThe Effect of MeasurementCorrelation of CountsSummaryFurther ReadingThe Birth-Death-Immigration ProcessIntroductionRate Equations for the ProcessEquation for the Generating FunctionGeneral Time-Dependent SolutionFluctuation Characteristics of a Birth-Death-Immigration PopulationSampling and Measurement ProcessesCorrelation of CountsSumma

Investigation of complexing in solutions of salt mixture In(NO/sub 3/)/sub 3/-NaVO/sub 3/

Energy Technology Data Exchange (ETDEWEB)

Nakhodnova, A N; Listratenko, I V

1987-05-01

Spectrophotometry, conductometry and pH-metry are used to investigate properties and composition of the solid phases of isomolar series of In(NO/sub 3/)/sub 3/-NaVO/sub 3/ salt mixture solutions and series of solutions having constant concentration of one of the components and varied of the other. Results of investigation are presented. It is stated that in the investigated solution series in weakly acid media HPA with the ratios (In/sup 3+/):(V/sup 5+/) being equal to 11:1, 6:1, and 1:9, are formed. Composition of the complexes is mainly defined by the ratio of the components in In(NO/sub 3/)/sub 3/ and NaVO/sub 3/ salt mixture solutions and the medium acidity. Compounds of Na/sub 2/OxIn/sub 2/O/sub 3/x2.5V/sub 2/O/sub 5/x8.5H/sub 2/O and Cs/sub 2/OxIn/sub 2/O/sub 3/x6V/sub 2/O/sub 5/x6.5H/sub 2/O empirical formulae are separated. Results of IR spectroscopy, derivatography and X-ray phase analysis of the corresponding salts are presented.

Introduction to partial differential equations from Fourier series to boundary-value problems

CERN Document Server

Broman, Arne

2010-01-01

This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.

New solutions of the confluent Heun equation

Directory of Open Access Journals (Sweden)

Harold Exton

1998-05-01

Full Text Available New compact triple series solutions of the confluent Heun equation (CHE are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations.

Quantitative relationship between adsorbed amount of solute and solvent composition

International Nuclear Information System (INIS)

Wang Yan; Geng Xindu; Zebolsky, Don M.

2003-01-01

A new adsorption isotherm that relates the amount of solute adsorbed to the solvent concentration is proposed. The new equation is derived from Geng and Shi's stoichiometric displacement model for adsorption (SDM-A). The obtained equation may be simplified to an expression containing two parameters. The equation with two parameters, valid for low concentrations of solute, is a logarithmically linear relationship. The intercept contains a thermodynamic equilibrium constant of the solute displacing solvent from the adsorbent. The slope is the negative value of the stoichiometric displacement parameter (Z), the average total number of solvent molecules displaced from an active site on the adsorbent and from the solute. Tests with a homologous series of aromatic alcohols by frontal analysis in reversed phase liquid chromatography demonstrate that experimental results fit the equation well

Approximate analytical solution of two-dimensional multigroup P-3 equations

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1981-01-01

Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)

Soliton solutions of coupled nonlinear Klein-Gordon equations

International Nuclear Information System (INIS)

Alagesan, T.; Chung, Y.; Nakkeeran, K.

2004-01-01

The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations

Magnetic Field Emission Comparison for Series-Parallel and Series-Series Wireless Power Transfer to Vehicles – PART 2/2

DEFF Research Database (Denmark)

Batra, Tushar; Schaltz, Erik

2014-01-01

Series-series and series-parallel topologies are the most favored topologies for design of wireless power transfer system for vehicle applications. The series-series topology has the advantage of reflecting only the resistive part on the primary side. On the other hand, the current source output...... characteristics of the series-parallel topology are more suited for the battery of the vehicle. This paper compares the two topologies in terms of magnetic emissions to the surroundings for the same input power, primary current, quality factor and inductors. Theoretical and simulation results show that the series...

Operational Solution to the Nonlinear Klein-Gordon Equation

Science.gov (United States)

Bengochea, G.; Verde-Star, L.; Ortigueira, M.

2018-05-01

We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions. Supported by Grant SEP-CONACYT 220603, the first author was supported by SEP-PRODEP through the project UAM-PTC-630, the third author was supported by Portuguese National Funds through the FCT Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013

New solutions of the generalized ellipsoidal wave equation

Directory of Open Access Journals (Sweden)

Harold Exton

1999-10-01

Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.

On the Hughes model and numerical aspects

KAUST Repository

Gomes, Diogo A.

2017-01-05

We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.

Optimization of recurrent neural networks for time series modeling

DEFF Research Database (Denmark)

Pedersen, Morten With

1997-01-01

The present thesis is about optimization of recurrent neural networks applied to time series modeling. In particular is considered fully recurrent networks working from only a single external input, one layer of nonlinear hidden units and a li near output unit applied to prediction of discrete time...... series. The overall objective s are to improve training by application of second-order methods and to improve generalization ability by architecture optimization accomplished by pruning. The major topics covered in the thesis are: 1. The problem of training recurrent networks is analyzed from a numerical...... of solution obtained as well as computation time required. 3. A theoretical definition of the generalization error for recurrent networks is provided. This definition justifies a commonly adopted approach for estimating generalization ability. 4. The viability of pruning recurrent networks by the Optimal...

Dynamic factor analysis in the frequency domain: causal modeling of multivariate psychophysiological time series

NARCIS (Netherlands)

Molenaar, P.C.M.

1987-01-01

Outlines a frequency domain analysis of the dynamic factor model and proposes a solution to the problem of constructing a causal filter of lagged factor loadings. The method is illustrated with applications to simulated and real multivariate time series. The latter applications involve topographic

Computing group cardinality constraint solutions for logistic regression problems.

Science.gov (United States)

Zhang, Yong; Kwon, Dongjin; Pohl, Kilian M

2017-01-01

We derive an algorithm to directly solve logistic regression based on cardinality constraint, group sparsity and use it to classify intra-subject MRI sequences (e.g. cine MRIs) of healthy from diseased subjects. Group cardinality constraint models are often applied to medical images in order to avoid overfitting of the classifier to the training data. Solutions within these models are generally determined by relaxing the cardinality constraint to a weighted feature selection scheme. However, these solutions relate to the original sparse problem only under specific assumptions, which generally do not hold for medical image applications. In addition, inferring clinical meaning from features weighted by a classifier is an ongoing topic of discussion. Avoiding weighing features, we propose to directly solve the group cardinality constraint logistic regression problem by generalizing the Penalty Decomposition method. To do so, we assume that an intra-subject series of images represents repeated samples of the same disease patterns. We model this assumption by combining series of measurements created by a feature across time into a single group. Our algorithm then derives a solution within that model by decoupling the minimization of the logistic regression function from enforcing the group sparsity constraint. The minimum to the smooth and convex logistic regression problem is determined via gradient descent while we derive a closed form solution for finding a sparse approximation of that minimum. We apply our method to cine MRI of 38 healthy controls and 44 adult patients that received reconstructive surgery of Tetralogy of Fallot (TOF) during infancy. Our method correctly identifies regions impacted by TOF and generally obtains statistically significant higher classification accuracy than alternative solutions to this model, i.e., ones relaxing group cardinality constraints. Copyright © 2016 Elsevier B.V. All rights reserved.

Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System

Directory of Open Access Journals (Sweden)

Chuanjun Dai

2013-01-01

Full Text Available We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.

Size and series effects on the economics of nuclear power plants

International Nuclear Information System (INIS)

Rouyer, J.L.; Marcetteau, P.; Nisan, S.

2001-01-01

This paper updates data and models concerning size and series effects on the economics of nuclear power plants. Size effect is the observation that, for a given technology, capital cost of a plant increases less rapidly than its capacity. The overall scaling exponent is derived from specific exponents for different plant items. It varies for industrial LWR and PHWR between 0.4 to 0.7. Series effect comprises two types of effects: a) fabrication in series of equipment, thus reducing unit cost with increased number of units; b) Increased efficiency through the feedback of experience obtained from the on-site realisation of a number of identical plants. Size and series effects are combined in the realisation of a full programme of a same standard model of nuclear power plants, for a given country or for several countries, in the same period of time (typically 10 years). Calculations have been performed to compare size and series effects for a 15000 MWe programme to be installed within 10 years, and reactor sizes varying from 600 MWe to 1500 MWe. The different options regarding the size of PWR standard model have also been compared on the basis of the least leveled electricity cost. The results of the calculations show that a standardised series of 1500 MWe appears presently the best solution in densely industrialized countries. In the long term, reactors of 1000 MWe, or less, (if new concepts sharply decrease unit cost per kW installed), may be preferred because of the associated large series effect. (authors)

Quantifying evolutionary dynamics from variant-frequency time series

Science.gov (United States)

Khatri, Bhavin S.

2016-09-01

From Kimura’s neutral theory of protein evolution to Hubbell’s neutral theory of biodiversity, quantifying the relative importance of neutrality versus selection has long been a basic question in evolutionary biology and ecology. With deep sequencing technologies, this question is taking on a new form: given a time-series of the frequency of different variants in a population, what is the likelihood that the observation has arisen due to selection or neutrality? To tackle the 2-variant case, we exploit Fisher’s angular transformation, which despite being discovered by Ronald Fisher a century ago, has remained an intellectual curiosity. We show together with a heuristic approach it provides a simple solution for the transition probability density at short times, including drift, selection and mutation. Our results show under that under strong selection and sufficiently frequent sampling these evolutionary parameters can be accurately determined from simulation data and so they provide a theoretical basis for techniques to detect selection from variant or polymorphism frequency time-series.

On the solution of elliptic partial differential equations on regions with corners

International Nuclear Information System (INIS)

Serkh, Kirill; Rokhlin, Vladimir

2016-01-01

In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

Elliptic equation rational expansion method and new exact travelling solutions for Whitham-Broer-Kaup equations

International Nuclear Information System (INIS)

Chen Yong; Wang Qi; Li Biao

2005-01-01

Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally

Small deformations of the Prasad-Sommerfield solution

International Nuclear Information System (INIS)

Adler, S.L.

1979-01-01

I study solutions of the static Euclidean anti-self-dual SU(2) Yang-Mills equations which differ by a small perturbation from the Prasad-Sommerfield solution. I find explicit expressions for two series of perturbation mode functions of angular momentum l and even and odd parity, and classify the modes according to several criteria. There are seven nondilatational modes which have singularities removable by gauge transformation: 3 translations (l = 1), 1 gauge mode (l = 0), and a family of 3 odd-parity gauge modes (l = 1). The translations and l = 0 gauge modes have nonvanishing, and normalizable, projections into the background gauge, while the odd-parity l = 1 modes have vanishing projection into the background gauge. Among the singular modes, there are an infinite number of modes, irregular at r = 0, which nonetheless satisfy the boundary conditions for finite-energy solutions on the sphere at infinity. I show, by discussing the analogous problem of the axially symmetric solutions of the stationary Einstein equations, that non-normalizable modes are relevant in determining whether a spherically symmetric solution of a nonlinear system has axially symmetric extensions. The analysis of perturbations around the Prasad-Sommerfield solution implies that if an axially symmetric extension exists, it cannot be reached by integration out along a tangent vector defined by a nonvanishing, nonsingular small-perturbation mode of the class explicitly constructed

Linking the Negative Binomial and Logarithmic Series Distributions via their Associated Series

OpenAIRE

SADINLE, MAURICIO

2008-01-01

The negative binomial distribution is associated to the series obtained by taking derivatives of the logarithmic series. Conversely, the logarithmic series distribution is associated to the series found by integrating the series associated to the negative binomial distribution. The parameter of the number of failures of the negative binomial distribution is the number of derivatives needed to obtain the negative binomial series from the logarithmic series. The reasoning in this article could ...

A novel six-degrees-of-freedom series-parallel manipulator

Energy Technology Data Exchange (ETDEWEB)

Gallardo-Alvarado, J.; Rodriguez-Castro, R.; Aguilar-Najera, C. R.; Perez-Gonzalez, L. [Instituto Tecnologico de Celaya, Celaya (Mexico)

2012-06-15

This paper addresses the description and kinematic analyses of a new non-redundant series-parallel manipulator. The primary feature of the robot is to have a decoupled topology consisting of a lower parallel manipulator, for controlling the orientation of the coupler platform, assembled in series connection with a upper parallel manipulator, for controlling the position of the output platform, capable to provide arbitrary poses to the output platform with respect to the fixed platform. The forward displacement analysis is carried-out in semi-closed form solutions by resorting to simple closure equations. On the other hand; the velocity, acceleration and singularity analyses of the manipulator are approached by means of the theory of screws. Simple and compact expressions are derived here for solving the infinitesimal kinematics by taking advantage of the concept of reciprocal screws. Furthermore, the analysis of the Jacobians of the robot shows that the lower parallel manipulator is practically free of singularities. In order to illustrate the performance of the manipulator, a numerical example which consists of solving the inverse/forward kinematics of the series-parallel manipulator as well as its singular configurations is provided.

Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

Institute of Scientific and Technical Information of China (English)

LI Shoufu

2005-01-01

A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

Directory of Open Access Journals (Sweden)

Mohammad Mehdi Rashidi

2008-01-01

Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

Triangular dislocation: an analytical, artefact-free solution

Science.gov (United States)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2013-01-01

Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

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.

Stabilization of periodic solutions in a tethered satellite system by damping injection

DEFF Research Database (Denmark)

Larsen, Martin Birkelund; Blanke, Mogens

2009-01-01

presents a control design for stabilizing these periodic solutions. The design consists of a control law for stabilizing the open-loop equilibrium and a bias term which forces the system trajectory away from the equilibrium. The tether needs to be positioned away from open-loop equilibrium for the tether...... to affect the orbit parameters. An approximation of the periodic solutions of the closed loop system is found as a series expansion in the parameter plane spanned by the controller gain and the bias term. The stability of the solutions is investigated using linear Floquet analysis of the variational...

The Magic Pill: The Branding of Impotence and the Positioning of Viagra as Its Solution through Edutainment.

Science.gov (United States)

Gesser-Edelsburg, Anat; Hijazi, Rana

2018-01-01

Product placement can be presented through edutainment. A drug such as Viagra is introduced or impotence is branded in movies and TV series in different ways to raise awareness of impotence disorder and Viagra as a solution. This study aims to analyze strategies of framing and branding Viagra and impotence disorder, based on a qualitative method analysis of 40 movies and TV series. Findings show that Viagra is shown as not only for older men but also for young and healthy men. Out of 40 movies and TV series in the study sample, in 14 (32.5%), the age of the target audience ranged from 20 to 40 years, in 12 (31.6%) movies and series, the age of the target audience was over 40, and in 12 (31.6%) movies and series, the target audience was very old (over 70). Viagra is shown as not only treating impotence but is presented as a wonder drug that provides a solution for psychological and social needs. The movies show usage instructions, side effects, and risks, and how to store the drug. We recommend that the viewing audience be educated for critical viewing of movies/series in order to empower viewers and give them tools for their decision-making processes concerning their health.

Semi-Analytic Solution of HIV and TB Co-Infection Model BOLARIN ...

African Journals Online (AJOL)

ADOWIE PERE

HIV/TB co-infection is the most powerful known risk factor for ... homotopy transform to generate a convergent series solution of ... the boundary of the domain Ω. The operator A can be divided into two parts L and N, where L is the linear part,.

A non-differentiable solution for the local fractional telegraph equation

Directory of Open Access Journals (Sweden)

Li Jie

2017-01-01

Full Text Available In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

Magnetic Field Emission Comparison for Series-Parallel and Series-Series Wireless Power Transfer to Vehicles – PART 1/2

DEFF Research Database (Denmark)

Batra, Tushar; Schaltz, Erik

2014-01-01

Resonant circuits of wireless power transfer system can be designed in four possible ways by placing the primary and secondary capacitor in a series or parallel order with respect to the corresponding inductor. The two topologies series-parallel and series-series under investigation have been...... already compared in terms of their output behavior (current or voltage source) and reflection of the secondary impedance on the primary side. In this paper it is shown that for the same power rating series-parallel topology emits lesser magnetic fields to the surroundings than its series...

Analytic solution of the Starobinsky model for inflation

Energy Technology Data Exchange (ETDEWEB)

Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)

2017-07-15

We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lemaitre-Robertson-Walker metric constitute an integrable system. The analytical solution in terms of a Painleve series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory. (orig.)

Electrochemical Noise Chaotic Analysis of NiCoAg Alloy in Hank Solution

Directory of Open Access Journals (Sweden)

D. Bahena

2011-01-01

Full Text Available The potential and current oscillations during corrosion of NiCoAg alloy in Hank solution were studied. Detailed nonlinear fractal analyses were used to characterize complex time series clearly showing that the irregularity in these time series corresponds to deterministic chaos rather than to random noise. The chaotic oscillations were characterized by power spectral densities, phase space, and Lyapunov exponents. Electrochemical impedance was also applied the fractal dimensions for the corroded surface was obtained, and a corrosion mechanism was proposed.

Approximate analytical solution of two-dimensional multigroup P-3 equations

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1981-01-01

Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de

On numerical solution of Burgers' equation by homotopy analysis method

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

A high-fidelity weather time series generator using the Markov Chain process on a piecewise level

Science.gov (United States)

Hersvik, K.; Endrerud, O.-E. V.

2017-12-01

A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.

Summation of series

CERN Document Server

Jolley, LB W

2004-01-01

Over 1,100 common series, all grouped for easy reference. Arranged by category, these series include arithmetical and geometrical progressions, powers and products of natural numbers, figurate and polygonal numbers, inverse natural numbers, exponential and logarithmic series, binomials, simple inverse products, factorials, trigonometrical and hyperbolic expansions, and additional series. 1961 edition.

Contractivity and Exponential Stability of Solutions to Nonlinear Neutral Functional Differential Equations in Banach Spaces

Institute of Scientific and Technical Information of China (English)

Wan-sheng WANG; Shou-fu LI; Run-sheng YANG

2012-01-01

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.

Explicit analytical solution of the nonlinear Vlasov Poisson system

International Nuclear Information System (INIS)

Skarka, V.; Mahajan, S.M.; Fijalkow, E.

1993-10-01

In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

Generalization of the geometric optical series approach for nonadiabatic scattering problems

International Nuclear Information System (INIS)

Herman, M.F.

1982-01-01

The geometric optical series approach of Bremmer is generalized for multisurface nonadiabatic scattering problems. This method yields the formal solution of the Schroedinger equation as an infinite series of multiple integrals. The zeroth order term corresponds to WKB propagation on a single adiabatic surface, while the general Nth order term involves N reflections and/or transitions between surfaces accompanied by ''free,'' single surface semiclassical propagation between the points of reflection and transition. Each term is integrated over all possible transition and reflection points. The adiabatic and diabatic limits of this expression are discussed. Numerical results, in which all reflections are ignored, are presented for curve crossing and noncrossing problems. These results are compared to exact quantum results and are shown to be highly accurate

Simultaneous determination of radionuclides separable into natural decay series by use of time-interval analysis

International Nuclear Information System (INIS)

Hashimoto, Tetsuo; Sanada, Yukihisa; Uezu, Yasuhiro

2004-01-01

A delayed coincidence method, time-interval analysis (TIA), has been applied to successive α-α decay events on the millisecond time-scale. Such decay events are part of the 220 Rn→ 216 Po (T 1/2 145 ms) (Th-series) and 219 Rn→ 215 Po (T 1/2 1.78 ms) (Ac-series). By using TIA in addition to measurement of 226 Ra (U-series) from α-spectrometry by liquid scintillation counting (LSC), two natural decay series could be identified and separated. The TIA detection efficiency was improved by using the pulse-shape discrimination technique (PSD) to reject β-pulses, by solvent extraction of Ra combined with simple chemical separation, and by purging the scintillation solution with dry N 2 gas. The U- and Th-series together with the Ac-series were determined, respectively, from alpha spectra and TIA carried out immediately after Ra-extraction. Using the 221 Fr→ 217 At (T 1/2 32.3 ms) decay process as a tracer, overall yields were estimated from application of TIA to the 225 Ra (Np-decay series) at the time of maximum growth. The present method has proven useful for simultaneous determination of three radioactive decay series in environmental samples. (orig.)

Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

Directory of Open Access Journals (Sweden)

Sun Huan

2016-01-01

Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

Structural Properties of the Cr(III)-Fe(III) (Oxy)Hydroxide Compositional Series: Insights for a Nanomaterial 'Solid Solution'

International Nuclear Information System (INIS)

Tang, Y.; Zhang, L.; Michel, F.M.; Harrington, R.; Parise, J.B.; Reeder, R.J.

2010-01-01

Chromium(III) (oxy)hydroxide and mixed Cr(III)-Fe(III) (oxy)hydroxides are environmentally important compounds for controlling chromium speciation and bioaccessibility in soils and aquatic systems and are also industrially important as precursors for materials and catalyst synthesis. However, direct characterization of the atomic arrangements of these materials is complicated because of their amorphous X-ray properties. This study involves synthesis of the complete Cr(III)-Fe(III) (oxy)hydroxide compositional series, and the use of complementary thermal, microscopic, spectroscopic, and scattering techniques for the evaluation of their structural properties. Thermal analysis results show that the Cr end member has a higher hydration state than the Fe end member, likely associated with the difference in water exchange rates in the first hydration spheres of Cr(III) and Fe(III). Three stages of weight loss are observed and are likely related to the loss of surface/structural water and hydroxyl groups. As compared to the Cr end member, the intermediate composition sample shows lower dehydration temperatures and a higher exothermic transition temperature. XANES analysis shows Cr(III) and Fe(III) to be the dominant oxidation states. XANES spectra also show progressive changes in the local structure around Cr and Fe atoms over the series. Pair distribution function (PDF) analysis of synchrotron X-ray total scattering data shows that the Fe end member is nanocrystalline ferrihydrite with an intermediate-range order and average coherent domain size of ∼27 (angstrom). The Cr end member, with a coherent domain size of ∼10 (angstrom), has only short-range order. The PDFs show progressive structural changes across the compositional series. High-resolution transmission electron microscopy (HRTEM) results also show the loss of structural order with increasing Cr content. These observations provide strong structural evidence of chemical substitution and progressive structural

The Washington Academy of Biomedical Engineering (WABME) Quarterly Workshops: Clinical Problems and Engineering Solutions

National Research Council Canada - National Science Library

Wong, Kenneth

2005-01-01

... University and Howard University. A prime component of WABME activities is a quarterly series of research workshops, which bring together problem-rich biomedical disciplines and solution-rich engineering and scientific disciplines...

On the state of phosphomolybdenovanadic heteropolyblue in aqueous solutions

International Nuclear Information System (INIS)

Kuznetsova, L.I.; Yurchenko, Eh.N.; Maksimovskaya, R.I.; Kirik, N.P.; Matveev, K.I.

1977-01-01

The effect has been investigated of pH solution on the state of the phosphomolybdenovanadic heteropolyblues of the 12. series, containing n=1,2,3,6 atoms of vanadium (6). It has been shown that the free VO 2+ intrusion into the sphere of heteropolyanions takes place alongside with pH increasing from 1 to 3. At the some time the rate of oxidation of the heteropolyblue solutions by oxygen and the optical density of solutions increase too. The dissociation constants of the heteropolyblue molecule in acid medium increase with increasing of the quantity of vanadium atoms. It has been shown that stability of heteropolyblue in relation to molybdenum decreases with increasing of its quantity in the heteropolyblue molecule. Using precipitation of the heteropolyanions by the cation of tetraethyl ammonium, it has been shown that heteropolyanions can consist of 1,2,3 and 6 atoms of V(6). The state of heteropolyblues in an aqueous solution is characterized by electron absorption spectra

Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation

Directory of Open Access Journals (Sweden)

Kanyuta Poochinapan

2014-01-01

Full Text Available Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.

Localization of Point Sources for Poisson Equation using State Observers

KAUST Repository

Majeed, Muhammad Usman

2016-08-09

A method based On iterative observer design is presented to solve point source localization problem for Poisson equation with riven boundary data. The procedure involves solution of multiple boundary estimation sub problems using the available Dirichlet and Neumann data from different parts of the boundary. A weighted sum of these solution profiles of sub-problems localizes point sources inside the domain. Method to compute these weights is also provided. Numerical results are presented using finite differences in a rectangular domain. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Localization of Point Sources for Poisson Equation using State Observers

KAUST Repository

Majeed, Muhammad Usman; Laleg-Kirati, Taous-Meriem

2016-01-01

A method based On iterative observer design is presented to solve point source localization problem for Poisson equation with riven boundary data. The procedure involves solution of multiple boundary estimation sub problems using the available Dirichlet and Neumann data from different parts of the boundary. A weighted sum of these solution profiles of sub-problems localizes point sources inside the domain. Method to compute these weights is also provided. Numerical results are presented using finite differences in a rectangular domain. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Symmetry theorems via the continuous steiner symmetrization

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L. Ragoub

2000-06-01

Full Text Available Using a new approach due to F. Brock called the Steiner symmetrization, we show first that if $u$ is a solution of an overdetermined problem in the divergence form satisfying the Neumann and non-constant Dirichlet boundary conditions, then $Omega$ is an N-ball. In addition, we show that we can relax the condition on the value of the Dirichlet boundary condition in the case of superharmonicity. Finally, we give an application to positive solutions of some semilinear elliptic problems in symmetric domains for the divergence case.

Some Numerical Aspects on Crowd Motion - The Hughes Model

KAUST Repository

Gomes, Diogo A.

2016-01-06

Here, we study a crowd model proposed by R. Hughes in [5] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solution. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two numerical examples.

Solutions of deformed d'Alembert equation with quantum conformal symmetry

International Nuclear Information System (INIS)

Dobrev, V.K.; Kostadinov, B.S.

1997-10-01

We construct explicit solutions of a conditionally quantum conformal invariant q-d'Alembert equation proposed earlier by one of us. We give two types of solutions - polynomial solutions and a q-deformation of the plane wave. The latter is a formal power series in the noncommutative coordinates of q-Minkowski space-time and four-momenta. This q-plane wave has analogous properties to the classical one, in particular, it has the properties of q-Lorentz covariance, and it satisfies the q-d'Alembert equation on the q-Lorentz covariant momentum cone. On the other hand, our q-plane wave is not an exponent or q-exponent. Thus, it differs conceptually from the classical plane wave and may serve as a regularization. (author)

Non-existence of black-hole solutions for the electroweak Einstein-Dirac-Yang/Mills equations

International Nuclear Information System (INIS)

Bernard, Yann

2006-01-01

We consider a static, spherically symmetric system of a Dirac particle interacting with classical gravity and an electroweak Yang-Mills field. It is shown that the only black-hole solutions of the corresponding coupled equations must be the extreme Reissner-Nordstroem solutions, locally near the event horizon. This work generalizes a series of papers published by F Finster, J Smoller and S-T Yau

The analytical solution to the 1D diffusion equation in heterogeneous media

International Nuclear Information System (INIS)

Ganapol, B.D.; Nigg, D.W.

2011-01-01

The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)

Interpretable Categorization of Heterogeneous Time Series Data

Science.gov (United States)

Lee, Ritchie; Kochenderfer, Mykel J.; Mengshoel, Ole J.; Silbermann, Joshua

2017-01-01

We analyze data from simulated aircraft encounters to validate and inform the development of a prototype aircraft collision avoidance system. The high-dimensional and heterogeneous time series dataset is analyzed to discover properties of near mid-air collisions (NMACs) and categorize the NMAC encounters. Domain experts use these properties to better organize and understand NMAC occurrences. Existing solutions either are not capable of handling high-dimensional and heterogeneous time series datasets or do not provide explanations that are interpretable by a domain expert. The latter is critical to the acceptance and deployment of safety-critical systems. To address this gap, we propose grammar-based decision trees along with a learning algorithm. Our approach extends decision trees with a grammar framework for classifying heterogeneous time series data. A context-free grammar is used to derive decision expressions that are interpretable, application-specific, and support heterogeneous data types. In addition to classification, we show how grammar-based decision trees can also be used for categorization, which is a combination of clustering and generating interpretable explanations for each cluster. We apply grammar-based decision trees to a simulated aircraft encounter dataset and evaluate the performance of four variants of our learning algorithm. The best algorithm is used to analyze and categorize near mid-air collisions in the aircraft encounter dataset. We describe each discovered category in detail and discuss its relevance to aircraft collision avoidance.

Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

Directory of Open Access Journals (Sweden)

Weiguo Rui

2014-01-01

Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem

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Won-Tak Hong

2016-01-01

Full Text Available We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1 as well as oscillating singularities (of type rαsin⁡(ϵlog⁡r. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.

Exact solutions to the supply chain equations for arbitrary, time-dependent demands

DEFF Research Database (Denmark)

Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn

2014-01-01

, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...

Thermal and solutal stratification in mixed convection three-dimensional flow of an Oldroyd-B nanofluid

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Tasawar Hayat

Full Text Available This paper investigates the double stratified effects in mixed convection three-dimensional flow of an Oldroyd-B nanofluid. The flow is due to a bidirectional stretching surface. Mathematical analysis is carried out using the temperature and concentration stratification effects. Brownian motion, thermophoresis and chemical reaction effects are also considered. The governing nonlinear boundary layer equations are first converted into the dimensionless ordinary differential equations and then solved for the convergent series solutions of velocity, temperature and nanoparticles concentration. Convergence analysis of the obtained series solutions is also checked and verified. Effects of various emerging parameters are studied in details. Numerical values of local Nusselt and Sherwood numbers are tabulated and analyzed. It is noticed that the impact of mixed convection parameter on temperature and nanoparticles concentration is quite similar. Both temperature and nanoparticles concentration are reduced for larger mixed convection parameter. Keywords: Three-dimensional flow, Oldroyd-B fluid, Nanoparticles, Mixed convection, Thermal and solutal stratification, Chemically reactive species

Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

OpenAIRE

Mi, Yuzhen

2016-01-01

This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.

Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

Directory of Open Access Journals (Sweden)

Yuzhen Mi

2016-01-01

Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.

Method of interior boundaries in a mixed problem of acoustic scattering

Directory of Open Access Journals (Sweden)

P. A. Krutitskii

1999-01-01

Full Text Available The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.

Inequalities among eigenvalues of Sturm–Liouville problems

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Kong Q

1999-01-01

Full Text Available There are well-known inequalities among the eigenvalues of Sturm–Liouville problems with periodic, semi-periodic, Dirichlet and Neumann boundary conditions. In this paper, for an arbitrary coupled self-adjoint boundary condition, we identify two separated boundary conditions corresponding to the Dirichlet and Neumann conditions in the classical case, and establish analogous inequalities. It is also well-known that the lowest periodic eigenvalue is simple; here we prove a similar result for the general case. Moreover, we show that the algebraic and geometric multiplicities of the eigenvalues of self-adjoint regular Sturm–Liouville problems with coupled boundary conditions are the same. An important step in our approach is to obtain a representation of the fundamental solutions for sufficiently negative values of the spectral parameter. Our approach yields the existence and boundedness from below of the eigenvalues of arbitrary self-adjoint regular Sturm–Liouville problems without using operator theory.

Zeolites as alcohol adsorbents from aqueous solutions

Directory of Open Access Journals (Sweden)

Cekova Blagica

2006-01-01

Full Text Available The potential usage of zeolites as adsorbents for the removal of organic molecules from water was investigated in a series of experiments with aqueous solutions of lower alcohols. This could represent a simple solution to the problem of cleaning up industrial wastewater as well as recovering valuable chemicals at relatively low costs. Adsorption isotherms of the Langmuir type were applied, and calculations showed that the amount of propanol adsorbed on silicalite corresponded to approximately 70% of the pore volume. The adsorption process is simple, and recovery of the more concentrated products is easily done by heat treatment and/or at lowered pressures. Adsorption experiments with aqueous acetone showed that silicalite had approximately the same adsorption capacity for acetone as for n-propanol. Heats of adsorption were determined calorimetrically.

A numerical model for the determination of periodic solutions of pipes subjected to non-conservative loads

International Nuclear Information System (INIS)

Velloso, P.A.; Galeao, A.C.

1989-05-01

This paper deals with nonlinear vibrations of pipes subjected to non-conservative loads. Periodic solutions of these problems are determined using a variational approach based on Hamilton's Principle combined with a Fourier series expansion to describe the displacement field time dependence. A finite element model which utilizes Hemite's cubic interpolation for both axial and transversal displacement amplitudes is used. This model is applied to the problem of a pipe subjected to a tangential and a normal follower force. The numerical results obtained with this model are compared with the corespondent solutions determined using a total lagrangian description for the Principle of Virtual Work, coupled with Newmark's step-by-step integration procedure. It is shown that for small to moderate displacement amplitudes the one-term Fourier series approximation compares fairly well with the predicted solution. For large displacements as least a two-term approximation should be utilized [pt

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

Science.gov (United States)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

Extraction of lanthanide(III) nitrates from water-salt solutions with n.-octanol

International Nuclear Information System (INIS)

Keskinov, V.A.; Kudrova, A.V.; Valueva, O.V.; Pyartman, A.K.

2004-01-01

Extraction of lanthanide(III) nitrates (Ln=La-Nd, Sm-Gd) from aqueous-salt solutions at 298.15 K was studied using solution of n.-octanol, its concentration 6.31 mol/l. It was ascertained that at Ln(NO 3 ) 3 concentration in aqueous phase below 0.6 mol/l, there is actually no extraction. At higher concentrations of nitrates in aqueous phase the content of lanthanides(III) in organic phase increases in the series La-Gd. Isotherms of extraction were ascertained, its phase equilibria being described mathematically. It is shown that extraction of lanthanide(III) nitrates with n.-octanol should be realized from concentrated aqueous solutions [ru

Modelling of series of types of automated trenchless works tunneling

Science.gov (United States)

Gendarz, P.; Rzasinski, R.

2016-08-01

Microtunneling is the newest method for making underground installations. Show method is the result of experience and methods applied in other, previous methods of trenchless underground works. It is considered reasonable to elaborate a series of types of construction of tunneling machines, to develop this particular earthworks method. There are many design solutions of machines, but the current goal is to develop non - excavation robotized machine. Erosion machines with main dimensions of the tunnels which are: 1600, 2000, 2500, 3150 are design with use of the computer aided methods. Series of types of construction of tunneling machines creating process was preceded by analysis of current state. The verification of practical methodology of creating the systematic part series was based on the designed erosion machines series of types. There were developed: method of construction similarity of the erosion machines, algorithmic methods of quantitative construction attributes variant analyzes in the I-DEAS advanced graphical program, relational and program parameterization. There manufacturing process of the parts will be created, which allows to verify the technological process on the CNC machines. The models of designed will be modified and the construction will be consulted with erosion machine users and manufacturers like: Tauber Rohrbau GmbH & Co.KG from Minster, OHL ZS a.s. from Brna,. The companies’ acceptance will result in practical verification by JUMARPOL company.

Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity

Directory of Open Access Journals (Sweden)

Alberto Lastra

2018-02-01

Full Text Available We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is a continuation of the precedent work [22] by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

Science.gov (United States)

Charles H. Luce; Daniele Tonina; Frank Gariglio; Ralph Applebee

2013-01-01

Work over the last decade has documented methods for estimating fluxes between streams and streambeds from time series of temperature at two depths in the streambed. We present substantial extension to the existing theory and practice of using temperature time series to estimate streambed water fluxes and thermal properties, including (1) a new explicit analytical...

From Fourier Series to Rapidly Convergent Series for Zeta(3)

DEFF Research Database (Denmark)

Scheufens, Ernst E

2011-01-01

The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such ......The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions...

Image reconstruction method for electrical capacitance tomography based on the combined series and parallel normalization model

International Nuclear Information System (INIS)

Dong, Xiangyuan; Guo, Shuqing

2008-01-01

In this paper, a novel image reconstruction method for electrical capacitance tomography (ECT) based on the combined series and parallel model is presented. A regularization technique is used to obtain a stabilized solution of the inverse problem. Also, the adaptive coefficient of the combined model is deduced by numerical optimization. Simulation results indicate that it can produce higher quality images when compared to the algorithm based on the parallel or series models for the cases tested in this paper. It provides a new algorithm for ECT application

Analysis of numerical solutions for Bateman equations

International Nuclear Information System (INIS)

Loch, Guilherme G.; Bevilacqua, Joyce S.

2013-01-01

The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)

Optimization of a pyrazole hit from FBDD into a novel series of indazoles as ketohexokinase inhibitors

Energy Technology Data Exchange (ETDEWEB)

Zhang, Xuqing; Song, Fengbing; Kuo, Gee-Hong; Xiang, Amy; Gibbs, Alan C.; Abad, Marta C.; Sun, Weimei; Kuo, Lawrence C.; Sui, Zhihua (J); (J-PRD)

2013-11-20

A series of indazoles have been discovered as KHK inhibitors from a pyrazole hit identified through fragment-based drug discovery (FBDD). The optimization process guided by both X-ray crystallography and solution activity resulted in lead-like compounds with good pharmaceutical properties.

Methods for obtaining sorption data from uranium-series disequilibria