Saturation behavior: a general relationship described by a simple second-order differential equation.

Science.gov (United States)

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical

THERMOKINETIC STUDY OF THE ZERO, FIRST AND SECOND ORDER REACTIONS IN A PSEUDO-ADIABATIC CALORIMETER: Numerical approach and experimental dat

Directory of Open Access Journals (Sweden)

Johanna Mendoza

2012-11-01

Full Text Available The signal produced by a pseudo-adiabaticcalorimeter is simulated by numericalsolution of the differential equations thatmodel the chemical kinetics [1], the thermalproperties of the calorimetric cell[2], and the response of the thermistorused as a thermometric sensor [3]. These equations show that the calorimetricsignal is related with concentrationin a complex way. Therefore, a comparisonbetween the signals of the threebasic kinetics reactions (zero, first andsecond order was made, as a first stepto obtain a standard procedure to followchemical kinetics using a calorimeter. Inorder to help understanding this relationship,the initial rate method was applied to the simulated data to assess the relationshipbetween the order and the kineticconstants calculated with those usedfor the simulations. As it was expected,the initial rate method for the calorimetricdata, do not give a slope directly relatedwith the order of the reaction, as itwould be produced, for example, in datafrom a spectrophotometer. However, alinear relationship was found betweenwhat we call the “calorimetric order”and the kinetic order. Finally, the developedprocedure was applied to the studyof the H2O2 decomposition catalyzedwith Fe3+ in homogeneous phase andwith activated carbon in heterogeneousphase, finding the order and the kineticsconstants of the global processes, whichwere in close agreement with those inthe literature.

Integration of differential equations by the pseudo-linear (PL) approximation

International Nuclear Information System (INIS)

Bonalumi, Riccardo A.

1998-01-01

A new method of integrating differential equations was originated with the technique of approximately calculating the integrals called the pseudo-linear (PL) procedure: this method is A-stable. This article contains the following examples: 1st order ordinary differential equations (ODEs), 2nd order linear ODEs, stiff system of ODEs (neutron kinetics), one-dimensional parabolic (diffusion) partial differential equations. In this latter case, this PL method coincides with the Crank-Nicholson method

Nonlinear elliptic equations of the second order

CERN Document Server

Han, Qing

2016-01-01

Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

A New Factorisation of a General Second Order Differential Equation

Science.gov (United States)

Clegg, Janet

2006-01-01

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

Science.gov (United States)

Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

2008-09-01

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

Science.gov (United States)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

P1-17: Pseudo-Haptics Using Motion-in-Depth Stimulus and Second-Order Motion Stimulus

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Shuichi Sato

2012-10-01

Full Text Available Modification of motion of the computer cursor during the manipulation by the observer evokes illusory haptic sensation (Lecuyer et al., 2004 ACM SIGCHI '04 239–246. This study investigates the pseudo-haptics using motion-in-depth and second-order motion. A stereoscopic display and a PHANTOM were used in the first experiment. A subject was asked to move a visual target at a constant speed in horizontal, vertical, or front-back direction. During the manipulation, the speed was reduced to 50% for 500 msec. The haptic sensation was measured using the magnitude estimation method. The result indicates that perceived haptic sensation from motion-in-depth was about 30% of that from horizontal or vertical motion. A 2D display and the PHANTOM were used in the second experiment. The motion cue was second order—in each frame, dots in a square patch reverses in contrast (i.e., all black dots become white and all white dots become black. The patch was moved in a horizontal direction. The result indicates that perceived haptic sensation from second-order motion was about 90% of that from first-order motion.

On oscillation of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, A.; Šremr, Jiří

2011-01-01

Roč. 54, - (2011), s. 69-81 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear second-order ordinary differential equation * Kamenev theorem * oscillation Subject RIV: BA - General Mathematics http://www.rmi.ge/jeomj/memoirs/vol54/abs54-4.htm

On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

International Nuclear Information System (INIS)

Man, Yiu-Kwong

2010-01-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. (fast track communication)

The lattice Boltzmann model for the second-order Benjamin–Ono equations

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

Variational formulation and projectional methods for the second order transport equation

International Nuclear Information System (INIS)

Borysiewicz, M.; Stankiewicz, R.

1979-01-01

Herein the variational problem for a second-order boundary value problem for the neutron transport equation is formulated. The projectional methods solving the problem are examined. The approach is compared with that based on the original untransformed form of the neutron transport equation

FORCED OSCILLATIONS OF SECOND ORDER SUPER-LINEAR DIFFERENTIAL EQUATION WITH IMPULSES

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.

Factorization of a class of almost linear second-order differential equations

International Nuclear Information System (INIS)

Estevez, P G; Kuru, S; Negro, J; Nieto, L M

2007-01-01

A general type of almost linear second-order differential equations, which are directly related to several interesting physical problems, is characterized. The solutions of these equations are obtained using the factorization technique, and their non-autonomous invariants are also found by means of scale transformations

Asymptotic behavior and stability of second order neutral delay differential equations

NARCIS (Netherlands)

Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd

2014-01-01

We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed

A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

International Nuclear Information System (INIS)

Adam, G.

1979-01-01

A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

Iterative oscillation results for second-order differential equations with advanced argument

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Irena Jadlovska

2017-07-01

Full Text Available This article concerns the oscillation of solutions to a linear second-order differential equation with advanced argument. Sufficient oscillation conditions involving limit inferior are given which essentially improve known results. We base our technique on the iterative construction of solution estimates and some of the recent ideas developed for first-order advanced differential equations. We demonstrate the advantage of our results on Euler-type advanced equation. Using MATLAB software, a comparison of the effectiveness of newly obtained criteria as well as the necessary iteration length in particular cases are discussed.

ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.

On nonnegative solutions of second order linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2004-01-01

Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics

Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

Directory of Open Access Journals (Sweden)

2009-02-01

Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.

Hyers-Ulam stability for second-order linear differential equations with boundary conditions

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Pasc Gavruta

2011-06-01

Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.

Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

Science.gov (United States)

Tisdell, Christopher C.

2017-07-01

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching 'well posedness' of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.

Oscillation of second order neutral dynamic equations with distributed delay

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Qiaoshun Yang

2016-06-01

Full Text Available In this paper, we establish new oscillation criteria for second order neutral dynamic equations with distributed delay by employing the generalized Riccati transformation. The obtained theorems essentially improve the oscillation results in the literature. And two examples are provided to illustrate to the versatility of our main results.

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

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

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

Dynamics of second order rational difference equations with open problems and conjectures

CERN Document Server

Kulenovic, Mustafa RS

2001-01-01

This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stability. Of paramount importance in their own right, the results presented also offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results in this monograph are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications. Each chapter contains a section of open problems and conjectures that will stimulate further research interest in working towards a complete understanding of the dynamics of the equation and its functional generalizations-many of them ideal for research project...

Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

Science.gov (United States)

Kougias, Ioannis E.

2009-01-01

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

Difference method for solving a nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients

Science.gov (United States)

Beshtokov, M. Kh.

2016-10-01

A nonlocal boundary value problem for a degenerating third-order pseudo-parabolic equation with variable coefficients is considered. For solving this problem, a priori estimates in the differential and difference forms are obtained. The a priori estimates imply the uniqueness and stability of the solution on a layer with respect to the initial data and the right-hand side and the convergence of the solution of the difference problem to the solution of the differential problem.

Periodic solutions of singular second order differential equations : upper and lower functions

Czech Academy of Sciences Publication Activity Database

Hakl, Robert; Torres, P.J.; Zamora, M.

2011-01-01

Roč. 74, č. 18 (2011), s. 7078-7093 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order differential equation * singularity at the phase variable * Rayleigh-Plesset equation Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11005049

Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

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Encinas A.M.

2018-02-01

Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

Stability analysis for neutral stochastic differential equation of second order driven by Poisson jumps

Science.gov (United States)

Chadha, Alka; Bora, Swaroop Nandan

2017-11-01

This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.

Some oscillation criteria for the second-order linear delay differential equation

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2011-01-01

Roč. 136, č. 2 (2011), s. 195-204 ISSN 0862-7959 Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order linear differential equation with a delay * oscillatory solution Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/141582

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

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

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Sankar Prasad Mondal

2016-06-01

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

Application of the Lie Symmetry Analysis for second-order fractional differential equations

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Mousa Ilie

2017-12-01

Full Text Available Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach.

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

International Nuclear Information System (INIS)

FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

CERN Document Server

Fan, W C; Powell, J L

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces

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Yongjin Li

2013-08-01

Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries

International Nuclear Information System (INIS)

Karimov, Ruslan Kh; Kozhevnikova, Larisa M

2010-01-01

The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain D=(0,∞)xΩ. Upper bounds are obtained, which give the rate of decay of the solutions as t→∞ as a function of the geometry of the unbounded domain Ω subset of R n , n≥2. Bibliography: 18 titles.

Myshkis type oscillation criteria for second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2015-01-01

Roč. 178, č. 1 (2015), s. 143-161 ISSN 0026-9255 Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillation criteria Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2015 http://link.springer.com/article/10.1007%2Fs00605-014-0719-y

Class of unconditionally stable second-order implicit schemes for hyperbolic and parabolic equations

International Nuclear Information System (INIS)

Lui, H.C.

The linearized Burgers equation is considered as a model u/sub t/ tau/sub x/ = bu/sub xx/, where the subscripts t and x denote the derivatives of the function u with respect to time t and space x; a and b are constants (b greater than or equal to 0). Numerical schemes for solving the equation are described that are second-order accurate, unconditionally stable, and dissipative of higher order. (U.S.)

Contact symmetries of general linear second-order ordinary differential equations: letter to the editor

NARCIS (Netherlands)

Martini, Ruud; Kersten, P.H.M.

1983-01-01

Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.

Differential and Difference Boundary Value Problem for Loaded Third-Order Pseudo-Parabolic Differential Equations and Difference Methods for Their Numerical Solution

Science.gov (United States)

Beshtokov, M. Kh.

2017-12-01

Boundary value problems for loaded third-order pseudo-parabolic equations with variable coefficients are considered. A priori estimates for the solutions of the problems in the differential and difference formulations are obtained. These a priori estimates imply the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer, as well as the convergence of the solution of each difference problem to the solution of the corresponding differential problem.

Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

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Bruno de Andrade

2009-01-01

Full Text Available We study the existence and uniqueness of almost automorphic (resp., pseudo-almost automorphic solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain.

Second-order differential-delay equation to describe a hybrid bistable device

Science.gov (United States)

Vallee, R.; Dubois, P.; Cote, M.; Delisle, C.

1987-08-01

The problem of a dynamical system with delayed feedback, a hybrid bistable device, characterized by n response times and described by an nth-order differential-delay equation (DDE) is discussed. Starting from a linear-stability analysis of the DDE, the effects of the second-order differential terms on the position of the first bifurcation and on the frequency of the resulting self-oscillation are shown. The effects of the third-order differential terms on the first bifurcation are also considered. Experimental results are shown to support the linear analysis.

Method of construction of the Riemann function for a second-order hyperbolic equation

Science.gov (United States)

Aksenov, A. V.

2017-12-01

A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001.xml?format=INT

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001. xml ?format=INT

EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.

Transformations of solutions for equations and hierarchies of pseudo-spherical type

CERN Document Server

Reyes, E G

2003-01-01

It is known that if an equation describes non-trivial one-parameter families of pseudo-spherical surfaces, its conservation laws, (generalized, nonlocal) symmetries and Baecklund transformations can be studied by geometrical means [4, 10]. In this letter it is pointed out that there exist correspondences, or 'generalized Baecklund transformations', between arbitrary solutions (satisfying some genericity conditions) of any two single equations describing pseudo-spherical surfaces. Then, the notion of a hierarchy of equations of pseudo-spherical type is introduced, and a theorem stating that there also exist correspondences between arbitrary solutions of any two such hierarchies is presented. A full account of these results appears elsewhere [12, 13]. (letter to the editor)

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

Energy Technology Data Exchange (ETDEWEB)

Zhao, J.M., E-mail: jmzhao@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); Tan, J.Y., E-mail: tanjy@hit.edu.cn [School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China); Liu, L.H., E-mail: lhliu@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China)

2013-01-01

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

Directory of Open Access Journals (Sweden)

Sufia Zulfa Ahmad

2016-01-01

Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.

Existence of solutions for nonlinear mixed type integrodifferential equation of second order

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Haribhau Laxman Tidke

2010-04-01

Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.

Conformal symmetry and non-relativistic second-order fluid dynamics

International Nuclear Information System (INIS)

Chao Jingyi; Schäfer, Thomas

2012-01-01

We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in the gradients of the hydrodynamic variables. At zeroth order, conformal symmetry implies a constraint on the equation of state, E 0 =2/3 P, where E 0 is the energy density and P is the pressure. At first order, conformal symmetry implies that the bulk viscosity must vanish. We show that at second order, conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier–Stokes form. We verify these results by solving the Boltzmann equation at second order in the gradient expansion. We find that only a subset of the terms allowed by conformal symmetry appear. - Highlights: ► We derive conformal constraints for the stress tensor of a scale invariant fluid. ► We determine the relaxation time in kinetic theory. ► We compute the rate of entropy production in second-order fluid dynamics.

EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.

Time-integration methods for finite element discretisations of the second-order Maxwell equation

NARCIS (Netherlands)

Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.

This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic

Higher-order Jordan Osserman pseudo-Riemannian manifolds

International Nuclear Information System (INIS)

Gilkey, Peter B; Ivanova, Raina; Zhang Tan

2002-01-01

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds

Higher-order Jordan Osserman pseudo-Riemannian manifolds

Energy Technology Data Exchange (ETDEWEB)

Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)

2002-09-07

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.

Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

International Nuclear Information System (INIS)

Olson, Gordon L.

2011-01-01

Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

Science.gov (United States)

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

Composition between mecd and runge-Kutta algorithm method for large system of second order differential equations

International Nuclear Information System (INIS)

Supriyono; Miyoshi, T.

1997-01-01

NECD Method and runge-Kutta method for large system of second order ordinary differential equations in comparing algorithm. The paper introduce a extrapolation method used for solving the large system of second order ordinary differential equation. We call this method the modified extrapolated central difference (MECD) method. for the accuracy and efficiency MECD method. we compare the method with 4-th order runge-Kutta method. The comparison results show that, this method has almost the same accuracy as the 4-th order runge-Kutta method, but the computation time is about half of runge-Kutta. The MECD was declare by the author and Tetsuhiko Miyoshi of the Dept. Applied Science Yamaguchi University Japan

On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1983-01-01

The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zeros of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052. xml

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zero s of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052.xml

Interval oscillation criteria for second-order forced impulsive delay differential equations with damping term.

Science.gov (United States)

Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra

2016-01-01

In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

Directory of Open Access Journals (Sweden)

Diem Dang Huan

2015-12-01

Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

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

Dynamics of second order in time evolution equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Chueshov, I.; Rezunenko, Oleksandr

123-124, č. 1 (2015), s. 126-149 ISSN 0362-546X R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor Subject RIV: BD - Theory of Information Impact factor: 1.125, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf

Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

Directory of Open Access Journals (Sweden)

Mervan Pašić

2014-01-01

Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.

Rethinking Pedagogy for Second-Order Differential Equations: A Simplified Approach to Understanding Well-Posed Problems

Science.gov (United States)

Tisdell, Christopher C.

2017-01-01

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching "well posedness" of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a…

A class of fully second order accurate projection methods for solving the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Liu Miaoer; Ren Yuxin; Zhang Hanxin

2004-01-01

In this paper, a continuous projection method is designed and analyzed. The continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the Navier-Stokes (N-S) equations in each time interval of a given time discretization. The local truncation error (LTE) analysis is applied to the continuous projection methods, which yields a sufficient condition for the continuous projection methods to be temporally second order accurate. Based on this sufficient condition, a fully second order accurate discrete projection method is proposed. A heuristic stability analysis is performed to this projection method showing that the present projection method can be stable. The stability of the present scheme is further verified through numerical experiments. The second order accuracy of the present projection method is confirmed by several numerical test cases

Sturm-Picone type theorems for second-order nonlinear differential equations

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Aydin Tiryaki

2014-06-01

Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Remark on periodic boundary-value problem for second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2018-01-01

Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

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

Directory of Open Access Journals (Sweden)

Maamar Andasmas

2016-04-01

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

Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

Directory of Open Access Journals (Sweden)

Mervan Pašić

2016-10-01

Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

Solution of Euler unsteady equations using a second order numerical scheme

International Nuclear Information System (INIS)

Devos, J.P.

1992-08-01

In thermal power plants, the steam circuits experience incidents due to the noise and vibration induced by trans-sonic flow. In these configurations, the compressible fluid can be considered the perfect ideal. Euler equations therefore constitute a good model. However, processing of the discontinuities induced by the shockwaves are a particular problem. We give a bibliographical synthesis of the work done on this subject. The research by Roe and Harten leads to TVD (Total Variation Decreasing) type schemes. These second order schemes generate no oscillation and converge towards physically acceptable weak solutions. (author). 12 refs

Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .

Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

KAUST Repository

Peng, Qiujin; Qiao, Zhonghua; Sun, Shuyu

2017-01-01

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L-infinity convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

Stability and Convergence Analysis of Second-Order Schemes for a Diffuse Interface Model with Peng-Robinson Equation of State

KAUST Repository

Peng, Qiujin

2017-09-18

In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L-infinity convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.

Estimates of solutions of certain classes of second-order differential equations in a Hilbert space

International Nuclear Information System (INIS)

Artamonov, N V

2003-01-01

Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained

A stochastic collocation method for the second order wave equation with a discontinuous random speed

KAUST Repository

Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

2012-01-01

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical

Oscillation and asymptotic properties of a class of second-order Emden-Fowler neutral differential equations.

Science.gov (United States)

Wang, Rui; Li, Qiqiang

2016-01-01

We consider a class of second-order Emden-Fowler equations with positive and nonpositve neutral coefficients. By using the Riccati transformation and inequalities, several oscillation and asymptotic results are established. Some examples are given to illustrate the main results.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

Science.gov (United States)

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

Directory of Open Access Journals (Sweden)

Wang Li

2008-01-01

Full Text Available We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form , where denotes the greatest integer function, is a real nonzero constant, and is almost periodic.

A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

KAUST Repository

Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong

2014-01-01

© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.

Multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects

Directory of Open Access Journals (Sweden)

Tengfei Shen

2015-12-01

Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.

The dynamics of second-order equations with delayed feedback and a large coefficient of delayed control

Science.gov (United States)

Kashchenko, Sergey A.

2016-12-01

The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.

Stability of a nonlinear second order equation under parametric bounded noise excitation

International Nuclear Information System (INIS)

Wiebe, Richard; Xie, Wei-Chau

2016-01-01

The motivation for the following work is a structural column under dynamic axial loads with both deterministic (harmonic transmitted forces from the surrounding structure) and random (wind and/or earthquake) loading components. The bounded noise used herein is a sinusoid with an argument composed of a random (Wiener) process deviation about a mean frequency. By this approach, a noise parameter may be used to investigate the behavior through the spectrum from simple harmonic forcing, to a bounded random process with very little harmonic content. The stability of both the trivial and non-trivial stationary solutions of an axially-loaded column (which is modeled as a second order nonlinear equation) under parametric bounded noise excitation is investigated by use of Lyapunov exponents. Specifically the effect of noise magnitude, amplitude of the forcing, and damping on stability of a column is investigated. First order averaging is employed to obtain analytical approximations of the Lyapunov exponents of the trivial solution. For the non-trivial stationary solution however, the Lyapunov exponents are obtained via Monte Carlo simulation as the stability equations become analytically intractable. (paper)

Second order finite volume scheme for Maxwell's equations with discontinuous electromagnetic properties on unstructured meshes

Energy Technology Data Exchange (ETDEWEB)

Ismagilov, Timur Z., E-mail: ismagilov@academ.org

2015-02-01

This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.

Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations

International Nuclear Information System (INIS)

Wang Haifeng; Popov, Pavel P.; Pope, Stephen B.

2010-01-01

We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes.

Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

Directory of Open Access Journals (Sweden)

Zhonghai Guo

2012-01-01

Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

Asymptotic behavior of second-order impulsive differential equations

Directory of Open Access Journals (Sweden)

Haifeng Liu

2011-02-01

Full Text Available In this article, we study the asymptotic behavior of all solutions of 2-th order nonlinear delay differential equation with impulses. Our main tools are impulsive differential inequalities and the Riccati transformation. We illustrate the results by an example.

On sign constant solutions of certain boundary value problems for second-order functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2005-01-01

Roč. 84, č. 2 (2005), s. 197-209 ISSN 0003-6811 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics http://www.tandfonline.com/doi/full/10.1080/00036810410001724427

Rapid expansion and pseudo spectral implementation for reverse time migration in VTI media

KAUST Repository

Pestana, Reynam C

2012-04-24

In isotropic media, we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media, P- and SV-waves are coupled, and the elastic wave equation should be used for RTM. For computational efficiency, a pseudo-acoustic wave equation is often used. This may be solved using a coupled system of second-order partial differential equations. We solve these using a pseudo spectral method and the rapid expansion method (REM) for the explicit time marching. This method generates a degenerate SV-wave in addition to the P-wave arrivals of interest. To avoid this problem, the elastic wave equation for vertical transversely isotropic (VTI) media can be split into separate wave equations for P- and SV-waves. These separate wave equations are stable, and they can be effectively used to model and migrate seismic data in VTI media where |ε- δ| is small. The artifact for the SV-wave has also been removed. The independent pseudo-differential wave equations can be solved one for each mode using the pseudo spectral method for the spatial derivatives and the REM for the explicit time advance of the wavefield. We show numerically stable and high-resolution modeling and RTM results for the pure P-wave mode in VTI media. © 2012 Sinopec Geophysical Research Institute.

Rapid expansion and pseudo spectral implementation for reverse time migration in VTI media

KAUST Repository

Pestana, Reynam C; Ursin, Bjø rn; Stoffa, Paul L

2012-01-01

In isotropic media, we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media, P- and SV-waves are coupled, and the elastic wave equation should be used for RTM. For computational efficiency, a pseudo-acoustic wave equation is often used. This may be solved using a coupled system of second-order partial differential equations. We solve these using a pseudo spectral method and the rapid expansion method (REM) for the explicit time marching. This method generates a degenerate SV-wave in addition to the P-wave arrivals of interest. To avoid this problem, the elastic wave equation for vertical transversely isotropic (VTI) media can be split into separate wave equations for P- and SV-waves. These separate wave equations are stable, and they can be effectively used to model and migrate seismic data in VTI media where |ε- δ| is small. The artifact for the SV-wave has also been removed. The independent pseudo-differential wave equations can be solved one for each mode using the pseudo spectral method for the spatial derivatives and the REM for the explicit time advance of the wavefield. We show numerically stable and high-resolution modeling and RTM results for the pure P-wave mode in VTI media. © 2012 Sinopec Geophysical Research Institute.

About sign-constancy of Green's functions for impulsive second order delay equations

Directory of Open Access Journals (Sweden)

Alexander Domoshnitsky

2014-01-01

Full Text Available We consider the following second order differential equation with delay \\[\\begin{cases} (Lx(t\\equiv{x''(t+\\sum_{j=1}^p {b_{j}(tx(t-\\theta_{j}(t}}=f(t, \\quad t\\in[0,\\omega],\\\\ x(t_j=\\gamma_{j}x(t_j-0, x'(t_j=\\delta_{j}x'(t_j-0, \\quad j=1,2,\\ldots,r. \\end{cases}\\] In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality \\(\\sum_{i=1}^p{b_i(t\\left(\\frac{1}{4}+r\\right}\\lt \\frac{2}{\\omega^2}\\ is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case \\(0\\lt \\gamma_i\\leq{1}\\, \\(0\\lt \\delta_i\\leq{1}\\ for \\(i=1,\\ldots ,p\\.

Pointwise second-order necessary optimality conditions and second-order sensitivity relations in optimal control

Science.gov (United States)

Frankowska, Hélène; Hoehener, Daniel

2017-06-01

This paper is devoted to pointwise second-order necessary optimality conditions for the Mayer problem arising in optimal control theory. We first show that with every optimal trajectory it is possible to associate a solution p (ṡ) of the adjoint system (as in the Pontryagin maximum principle) and a matrix solution W (ṡ) of an adjoint matrix differential equation that satisfy a second-order transversality condition and a second-order maximality condition. These conditions seem to be a natural second-order extension of the maximum principle. We then prove a Jacobson like necessary optimality condition for general control systems and measurable optimal controls that may be only ;partially singular; and may take values on the boundary of control constraints. Finally we investigate the second-order sensitivity relations along optimal trajectories involving both p (ṡ) and W (ṡ).

STEADY STATE AND PSEUDO-TRANSIENT ELECTRIC POTENTIAL USING THE POISSONBOLTZMANN EQUATION

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L. C. dos Santos

2015-03-01

Full Text Available A method for analysis of the electric potential profile in saline solutions was developed for systems with one or two infinite flat plates. A modified Poisson-Boltzmann equation, taking into account nonelectrostatic interactions between ions and surfaces, was used. To solve the stated problem in the steady-state approach the finite-difference method was used. For the formulated pseudo-transient problem, we solved the set of ordinary differential equations generated from the algebraic equations of the stationary case. A case study was also carried out in relation to temperature, solution concentration, surface charge and salt-type. The results were validated by the stationary problem solution, which had also been used to verify the ionic specificity for different salts. The pseudo-transient approach allowed a better understanding of the dynamic behavior of the ion-concentration profile and other properties due to the surface charge variation.

Error analysis of Newmark's method for the second order equation with inhomogeneous term

International Nuclear Information System (INIS)

Chiba, F.; Kako, T.

2000-01-01

For the second order time evolution equation with a general dissipation term, we introduce a recurrence relation of Newmark's method. Deriving an energy inequality from this relation, we consider the stability and the convergence criteria of Newmark's method. We treat a dissipation term under the assumption that the coefficient-damping matrix is constant in time and non-negative. We can relax however the assumptions for the dissipation and the rigidity matrices to be arbitrary symmetric matrices. (author)

First and second order operator splitting methods for the phase field crystal equation

International Nuclear Information System (INIS)

Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub

2015-01-01

In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods

Existence of pseudo almost periodic solutions for a class of partial functional differential equations

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Hui-Sheng Ding

2013-04-01

Full Text Available In this paper, we first introduce a new class of pseudo almost periodic type functions and investigate some properties of pseudo almost periodic type functions; and then we discuss the existence of pseudo almost periodic solutions to the class of abstract partial functional differential equations $x'(t=Ax(t+f(t,x_t$ with finite delay in a Banach space X.

Relativistic dissipative hydrodynamic equations at the second order for multi-component systems with multiple conserved currents

International Nuclear Information System (INIS)

Monnai, Akihiko; Hirano, Tetsufumi

2010-01-01

We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.

On a second order of accuracy stable difference scheme for the solution of a source identification problem for hyperbolic-parabolic equations

Science.gov (United States)

Ashyralyyeva, Maral; Ashyraliyev, Maksat

2016-08-01

In the present paper, a second order of accuracy difference scheme for the approximate solution of a source identification problem for hyperbolic-parabolic equations is constructed. Theorem on stability estimates for the solution of this difference scheme and their first and second order difference derivatives is presented. In applications, this abstract result permits us to obtain the stability estimates for the solutions of difference schemes for approximate solutions of two source identification problems for hyperbolic-parabolic equations.

Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

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M. P. Markakis

2010-01-01

Full Text Available Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1 equations. Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

International Nuclear Information System (INIS)

Casas, E.; Troeltzsch, F.

1999-01-01

In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem

Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes.

Science.gov (United States)

Tang, Chen; Han, Lin; Ren, Hongwei; Zhou, Dongjian; Chang, Yiming; Wang, Xiaohang; Cui, Xiaolong

2008-10-01

We derive the second-order oriented partial-differential equations (PDEs) for denoising in electronic-speckle-pattern interferometry fringe patterns from two points of view. The first is based on variational methods, and the second is based on controlling diffusion direction. Our oriented PDE models make the diffusion along only the fringe orientation. The main advantage of our filtering method, based on oriented PDE models, is that it is very easy to implement compared with the published filtering methods along the fringe orientation. We demonstrate the performance of our oriented PDE models via application to two computer-simulated and experimentally obtained speckle fringes and compare with related PDE models.

Multiple periodic solutions to a class of second-order nonlinear mixed-type functional differential equations

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Xiao-Bao Shu

2005-01-01

Full Text Available By means of variational structure and Z2 group index theory, we obtain multiple periodic solutions to a class of second-order mixed-type differential equations x''(t−τ+f(t,x(t,x(t−τ,x(t−2τ=0 and x''(t−τ+λ(tf1(t,x(t,x(t−τ,x(t−2τ=x(t−τ.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Science.gov (United States)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

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Fairouz Zouyed

2015-01-01

Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

Modeling of second order space charge driven coherent sum and difference instabilities

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Yao-Shuo Yuan

2017-10-01

Full Text Available Second order coherent oscillation modes in intense particle beams play an important role for beam stability in linear or circular accelerators. In addition to the well-known second order even envelope modes and their instability, coupled even envelope modes and odd (skew modes have recently been shown in [Phys. Plasmas 23, 090705 (2016PHPAEN1070-664X10.1063/1.4963851] to lead to parametric instabilities in periodic focusing lattices with sufficiently different tunes. While this work was partly using the usual envelope equations, partly also particle-in-cell (PIC simulation, we revisit these modes here and show that the complete set of second order even and odd mode phenomena can be obtained in a unifying approach by using a single set of linearized rms moment equations based on “Chernin’s equations.” This has the advantage that accurate information on growth rates can be obtained and gathered in a “tune diagram.” In periodic focusing we retrieve the parametric sum instabilities of coupled even and of odd modes. The stop bands obtained from these equations are compared with results from PIC simulations for waterbag beams and found to show very good agreement. The “tilting instability” obtained in constant focusing confirms the equivalence of this method with the linearized Vlasov-Poisson system evaluated in second order.

Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback

International Nuclear Information System (INIS)

Ding Xiaohua; Su Huan; Liu Mingzhu

2008-01-01

The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found

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....

Mixed hyperbolic-second-order-parabolic formulations of general relativity

International Nuclear Information System (INIS)

Paschalidis, Vasileios

2008-01-01

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials

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Jianping Liu

2016-01-01

Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.

Elastic properties of graphene: A pseudo-beam model with modified internal bending moment and its application

Science.gov (United States)

Xia, Z. M.; Wang, C. G.; Tan, H. F.

2018-04-01

A pseudo-beam model with modified internal bending moment is presented to predict elastic properties of graphene, including the Young's modulus and Poisson's ratio. In order to overcome a drawback in existing molecular structural mechanics models, which only account for pure bending (constant bending moment), the presented model accounts for linear bending moments deduced from the balance equations. Based on this pseudo-beam model, an analytical prediction is accomplished to predict the Young's modulus and Poisson's ratio of graphene based on the equation of the strain energies by using Castigliano second theorem. Then, the elastic properties of graphene are calculated compared with results available in literature, which verifies the feasibility of the pseudo-beam model. Finally, the pseudo-beam model is utilized to study the twisting wrinkling characteristics of annular graphene. Due to modifications of the internal bending moment, the wrinkling behaviors of graphene sheet are predicted accurately. The obtained results show that the pseudo-beam model has a good ability to predict the elastic properties of graphene accurately, especially the out-of-plane deformation behavior.

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo-observations

DEFF Research Database (Denmark)

Jacobsen, Martin; Martinussen, Torben

2016-01-01

Pseudo-values have proven very useful in censored data analysis in complex settings such as multi-state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These r......Pseudo-values have proven very useful in censored data analysis in complex settings such as multi-state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results....... These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second-order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo-values still seem unclear. In this paper......, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U-statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error...

First-order partial differential equations

CERN Document Server

Rhee, Hyun-Ku; Amundson, Neal R

2001-01-01

This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

Numerical investigation of sixth order Boussinesq equation

Science.gov (United States)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Estimates of the stabilization rate as t→∞ of solutions of the first mixed problem for a quasilinear system of second-order parabolic equations

International Nuclear Information System (INIS)

Kozhevnikova, L M; Mukminov, F Kh

2000-01-01

A quasilinear system of parabolic equations with energy inequality is considered in a cylindrical domain {t>0}xΩ. In a broad class of unbounded domains Ω two geometric characteristics of a domain are identified which determine the rate of convergence to zero as t→∞ of the L 2 -norm of a solution. Under additional assumptions on the coefficients of the quasilinear system estimates of the derivatives and uniform estimates of the solution are obtained; they are proved to be best possible in the order of convergence to zero in the case of one semilinear equation

Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

International Nuclear Information System (INIS)

Semenova, V.N.

2016-01-01

A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

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Chuanyi Zhang

2008-06-01

Full Text Available We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form (x(t+x(t−1′′=qx(2[(t+1/2]+f(t, where [⋅] denotes the greatest integer function, q is a real nonzero constant, and f(t is almost periodic.

Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations

National Research Council Canada - National Science Library

Mitchell, Jason

2002-01-01

A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...

Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

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Jaroslav Jaroš

2015-01-01

Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

Vapor-liquid equilibrium prediction with pseudo-cubic equation of state for binary mixtures containing hydrogen, helium, or neon

Energy Technology Data Exchange (ETDEWEB)

Kato, M.; Tanaka, H. (Nihon Univ.,Fukushima, (Japan). Faculty of Enineering)

1990-03-01

As an equation of state of vapor-liquid equilibrium, an original pseudo-cubic equation of state was previously proposed by the authors of this report and its study is continued. In the present study, new effective critical values of hydrogen, helium and neon were determined empirically from vapor-liquid equilibrium data of literature values against their critical temperatures, critical pressures and critical volumes. The vapor-liquid equilibrium relations of binary system quantum gas mixtures were predicted combining the conventinal pseudo-cubic equation of state and the new effective critical values, and without using binary heteromolecular interaction parameter. The predicted values of hydrogen-ethylene, helium-propane and neon-oxygen systems were compared with literature values. As a result, it was indicated that the vapor-liquid relations of binary system mixtures containing hydrogen, helium and neon can be predicted with favorable accuracy combining the effective critical values and the three parameter pseudo-cubic equation of state. 37 refs., 3 figs., 4 tabs.

A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

Science.gov (United States)

Burtyka, Filipp

2018-03-01

The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

Analyzing a stochastic time series obeying a second-order differential equation.

Science.gov (United States)

Lehle, B; Peinke, J

2015-06-01

The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.

The number of zero solutions for complex canonical differential equation of second order with constant coefficients in the first quadrant

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Vujaković Jelena

2016-01-01

Full Text Available The study of complex differential equations in recent years has opened up some of questions concerning the determination of the frequency of zero solutions, the distribution of zero, oscillation of the solution, asymptotic behavior, rank growth and so on. Besides, this is solved by only some classes of differential equations. In this paper, our aim was to determine the number of zeros and their arrangement in the first quadrant, for the complex canonical differential equation of the second order. The accuracy of our results, we illustrate with two examples.

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

Science.gov (United States)

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

Reanalysis of Rate Data for the Reaction CH3 + CH3 → C2H6 Using Revised Cross Sections and a Linearized Second-Order Master Equation.

Science.gov (United States)

Blitz, M A; Green, N J B; Shannon, R J; Pilling, M J; Seakins, P W; Western, C M; Robertson, S H

2015-07-16

Rate coefficients for the CH3 + CH3 reaction, over the temperature range 300-900 K, have been corrected for errors in the absorption coefficients used in the original publication ( Slagle et al., J. Phys. Chem. 1988 , 92 , 2455 - 2462 ). These corrections necessitated the development of a detailed model of the B̃(2)A1' (3s)-X̃(2)A2″ transition in CH3 and its validation against both low temperature and high temperature experimental absorption cross sections. A master equation (ME) model was developed, using a local linearization of the second-order decay, which allows the use of standard matrix diagonalization methods for the determination of the rate coefficients for CH3 + CH3. The ME model utilized inverse Laplace transformation to link the microcanonical rate constants for dissociation of C2H6 to the limiting high pressure rate coefficient for association, k∞(T); it was used to fit the experimental rate coefficients using the Levenberg-Marquardt algorithm to minimize χ(2) calculated from the differences between experimental and calculated rate coefficients. Parameters for both k∞(T) and for energy transfer ⟨ΔE⟩down(T) were varied and optimized in the fitting procedure. A wide range of experimental data were fitted, covering the temperature range 300-2000 K. A high pressure limit of k∞(T) = 5.76 × 10(-11)(T/298 K)(-0.34) cm(3) molecule(-1) s(-1) was obtained, which agrees well with the best available theoretical expression.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

Science.gov (United States)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

Science.gov (United States)

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

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)

First order and second order fermi acceleration of energetic charged particles by shock waves

International Nuclear Information System (INIS)

Webb, G.M.

1983-01-01

Steady state solutions of the cosmic ray transport equation describing first order Fermi acceleration of energetic charged particles at a plane shock (without losses) and second order Fermi acceleration in the downstream region of the shock are derived. The solutions for the isotropic part of the phase space distribution function are expressible as eigenfunction expansions, being superpositions of series of power law momentum spectra, with the power law indices being the roots of an eigenvalue equation. The above exact analytic solutions are for the case where the spatial diffusion coefficient kappa is independent of momentum. The solutions in general depend on the shock compression ratio, the modulation parameters V 1 L/kappa 1 , V 2 L/kappa 2 (V is the plasma velocity, kappa is the energetic particle diffusion coefficient, and L a characteristic length over which second order Fermi acceleration is effective) in the upstream and downstream regions of the shock, respectively, and also on a further dimensionless parameter, zeta, characterizing second order Fermi acceleration. In the limit as zeta→0 (no second order Fermi acceleration) the power law momentum spectrum characteristic of first order Fermi acceleration (depending only on the shock compression ratio) obtained previously is recovered. Perturbation solutions for the case where second order Fermi effects are small, and for realistic diffusion coefficients (kappainfinityp/sup a/, a>0, p = particle momentum), applicable at high momenta, are also obtained

Nonlinear partial differential equations of second order

CERN Document Server

Dong, Guangchang

1991-01-01

This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

Transport coefficients in second-order non-conformal viscous hydrodynamics

International Nuclear Information System (INIS)

Ryblewski, Radoslaw

2015-01-01

Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory. (paper)

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer

Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type

Directory of Open Access Journals (Sweden)

Yingzhu Wu

2016-12-01

Full Text Available Abstract In this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral type ( r ( t | z ′ ( t | α − 1 z ′ ( t ′ + q ( t | x ( σ ( t | β − 1 x ( σ ( t = 0 , $$\\bigl(r(t\\bigl\\vert z^{\\prime}(t\\bigr\\vert ^{\\alpha-1}z^{\\prime}(t \\bigr^{\\prime}+q(t\\bigl\\vert x\\bigl(\\sigma(t\\bigr\\bigr\\vert ^{\\beta-1}x \\bigl(\\sigma(t \\bigr=0, $$ where z ( t = x ( t + p ( t x ( τ ( t $z(t=x(t+p(tx(\\tau(t$ , α > 0 $\\alpha>0$ and β > 0 $\\beta>0$ are established. Our results improve some well-known results which were published recently in the literature. Some illustrating examples are also provided to show the importance of our results.

On nonlinear differential equation with exact solutions having various pole orders

International Nuclear Information System (INIS)

Kudryashov, N.A.

2015-01-01

We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation

Science.gov (United States)

Bonelli, Antonio; Ruffo, Stefano

Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the "ordered" and "chaotic" distribution of such pairs by solving the eigenvalue problem for two-dimensional modular transformations over integers. We conjecture that the optimal uniformity for pair distribution is obtained when the slope of linear modular eigenspaces takes the value n opt =maxint (p/√ {p-1}), where p is a prime number. We then propose a new generator of pairs of independent pseudo-random numbers, which realizes an optimal uniform distribution (in the "statistical" sense) of points on the unit square (0, 1] × (0, 1]. The method can be easily generalized to the generation of k-tuples of random numbers (with k>2).

Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times

Energy Technology Data Exchange (ETDEWEB)

Witzany, Vojtěch; Lämmerzahl, Claus, E-mail: vojtech.witzany@zarm.uni-bremen.de, E-mail: claus.laemmerzahl@zarm.uni-bremen.de [ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen (Germany)

2017-06-01

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

Second-order Optimality Conditions for Optimal Control of the Primitive Equations of the Ocean with Periodic Inputs

International Nuclear Information System (INIS)

Tachim Medjo, T.

2011-01-01

We investigate in this article the Pontryagin's maximum principle for control problem associated with the primitive equations (PEs) of the ocean with periodic inputs. We also derive a second-order sufficient condition for optimality. This work is closely related to Wang (SIAM J. Control Optim. 41(2):583-606, 2002) and He (Acta Math. Sci. Ser. B Engl. Ed. 26(4):729-734, 2006), in which the authors proved similar results for the three-dimensional Navier-Stokes (NS) systems.

A stochastic collocation method for the second order wave equation with a discontinuous random speed

KAUST Repository

Motamed, Mohammad

2012-08-31

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.

Temporal Frequency Modulates Reaction Time Responses to First-Order and Second-Order Motion

Science.gov (United States)

Hutchinson, Claire V.; Ledgeway, Tim

2010-01-01

This study investigated the effect of temporal frequency and modulation depth on reaction times for discriminating the direction of first-order (luminance-defined) and second-order (contrast-defined) motion, equated for visibility using equal multiples of direction-discrimination threshold. Results showed that reaction times were heavily…

Structural changes of small amplitude kinetic Alfvén solitary waves due to second-order corrections

International Nuclear Information System (INIS)

Choi, Cheong R.

2015-01-01

The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-order equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites

Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

Directory of Open Access Journals (Sweden)

Iacob Theodor-Felix

2015-12-01

Full Text Available We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation

Institute of Scientific and Technical Information of China (English)

ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo

2007-01-01

A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.

Generalized rate-equation analysis of excitation exchange between silicon nanoclusters and erbium ions

International Nuclear Information System (INIS)

Kenyon, A. J.; Wojdak, M.; Ahmad, I.; Loh, W. H.; Oton, C. J.

2008-01-01

We discuss the use of rate equations to analyze the sensitization of erbium luminescence by silicon nanoclusters. In applying the general form of second-order coupled rate-equations to the Si nanocluster-erbium system, we find that the photoluminescence dynamics cannot be described using a simple rate equation model. Both rise and fall times exhibit a stretched exponential behavior, which we propose arises from a combination of a strongly distance-dependent nanocluster-erbium interaction, along with the finite size distribution and indirect band gap of the silicon nanoclusters. Furthermore, the low fraction of erbium ions that can be excited nonresonantly is a result of the small number of ions coupled to nanoclusters

Nonlocal higher order evolution equations

KAUST Repository

Rossi, Julio D.

2010-06-01

In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.

Solving the radiation diffusion and energy balance equations using pseudo-transient continuation

International Nuclear Information System (INIS)

Shestakov, A.I.; Greenough, J.A.; Howell, L.H.

2005-01-01

We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks

First- and second-order charged particle optics

International Nuclear Information System (INIS)

Brown, K.L.; Servranckx, R.V.

1984-07-01

Since the invention of the alternating gradient principle there has been a rapid evolution of the mathematics and physics techniques applicable to charged particle optics. In this publication we derive a differential equation and a matrix algebra formalism valid to second-order to present the basic principles governing the design of charged particle beam transport systems. A notation first introduced by John Streib is used to convey the essential principles dictating the design of such beam transport systems. For example the momentum dispersion, the momentum resolution, and all second-order aberrations are expressed as simple integrals of the first-order trajectories (matrix elements) and of the magnetic field parameters (multipole components) characterizing the system. 16 references, 30 figures

A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

Energy Technology Data Exchange (ETDEWEB)

Wang, Bin, E-mail: wangbinmaths@gmail.com [Department of Mathematics, Nanjing University, State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing 210093 (China); Wu, Xinyuan, E-mail: xywu@nju.edu.cn [Department of Mathematics, Nanjing University, State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing 210093 (China)

2012-03-05

This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q{sup ″}(t)+Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=−∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=1/2 p{sup T}p+1/2 q{sup T}Mq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi–Pasta–Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method. -- Highlights: ► A novel high order energy-preserving integrator AAVF-GL is proposed. ► The important properties of the new integrator AAVF-GL are shown. ► Numerical experiment is carried out compared with AVF method etc. appeared recently.

Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

Directory of Open Access Journals (Sweden)

Boris V. Kapitonov

2010-02-01

Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

Green's matrix for a second-order self-adjoint matrix differential operator

International Nuclear Information System (INIS)

Sisman, Tahsin Cagri; Tekin, Bayram

2010-01-01

A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.

Well-Balanced Second-Order Approximation of the Shallow Water Equations With Friction via Continuous Galerkin Finite Elements

Science.gov (United States)

Quezada de Luna, M.; Farthing, M.; Guermond, J. L.; Kees, C. E.; Popov, B.

2017-12-01

The Shallow Water Equations (SWEs) are popular for modeling non-dispersive incompressible water waves where the horizontal wavelength is much larger than the vertical scales. They can be derived from the incompressible Navier-Stokes equations assuming a constant vertical velocity. The SWEs are important in Geophysical Fluid Dynamics for modeling surface gravity waves in shallow regimes; e.g., in the deep ocean. Some common geophysical applications are the evolution of tsunamis, river flooding and dam breaks, storm surge simulations, atmospheric flows and others. This work is concerned with the approximation of the time-dependent Shallow Water Equations with friction using explicit time stepping and continuous finite elements. The objective is to construct a method that is at least second-order accurate in space and third or higher-order accurate in time, positivity preserving, well-balanced with respect to rest states, well-balanced with respect to steady sliding solutions on inclined planes and robust with respect to dry states. Methods fulfilling the desired goals are common within the finite volume literature. However, to the best of our knowledge, schemes with the above properties are not well developed in the context of continuous finite elements. We start this work based on a finite element method that is second-order accurate in space, positivity preserving and well-balanced with respect to rest states. We extend it by: modifying the artificial viscosity (via the entropy viscosity method) to deal with issues of loss of accuracy around local extrema, considering a singular Manning friction term handled via an explicit discretization under the usual CFL condition, considering a water height regularization that depends on the mesh size and is consistent with the polynomial approximation, reducing dispersive errors introduced by lumping the mass matrix and others. After presenting the details of the method we show numerical tests that demonstrate the well

Structural equations for Killing tensors of order two. II

International Nuclear Information System (INIS)

Hauser, I.; Malhiot, R.J.

1975-01-01

In a preceding paper, a new form of the structural equations for any Killing tensor of order two have been derived; these equations constitute a system analogous to the Killing vector equations Nabla/sub alpha/ K/sub beta/ = ω/sub alpha beta/ = -ω/sub beta alpha/ and Nabla/sub gamma/ ω/sub alpha beta = R/sub alpha beta gamma delta/ K/sup delta/. The first integrability condition for the Killing tensor structural equations is now derived. The structural equations and the integrability condition have forms which can readily be expressed in terms of a null tetrad to furnish a Killing tensor parallel of the Newman--Penrose equations; this is briefly described. The integrability condition implies the new result, for any given space--time, that the dimension of the set of second-order Killing tensors attains its maximum possible value of 50 only if the space--time is of constant curvature. Potential applications of the structural equations are discussed

On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

Directory of Open Access Journals (Sweden)

Emmanuel K. Essel

2014-01-01

Full Text Available We prove that the totally nonlinear second-order neutral differential equation \\[\\frac{d^2}{dt^2}x(t+p(t\\frac{d}{dt}x(t+q(th(x(t\\] \\[=\\frac{d}{dt}c(t,x(t-\\tau(t+f(t,\\rho(x(t,g(x(t-\\tau(t\\] has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point theorem.

Blow-up of solutions for the sixth-order thin film equation with ...

Indian Academy of Sciences (India)

College of Mathematics and Statistics, Nanjing University of Information ... By using the improved energy estimate method and by constructing second-order ... In the last 20 years, higher-order nonlinear parabolic partial differential ... in [11] to deal with the second-order p-Laplacian equation (see also [12–14] for further.

Thermodynamic Analysis of Chemically Reacting Mixtures-Comparison of First and Second Order Models.

Science.gov (United States)

Pekař, Miloslav

2018-01-01

Recently, a method based on non-equilibrium continuum thermodynamics which derives thermodynamically consistent reaction rate models together with thermodynamic constraints on their parameters was analyzed using a triangular reaction scheme. The scheme was kinetically of the first order. Here, the analysis is further developed for several first and second order schemes to gain a deeper insight into the thermodynamic consistency of rate equations and relationships between chemical thermodynamic and kinetics. It is shown that the thermodynamic constraints on the so-called proper rate coefficient are usually simple sign restrictions consistent with the supposed reaction directions. Constraints on the so-called coupling rate coefficients are more complex and weaker. This means more freedom in kinetic coupling between reaction steps in a scheme, i.e., in the kinetic effects of other reactions on the rate of some reaction in a reacting system. When compared with traditional mass-action rate equations, the method allows a reduction in the number of traditional rate constants to be evaluated from data, i.e., a reduction in the dimensionality of the parameter estimation problem. This is due to identifying relationships between mass-action rate constants (relationships which also include thermodynamic equilibrium constants) which have so far been unknown.

Investigating local network interactions underlying first- and second-order processing.

Science.gov (United States)

Ellemberg, Dave; Allen, Harriet A; Hess, Robert F

2004-01-01

We compared the spatial lateral interactions for first-order cues to those for second-order cues, and investigated spatial interactions between these two types of cues. We measured the apparent modulation depth of a target Gabor at fixation, in the presence and the absence of horizontally flanking Gabors. The Gabors' gratings were either added to (first-order) or multiplied with (second-order) binary 2-D noise. Apparent "contrast" or modulation depth (i.e., the perceived difference between the high and low luminance regions for the first-order stimulus, or between the high and low contrast regions for the second-order stimulus) was measured with a modulation depth-matching paradigm. For each observer, the first- and second-order Gabors were equated for apparent modulation depth without the flankers. Our results indicate that at the smallest inter-element spacing, the perceived reduction in modulation depth is significantly smaller for the second-order than for the first-order stimuli. Further, lateral interactions operate over shorter distances and the spatial frequency and orientation tuning of the suppression effect are broader for second- than first-order stimuli. Finally, first- and second-order information interact in an asymmetrical fashion; second-order flankers do not reduce the apparent modulation depth of the first-order target, whilst first-order flankers reduce the apparent modulation depth of the second-order target.

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2007-01-01

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

The gravitational wave stress–energy (pseudo)-tensor in modified gravity

Science.gov (United States)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy–momentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stress–energy pseudo-tensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau–Lifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, Jordan–Fierz–Brans–Dicky theoy, and Einstein-Æther theory to find the gravitational wave stress–energy pseudo-tensor and calculate the rate at which energy and linear momentum is carried away from the system. The stress–energy tensor and the rate of linear momentum loss in Einstein-Æther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stress–energy pseudo-tensor can be functionally different. We also find that the Noether method yields a stress–energy tensor that is not symmetric or gauge-invariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in Einstein-Æther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.

Extended rate equations

International Nuclear Information System (INIS)

Shore, B.W.

1981-01-01

The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

Stepanov-like weighted pseudo almost automorphic solutions to ...

Indian Academy of Sciences (India)

Abstract. In this article, we study the concept of Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. We establish the results with Lipschitz condition and without Lipschitz condition on the forcing term. An interesting example is presented to illustrate the main ...

Reactor dynamics experiment of nuclear ship Mutsu using pseudo random signal (II). The second experiment

International Nuclear Information System (INIS)

Hayashi, Koji; Shimazaki, Junya; Nabeshima, Kunihiko; Ochiai, Masaaki; Shinohara, Yoshikuni; Inoue, Kimihiko.

1995-01-01

In order to investigate dynamics of the reactor plant of the nuclear ship Mutsu, the second reactor noise experiment using pseudo random binary sequences (PRBS) was performed on August 30, 1991 in the third experimental navigation. The experiments using both reactivity and load disturbances were performed at 50% of reactor power and under a quiet sea condition. Each PRBS was applied by manual operation of the control rod or the main steam valve. Various signals of the plant responses and of the acceleration of ship motion were measured. Furthermore, natural reactor noise signals were measured after each PRBS experiment in order to evaluate the effects of the PRBS disturbances. This paper summarizes the planning of the experiment, the instruction for the experiment and logs, the data recording conditions, recorded signal wave forms and the results of power spectral analysis. (author)

A NEW OSCILLATION CRITERION FOR FIRST ORDER NEUTRAL DELAY DIFFERENTIAL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.

Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

Science.gov (United States)

de Souza, S. M.; Rojas, Onofre

2018-01-01

There are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of chain structures, which exhibit unexpected behaviors quite similar to the first and second order phase transition, which could be confused naively with an authentic phase transition. Through the analysis of the first derivative of free energy, such as entropy, magnetization, and internal energy, a "sudden" jump that closely resembles a first-order phase transition at finite temperature occurs. However, by analyzing the second derivative of free energy, such as specific heat and magnetic susceptibility at finite temperature, it behaves quite similarly to a second-order phase transition exhibiting an astonishingly sharp and fine peak. The correlation length also confirms the evidence of this pseudo-transition temperature, where a sharp peak occurs at the pseudo-critical temperature. We also present the necessary conditions for the emergence of these quasi-phases and pseudo-transitions.

Kinetics of two simultaneous second-order reactions occurring in different zones

International Nuclear Information System (INIS)

Dole, M.; Hsu, C.S.; Patel, V.M.; Patel, G.N.

1975-01-01

Equations have been derived for the case of free radicals recombining according to the second-order kinetics with or without diffusion control under the conditions that there are two simultaneous spatially separated recombination reactions but that only the overall free-radical concentration can be observed. The properties of these equations are discussed and methods for determining the three independent parameters in the first case and five in the second developed. The resulting equations have been applied to the interpretation of data obtained in studying the decay of allyl chain free radicals in irradiated extended chain crystalline polyethylene

The Cauchy problem for higher order abstract differential equations

CERN Document Server

Xiao, Ti-Jun

1998-01-01

This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.

SEARCHING FOR LOW WEIGHT PSEUDO-CODEWORDS

International Nuclear Information System (INIS)

Chertkov, Michael; Stepanov, Mikhail

2007-01-01

Belief Propagation (BP) and Linear Programming (LP) decodings of LDPC codes are discussed. The authors summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes. Instantons are special, code and decoding specific, configurations of the channel noise contributing most to the Frame-Error-Rate (FER). Instantons are decoded into pseudo-codewords. Instanton/pseudo-codeword with the lowest weight describes the largest Signal-to-Noise-Ratio (SNR) asymptotic of FER, while the whole spectra of the low weight instantons is descriptive of the FER vs. SNR profile in the extended error-floor domain. First, they describe a general optimization method that allows to find the instantons for any coding/decoding. Second, they introduce LP-specific pseudo-codeword search algorithm that allows efficient calculations of the pseudo-codeword spectra. Finally, they discuss results of combined BP/LP error-floor exploration experiments for two mode codes.

SEARCHING FOR LOW WEIGHT PSEUDO-CODEWORDS

Energy Technology Data Exchange (ETDEWEB)

CHERTKOV, MICHAEL [Los Alamos National Laboratory; STEPANOV, MIKHAIL [Los Alamos National Laboratory

2007-01-23

Belief Propagation (BP) and Linear Programming (LP) decodings of LDPC codes are discussed. The authors summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes. Instantons are special, code and decoding specific, configurations of the channel noise contributing most to the Frame-Error-Rate (FER). Instantons are decoded into pseudo-codewords. Instanton/pseudo-codeword with the lowest weight describes the largest Signal-to-Noise-Ratio (SNR) asymptotic of FER, while the whole spectra of the low weight instantons is descriptive of the FER vs. SNR profile in the extended error-floor domain. First, they describe a general optimization method that allows to find the instantons for any coding/decoding. Second, they introduce LP-specific pseudo-codeword search algorithm that allows efficient calculations of the pseudo-codeword spectra. Finally, they discuss results of combined BP/LP error-floor exploration experiments for two mode codes.

A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations

International Nuclear Information System (INIS)

Introini, C.; Belliard, M.; Fournier, C.

2014-01-01

In this paper, we propose a second order penalized direct forcing method to deal with fluid-structure interaction problems involving complex static or time-varying geometries. As this work constitutes a first step toward more complicated problems, our developments are restricted to Dirichlet boundary condition in purely hydraulic context. The proposed method belongs to the class of immersed boundary techniques and consists in immersing the physical domain in a Cartesian fictitious one of simpler geometry on fixed grids. A penalized forcing term is added to the momentum equation to take the boundary conditions around/inside the obstacles into account. This approach avoids the tedious task of re-meshing and allows us to use fast and accurate numerical schemes. In contrary, as the immersed boundary is described by a set of Lagrangian points that does not generally coincide with those of the Eulerian grid, numerical procedures are required to reconstruct the velocity field near the immersed boundary. Here, we develop a second order linear interpolation scheme and we compare it to a simpler model of order one. As far as the governing equations are concerned, we use a particular fractional-step method in which the penalized forcing term is distributed both in prediction and correction equations. The accuracy of the proposed method is assessed through 2-D numerical experiments involving static and rotating solids. We show in particular that the numerical rate of convergence of our method is quasi-quadratic. (authors)

Second-Rate Coverage of Second-Order Elections: Czech and Slovak Elections to the EP in the Media

Directory of Open Access Journals (Sweden)

Jan Kovář

2010-12-01

Full Text Available Elections to the European Parliament (EP are considered second-order national elections (SOE. The SOE model suggests that there is a qualitative difference between different types of elections depending on the perception of what is at stake. Compared to first order elections, in second order elections there is less at stake because they do not determine the composition of government. Given that voters behave differently in second-order elections, the question arises: do the media also consider second-order elections less interesting and therefore devote to them less coverage? The media play a crucial role in informing citizens about such events as elections; they function as intermediaries between the electorate and the political arena. However, little is known about how EU issues are covered in the media, particularly in the new EU member states. Conducting a content analysis and applying the second-order election model, this paper analyses TV news coverage of the 2004 and 2009 European elections in the Czech Republic and Slovakia in a comparative fashion. The findings are discussed in the light of existing research literature on the EU’s legitimacy as well as its alleged democratic and communication deficit, not least because the EU relies on the media in strengthening (albeit indirectly its legitimacy by increasing citizen awareness of its activities.

Studies on Microwave Heated Drying-rate Equations of Foods

OpenAIRE

呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右

1990-01-01

In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...

Oscillation criteria for third order nonlinear delay differential equations with damping

Directory of Open Access Journals (Sweden)

Said R. Grace

2015-01-01

Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

Pseudo-Haptic Feedback in Teleoperation.

Science.gov (United States)

Neupert, Carsten; Matich, Sebastian; Scherping, Nick; Kupnik, Mario; Werthschutzky, Roland; Hatzfeld, Christian

2016-01-01

In this paper, we develop possible realizations of pseudo-haptic feedback in teleoperation systems based on existing works for pseudo-haptic feedback in virtual reality and the intended applications. We derive four potential factors affecting the performance of haptic feedback (calculation operator, maximum displacement, offset force, and scaling factor), which are analyzed in three compliance identification experiments. First, we analyze the principle usability of pseudo-haptic feedback by comparing information transfer measures for teleoperation and direct interaction. Pseudo-haptic interaction yields well above-chance performance, while direct interaction performs almost perfectly. In order to optimize pseudo-haptic feedback, in the second study we perform a full-factorial experimental design with 36 subjects performing 6,480 trials with 36 different treatments. Information transfer ranges from 0.68 bit to 1.72 bit in a task with a theoretical maximum of 2.6 bit, with a predominant effect of the calculation operator and a minor effect of the maximum displacement. In a third study, short- and long-term learning effects are analyzed. Learning effects regarding the performance of pseudo-haptic feedback cannot be observed for single-day experiments. Tests over 10 days show a maximum increase in information transfer of 0.8 bit. The results show the feasibility of pseudo-haptic feedback for teleoperation and can be used as design basis for task-specific systems.

Geometric model of pseudo-distance measurement in satellite location systems

Science.gov (United States)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

RDTM solution of Caputo time fractional-order hyperbolic telegraph equation

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2013-03-01

Full Text Available In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE. The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM. The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.

Solution of second order supersymmetrical intertwining relations in Minkowski plane

Energy Technology Data Exchange (ETDEWEB)

Ioffe, M. V., E-mail: m.ioffe@spbu.ru; Kolevatova, E. V., E-mail: e.v.kolev@yandex.ru [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034 (Russian Federation); Nishnianidze, D. N., E-mail: cutaisi@yahoo.com [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034 (Russian Federation); Akaki Tsereteli State University, 4600 Kutaisi, Georgia (United States)

2016-08-15

Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.

Constrained generalized mechanics. The second-order case

International Nuclear Information System (INIS)

Tapia, V.

1985-01-01

The Dirac formalism for constrained systems is developed for systems described by a Lagrangian depending on up to a second-order time derivatives of the generalized co-ordinates (accelerations). It turns out that for a Lagrangian of this kind differing by a total time derivative from a Lagrangian depending on only up to first-order time-derivatives of the generalized co-ordinates (velocities), both classical mechanics at the Lagrangian level are the same; at the Hamiltonian level the two classical mechanics differ conceptually even when the solutions to both sets of Hamiltonian equations of motion are the same

Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

International Nuclear Information System (INIS)

Yasa, F.; Anli, F.; Guengoer, S.

2007-01-01

We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

On the second-order temperature jump coefficient of a dilute gas

Science.gov (United States)

Radtke, Gregg A.; Hadjiconstantinou, N. G.; Takata, S.; Aoki, K.

2012-09-01

We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

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.

Pseudo-supersymmetry and the domain-wall/cosmology correspondence

International Nuclear Information System (INIS)

Skenderis, Kostas; Townsend, Paul K

2007-01-01

The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain-wall solutions that admit a Killing spinor are shown to correspond to a cosmology that admits a pseudo-Killing spinor; whereas the Killing spinor obeys a Dirac-type equation with Hermitian 'mass'-matrix, the corresponding pseudo-Killing spinor obeys a Dirac-type equation with a anti-Hermitian 'mass'-matrix. We comment on some implications of (pseudo)supersymmetry

Second order numerical method of two-fluid model of air-water flow

International Nuclear Information System (INIS)

Tiselj, I.; Petelin, S.

1995-01-01

Model considered in this paper is six-equation two-fluid model used in computer code RELAP5. Air-water equations were taken in a code named PDE to avoid additional problems caused by condensation or vaporization. Terms with space derivatives were added in virtual mass term in momentum equations to ensure the hyperbolicity of the equations. Numerical method in PDE code is based on approximate Riemann solvers. Equations are solved on non-staggered grid with explicit time advancement and with upwind discretization of the convective terms in characteristic form of the equations. Flux limiters are used to find suitable combinations of the first (upwind) and the second order (Lax-Wendroff) discretization s which ensure second order accuracy on smooth solutions and damp oscillations around the discontinuities. Because of the small time steps required and because of its non-dissipative nature the scheme is suitable for the prediction of the fast transients: pressure waves, shock and rarefaction waves, water hammer or critical flow. Some preliminary results are presented for a shock tube problem and for Water Faucet problem - problems usually used as benchmarks for two-fluid computer codes. (author)

RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions

International Nuclear Information System (INIS)

Hackbusch, W.

1983-01-01

1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration

A high order solver for the unbounded Poisson equation

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...... of convergence consistent with the moments conserved by the applied smoothing function. In the hybrid particle-mesh method of Hockney and Eastwood (HE) the particles are interpolated onto a regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values...... and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight...

Third-order optical intensity correlation measurements of pseudo-thermal light

International Nuclear Information System (INIS)

Chen Xi-Hao; Wu Wei; Meng Shao-Ying; Li Ming-Fei

2014-01-01

Third-order Hanbrury Brown—Twiss and double-slit interference experiments with a pseudo-thermal light are performed by recording intensities in single, double and triple optical paths, respectively. The experimental results verifies the theoretical prediction that the indispensable condition for achieving a interference pattern or ghost image in Nth-order intensity correlation measurements is the synchronous detection of the same light field by each reference detector, no matter the intensities recorded in one, or two, or N optical paths. It is shown that, when the reference detectors are scanned in the opposite directions, the visibility and resolution of the third-order spatial correlation function of thermal light is much better than that scanned in the same direction, but it is no use for obtaining the Nth-order interference pattern or ghost image in the thermal Nth-order interference or ghost imaging. (general)

Comparison of second and third orders Runge-Kutta methods for ...

African Journals Online (AJOL)

This work is concerned with the analysis of second and third orders Runge- Kutta formulae capable of solving initial value problems in Ordinary Differential Equations of the form: y1 = f(x, y), y(x0) = y0, a £ x £ b. The intention is to find out which of these two orders can improve the performance of results when implemented ...

On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

Energy Technology Data Exchange (ETDEWEB)

Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

2005-01-28

Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs

Directory of Open Access Journals (Sweden)

K. S. Mahomed

2012-01-01

Full Text Available Symmetries of the fundamental first integrals for scalar second-order ordinary differential equations (ODEs which are linear or linearizable by point transformations have already been obtained. Firstly we show how one can determine the relationship between the symmetries and the first integrals of linear or linearizable scalar ODEs of order two. Secondly, a complete classification of point symmetries of first integrals of such linear ODEs is studied. As a consequence, we provide a counting theorem for the point symmetries of first integrals of scalar linearizable second-order ODEs. We show that there exists the 0-, 1-, 2-, or 3-point symmetry cases. It is shown that the maximal algebra case is unique.

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Exact solutions of the Fokker-Planck equation from an nth order supersymmetric quantum mechanics approach

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, Axel [Escuela Superior de Fisica y Matematicas, IPN, Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, Edificio 9, 07738 Mexico D.F. (Mexico)], E-mail: xbataxel@gmail.com; Rivas, Jesus Morales [Universidad Autonoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico D.F. (Mexico)], E-mail: jmr@correo.azc.uam.mx; Pena Gil, Jose Juan [Universidad Autonoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico D.F. (Mexico)], E-mail: jjpg@correo.azc.uam.mx; Garcia-Ravelo, Jesus [Escuela Superior de Fisica y Matematicas, IPN, Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, Edificio 9, 07738 Mexico D.F. (Mexico)], E-mail: ravelo@esfm.ipn.mx; Roy, Pinaki [Physics and Applied Mathematics Unit, Indian Statistical Institute, Calcutta-700108 (India)], E-mail: pinaki@isical.ac.in

2009-04-20

We generalize the formalism of nth order Supersymmetric Quantum Mechanics (n-SUSY) to the Fokker-Planck equation for constant diffusion coefficient and stationary drift potential. The SUSY partner drift potentials and the corresponding solutions of the Fokker-Planck equation are given explicitly. As an application, we generate new solutions of the Fokker-Planck equation by means of our first- and second-order transformation.

Exact solutions of the Fokker-Planck equation from an nth order supersymmetric quantum mechanics approach

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Rivas, Jesus Morales; Pena Gil, Jose Juan; Garcia-Ravelo, Jesus; Roy, Pinaki

2009-01-01

We generalize the formalism of nth order Supersymmetric Quantum Mechanics (n-SUSY) to the Fokker-Planck equation for constant diffusion coefficient and stationary drift potential. The SUSY partner drift potentials and the corresponding solutions of the Fokker-Planck equation are given explicitly. As an application, we generate new solutions of the Fokker-Planck equation by means of our first- and second-order transformation.

Problems which are well posed in a generalized sense with applications to the Einstein equations

International Nuclear Information System (INIS)

Kreiss, H-O; Winicour, J

2006-01-01

In the harmonic description of general relativity, the principal part of the Einstein equations reduces to a constrained system of ten curved space wave equations for the components of the spacetime metric. We use the pseudo- differential theory of systems which are strongly well posed in the generalized sense to establish the well posedness of constraint-preserving boundary conditions for this system when treated in a second-order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation

Pseudo-Newtonian planar circular restricted 3-body problem

International Nuclear Information System (INIS)

Dubeibe, F.L.; Lora-Clavijo, F.D.; González, Guillermo A.

2017-01-01

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor–Hoenselaers–Perjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter ϵ, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.

Pseudo-Newtonian planar circular restricted 3-body problem

Energy Technology Data Exchange (ETDEWEB)

Dubeibe, F.L., E-mail: fldubeibem@unal.edu.co [Facultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio (Colombia); Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Lora-Clavijo, F.D., E-mail: fadulora@uis.edu.co [Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); González, Guillermo A., E-mail: guillermo.gonzalez@saber.uis.edu.co [Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia)

2017-02-12

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor–Hoenselaers–Perjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter ϵ, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.

Periodic solutions to second-order indefinite singular equations

Czech Academy of Sciences Publication Activity Database

Hakl, Robert; Zamora, M.

2017-01-01

Roč. 263, č. 1 (2017), s. 451-469 ISSN 0022-0396 Institutional support: RVO:67985840 Keywords : degree theory * indefinite singularity * periodic solution * singular differential equation Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039617301134

Dynamics of massless higher spins in the second order in curvatures

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A [International Centre for Theoretical Physics, Trieste (Italy)

1990-04-05

The consistent equations of motion of interacting massless fields of all spins s=0, 1/2, 1, ..., {infinity} are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (orig.).

Existence of a solution to the Dirichlet problem associated to a second-order differential equation with singularities: the method of lower and upper functions

Czech Academy of Sciences Publication Activity Database

Hakl, Robert; Zamora, M.

2013-01-01

Roč. 20, č. 3 (2013), s. 469-491 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order singular equation * Dirichlet problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0030/gmj-2013-0030. xml ?format=INT

Finite difference schemes for second order systems describing black holes

International Nuclear Information System (INIS)

Motamed, Mohammad; Kreiss, H-O.; Babiuc, M.; Winicour, J.; Szilagyi, B.

2006-01-01

In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem

Nodal approximations of varying order by energy group for solving the diffusion equation

International Nuclear Information System (INIS)

Broda, J.T.

1992-02-01

The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the same order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics.

Science.gov (United States)

Yang, Mino

2007-06-07

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.

Dynamics of massless higher spins in the second order in curvatures

International Nuclear Information System (INIS)

Vasiliev, M.A.

1989-08-01

The consistent equations of motion of interacting fields of all spins s=0,1/2,1...∞ are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (author). 14 refs

Nonlinear second- and first-sound wave equations in 3He-4He mixtures

International Nuclear Information System (INIS)

Mohazzab, Masoud; Mulders, Norbert

2000-01-01

We derive nonlinear Burgers equations for first and second sound in mixtures of 3 He- 4 He, using a reductive perturbation method and obtain expressions for the nonlinear and dissipation coefficients. We further find a diffusion equation for a coupled temperature-concentration mode. The amplitude of first (second) sound generated from second (first) sound in mixtures is also derived. Our derivation includes the dependence of thermodynamical quantities on temperature, pressure, and 3 He concentration, and is valid up to a first order in terms of the isobaric expansion coefficient. We show that close to the λ line the nonlinearity of second sound in mixtures is enhanced as compared with pure 4 He

New second order Mumford-Shah model based on Γ-convergence approximation for image processing

Science.gov (United States)

Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Bai, Li

2016-05-01

In this paper, a second order variational model named the Mumford-Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford-Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H1 regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss-Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.

Approximating second-order vector differential operators on distorted meshes in two space dimensions

International Nuclear Information System (INIS)

Hermeline, F.

2008-01-01

A new finite volume method is presented for approximating second-order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite therefore, the most powerful linear solvers can be applied. The method has been tested on a few second-order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second-order accurate and locking-free. (authors)

Theory of relaxation phenomena in a spin-3/2 Ising system near the second-order phase transition temperature

International Nuclear Information System (INIS)

Keskin, Mustafa; Canko, Osman

2005-01-01

The relaxation behavior of the spin-3/2 Ising model Hamiltonian with bilinear and biquadratic interactions near the second-order phase transition temperature or critical temperature is studied by means of the Onsager's theory of irreversible thermodynamics or the Onsager reciprocity theorem (ORT). First, we give the equilibrium case briefly within the molecular-field approximation in order to study the relaxation behavior by using the ORT. Then, the ORT is applied to the model and the kinetic equations are obtained. By solving these equations, three relaxation times are calculated and examined for temperatures near the second-order phase transition temperature. It is found that one of the relaxation times goes to infinity near the critical temperature on either side, the second relaxation time makes a cusp at the critical temperature and third one behaves very differently in which it terminates at the critical temperature while approaching it, then showing a 'flatness' property and then decreases. We also study the influences of the Onsager rate coefficients on the relaxation times. The behavior of these relaxation times is discussed and compared with the spin-1/2 and spin-1 Ising systems

Groups of integral transforms generated by Lie algebras of second-and higher-order differential operators

International Nuclear Information System (INIS)

Steinberg, S.; Wolf, K.B.

1979-01-01

The authors study the construction and action of certain Lie algebras of second- and higher-order differential operators on spaces of solutions of well-known parabolic, hyperbolic and elliptic linear differential equations. The latter include the N-dimensional quadratic quantum Hamiltonian Schroedinger equations, the one-dimensional heat and wave equations and the two-dimensional Helmholtz equation. In one approach, the usual similarity first-order differential operator algebra of the equation is embedded in the larger one, which appears as a quantum-mechanical dynamic algebra. In a second approach, the new algebra is built as the time evolution of a finite-transformation algebra on the initial conditions. In a third approach, the algebra to inhomogeneous similarity algebra is deformed to a noncompact classical one. In every case, we can integrate the algebra to a Lie group of integral transforms acting effectively on the solution space of the differential equation. (author)

Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2015-01-01

the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

Elliptic partial differential equations of second order

CERN Document Server

Gilbarg, David

2001-01-01

From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985.

(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing

Energy Technology Data Exchange (ETDEWEB)

Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-11-30

The Second-Level Adjoint Sensitivity System (2nd-LASS) that yields the second-order sensitivities of a response of uncollided particles with respect to isotope densities, cross sections, and source emission rates is derived in Refs. 1 and 2. In Ref. 2, we solved problems for the uncollided leakage from a homogeneous sphere and a multiregion cylinder using the PARTISN multigroup discrete-ordinates code. In this memo, we derive solutions of the 2nd-LASS for the particular case when the response is a flux or partial current density computed at a single point on the boundary, and the inner products are computed using ray-tracing. Both the PARTISN approach and the ray-tracing approach are implemented in a computer code, SENSPG. The next section of this report presents the equations of the 1st- and 2nd-LASS for uncollided particles and the first- and second-order sensitivities that use the solutions of the 1st- and 2nd-LASS. Section III presents solutions of the 1st- and 2nd-LASS equations for the case of ray-tracing from a detector point. Section IV presents specific solutions of the 2nd-LASS and derives the ray-trace form of the inner products needed for second-order sensitivities. Numerical results for the total leakage from a homogeneous sphere are presented in Sec. V and for the leakage from one side of a two-region slab in Sec. VI. Section VII is a summary and conclusions.

On the dynamics of second-order Lagrangian systems

Directory of Open Access Journals (Sweden)

Ronald Adams

2017-04-01

Full Text Available In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution equations for broken geodesic curves that could be used to investigate more general systems or closed characteristics.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

Science.gov (United States)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Algebraic properties of first integrals for systems of second-order ...

African Journals Online (AJOL)

Symmetries of the rst integrals for scalar linear or linearizable second- order ordinary differential equations (ODEs) have already been derived and shown to exhibit interesting properties. One of these is that the symmetry algebra sl(3; R ) is generated by the three triplets of symmetries of the functionally independent first ...

Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

Directory of Open Access Journals (Sweden)

Haotao Cai

2017-01-01

Full Text Available We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.

Riccati-parameter solutions of nonlinear second-order ODEs

International Nuclear Information System (INIS)

Reyes, M A; Rosu, H C

2008-01-01

It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure

Discrete Weighted Pseudo-Almost Automorphy and Applications

Directory of Open Access Journals (Sweden)

Zhinan Xia

2014-01-01

Full Text Available We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

Pseudo-differential operators on manifolds with singularities

CERN Document Server

Schulze, B-W

1991-01-01

The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

Boundary-value problems for first and second order functional differential inclusions

Directory of Open Access Journals (Sweden)

Shihuang Hong

2003-03-01

Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.

Radiation-reaction force on a small charged body to second order

Science.gov (United States)

Moxon, Jordan; Flanagan, Éanna

2018-05-01

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.

Critical Opalescence around the QCD Critical Point and Second-order Relativistic Hydrodynamic Equations Compatible with Boltzmann Equation

International Nuclear Information System (INIS)

Kunihiro, Teiji; Minami, Yuki; Tsumura, Kyosuke

2009-01-01

The dynamical density fluctuations around the QCD critical point (CP) are analyzed using relativistic dissipative fluid dynamics, and we show that the sound mode around the QCD CP is strongly attenuated whereas the thermal fluctuation stands out there. We speculate that if possible suppression or disappearance of a Mach cone, which seems to be created by the partonic jets at RHIC, is observed as the incident energy of the heavy-ion collisions is decreased, it can be a signal of the existence of the QCD CP. We have presented the Israel-Stewart type fluid dynamic equations that are derived rigorously on the basis of the (dynamical) renormalization group method in the second part of the talk, which we omit here because of a lack of space.

Critical Opalescence around the QCD Critical Point and Second-order Relativistic Hydrodynamic Equations Compatible with Boltzmann Equation

Science.gov (United States)

Kunihiro, Teiji; Minami, Yuki; Tsumura, Kyosuke

2009-11-01

The dynamical density fluctuations around the QCD critical point (CP) are analyzed using relativistic dissipative fluid dynamics, and we show that the sound mode around the QCD CP is strongly attenuated whereas the thermal fluctuation stands out there. We speculate that if possible suppression or disappearance of a Mach cone, which seems to be created by the partonic jets at RHIC, is observed as the incident energy of the heavy-ion collisions is decreased, it can be a signal of the existence of the QCD CP. We have presented the Israel-Stewart type fluid dynamic equations that are derived rigorously on the basis of the (dynamical) renormalization group method in the second part of the talk, which we omit here because of a lack of space.

Thermodynamic properties and adsorption behaviour of hydrogel nanocomposites for cadmium removal from mine effluents

CSIR Research Space (South Africa)

Fosso-Kankeu, E

2017-04-01

Full Text Available followed the pseudo-second-order rate equation, whereas, the adsorption isotherm followed both the Freundlich and Langmuir isotherm models. The thermodynamics studies revealed that the adsorption processes were spontaneous and endothermic in nature...

q-Karamata functions and second order q-difference equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel; Vítovec, J.

-, č. 24 (2011), s. 1-20 ISSN 1417-3875 Institutional research plan: CEZ:AV0Z10190503 Keywords : regularly varying functions * rapidly varying functions * q-difference equations Subject RIV: BA - General Mathematics Impact factor: 0.557, year: 2011

Exact polynomial solutions of second order differential equations and their applications

International Nuclear Information System (INIS)

Zhang Yaozhong

2012-01-01

We find all polynomials Z(z) such that the differential equation where X(z), Y(z), Z(z) are polynomials of degree at most 4, 3, 2, respectively, has polynomial solutions S(z) = ∏ n i=1 (z − z i ) of degree n with distinct roots z i . We derive a set of n algebraic equations which determine these roots. We also find all polynomials Z(z) which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schrödinger-type differential equations describing: (1) two Coulombically repelling electrons on a sphere; (2) Schrödinger equation from the kink stability analysis of φ 6 -type field theory; (3) static perturbations for the non-extremal Reissner–Nordström solution; (4) planar Dirac electron in Coulomb and magnetic fields; and (5) O(N) invariant decatic anharmonic oscillator. (paper)

Monge-Ampere equations and tensorial functors

International Nuclear Information System (INIS)

Tunitsky, Dmitry V

2009-01-01

We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

Second Order Ideal-Ward Continuity

Directory of Open Access Journals (Sweden)

Bipan Hazarika

2014-01-01

Full Text Available The main aim of the paper is to introduce a concept of second order ideal-ward continuity in the sense that a function f is second order ideal-ward continuous if I-limn→∞Δ2f(xn=0 whenever I-limn→∞Δ2xn=0 and a concept of second order ideal-ward compactness in the sense that a subset E of R is second order ideal-ward compact if any sequence x=(xn of points in E has a subsequence z=(zk=(xnk of the sequence x such that I-limk→∞Δ2zk=0 where Δ2zk=zk+2-2zk+1+zk. We investigate the impact of changing the definition of convergence of sequences on the structure of ideal-ward continuity in the sense of second order ideal-ward continuity and compactness of sets in the sense of second order ideal-ward compactness and prove related theorems.

Limit Properties of Solutions of Singular Second-Order Differential Equations

Directory of Open Access Journals (Sweden)

Weinmüller Ewa

2009-01-01

Full Text Available We discuss the properties of the differential equation , a.e. on , where , and satisfies the -Carathéodory conditions on for some . A full description of the asymptotic behavior for of functions satisfying the equation a.e. on is given. We also describe the structure of boundary conditions which are necessary and sufficient for to be at least in . As an application of the theory, new existence and/or uniqueness results for solutions of periodic boundary value problems are shown.

Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

2011-01-01

A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...

Equation of state at finite net-baryon density using Taylor coefficients up to sixth order

International Nuclear Information System (INIS)

Huovinen, Pasi; Petreczky, Péter; Schmidt, Christian

2014-01-01

We employ the lattice QCD data on Taylor expansion coefficients up to sixth order to construct an equation of state at finite net-baryon density. When we take into account how hadron masses depend on lattice spacing and quark mass, the coefficients evaluated using the p4 action are equal to those of hadron resonance gas at low temperature. Thus the parametrised equation of state can be smoothly connected to the hadron resonance gas equation of state. We see that the equation of state using Taylor coefficients up to second order is realistic only at low densities, and that at densities corresponding to s/n B ≳40, the expansion converges by the sixth order term

Remarks on second-order quadratic systems in algebras

Directory of Open Access Journals (Sweden)

Art Sagle

2017-10-01

Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

Nonoscillation criteria for half-linear second order difference equations

Czech Academy of Sciences Publication Activity Database

Došlý, Ondřej; Řehák, Pavel

2001-01-01

Roč. 42, - (2001), s. 453-464 ISSN 0898-1221 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Keywords : half-linear difference equation%nonoscillation criteria%variational principle Subject RIV: BA - General Mathematics Impact factor: 0.383, year: 2001

An extended integrable fractional-order KP soliton hierarchy

International Nuclear Information System (INIS)

Li Li

2011-01-01

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

An extended integrable fractional-order KP soliton hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2011-01-17

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

Binocular Combination of Second-Order Stimuli

Science.gov (United States)

Zhou, Jiawei; Liu, Rong; Zhou, Yifeng; Hess, Robert F.

2014-01-01

Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements. PMID:24404180

Polymer density functional theory approach based on scaling second-order direct correlation function.

Science.gov (United States)

Zhou, Shiqi

2006-06-01

A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations

International Nuclear Information System (INIS)

Boukir, K.

1994-06-01

This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs

On the second-order homogenization of wave motion in periodic media and the sound of a chessboard

Science.gov (United States)

Wautier, Antoine; Guzina, Bojan B.

2015-05-01

The goal of this study is to better understand the mathematical structure and ramifications of the second-order homogenization of low-frequency wave motion in periodic solids. To this end, multiple-scales asymptotic approach is applied to the scalar wave equation (describing anti-plane shear motion) in one and two spatial dimensions. In contrast to previous studies where the second-order homogenization has lead to the introduction of a single fourth-order derivative in the governing equation, present investigation demonstrates that such (asymptotic) approach results in a family of field equations uniting spatial, temporal, and mixed fourth-order derivatives - that jointly control incipient wave dispersion. Given the consequent freedom in selecting the affiliated lengthscale parameters, the notion of an optimal asymptotic model is next considered in a one-dimensional setting via its ability to capture the salient features of wave propagation within the first Brillouin zone, including the onset and magnitude of the phononic band gap. In the context of two-dimensional wave propagation, on the other hand, the asymptotic analysis is first established in a general setting, exposing the constant shear modulus as sufficient condition under which the second-order approximation of a bi-periodic elastic solid is both isotropic and limited to even-order derivatives. On adopting a chessboard-like periodic structure (with contrasts in both modulus and mass density) as a testbed for in-depth analytical treatment, it is next shown that the second-order approximation of germane wave motion is governed by a family fourth-order differential equations that: (i) entail exclusively even-order derivatives and homogenization coefficients that depend explicitly on the contrast in mass density; (ii) describe anisotropic wave dispersion characterized by the "sin4 θ +cos4 θ" term, and (iii) include the asymptotic model for a square lattice of circular inclusions as degenerate case. For

On periodic solutions to second-order Duffing type equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Šremr, Jiří

2018-01-01

Roč. 40, April (2018), s. 215-242 ISSN 1468-1218 Institutional support: RVO:67985840 Keywords : periodic solution * Duffing type equation * positive solution Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.659, year: 2016 http://www. science direct.com/ science /article/pii/S1468121817301335?via%3Dihub

A unified model for transfer alignment at random misalignment angles based on second-order EKF

International Nuclear Information System (INIS)

Cui, Xiao; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo; Mei, Chunbo

2017-01-01

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles. (paper)

A unified model for transfer alignment at random misalignment angles based on second-order EKF

Science.gov (United States)

Cui, Xiao; Mei, Chunbo; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo

2017-04-01

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

Symmetries, integrals, and three-dimensional reductions of Plebanski's second heavenly equation

International Nuclear Information System (INIS)

Neyzi, F.; Sheftel, M. B.; Yazici, D.

2007-01-01

We study symmetries and conservation laws for Plebanski's second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems

Generalised linear models for correlated pseudo-observations, with applications to multi-state models

DEFF Research Database (Denmark)

Andersen, Per Kragh; Klein, John P.; Rosthøj, Susanne

2003-01-01

Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model......Generalised estimating equation; Generalised linear model; Jackknife pseudo-value; Logistic regression; Markov Model; Multi-state model...

Empirical equations for the prediction of PGA and pseudo spectral accelerations using Iranian strong-motion data

Science.gov (United States)

Zafarani, H.; Luzi, Lucia; Lanzano, Giovanni; Soghrat, M. R.

2018-01-01

A recently compiled, comprehensive, and good-quality strong-motion database of the Iranian earthquakes has been used to develop local empirical equations for the prediction of peak ground acceleration (PGA) and 5%-damped pseudo-spectral accelerations (PSA) up to 4.0 s. The equations account for style of faulting and four site classes and use the horizontal distance from the surface projection of the rupture plane as a distance measure. The model predicts the geometric mean of horizontal components and the vertical-to-horizontal ratio. A total of 1551 free-field acceleration time histories recorded at distances of up to 200 km from 200 shallow earthquakes (depth < 30 km) with moment magnitudes ranging from Mw 4.0 to 7.3 are used to perform regression analysis using the random effects algorithm of Abrahamson and Youngs (Bull Seism Soc Am 82:505-510, 1992), which considers between-events as well as within-events errors. Due to the limited data used in the development of previous Iranian ground motion prediction equations (GMPEs) and strong trade-offs between different terms of GMPEs, it is likely that the previously determined models might have less precision on their coefficients in comparison to the current study. The richer database of the current study allows improving on prior works by considering additional variables that could not previously be adequately constrained. Here, a functional form used by Boore and Atkinson (Earthquake Spect 24:99-138, 2008) and Bindi et al. (Bull Seism Soc Am 9:1899-1920, 2011) has been adopted that allows accounting for the saturation of ground motions at close distances. A regression has been also performed for the V/H in order to retrieve vertical components by scaling horizontal spectra. In order to take into account epistemic uncertainty, the new model can be used along with other appropriate GMPEs through a logic tree framework for seismic hazard assessment in Iran and Middle East region.

Wetting transitions: First order or second order

International Nuclear Information System (INIS)

Teletzke, G.F.; Scriven, L.E.; Davis, H.T.

1982-01-01

A generalization of Sullivan's recently proposed theory of the equilibrium contact angle, the angle at which a fluid interface meets a solid surface, is investigated. The generalized theory admits either a first-order or second-order transition from a nonzero contact angle to perfect wetting as a critical point is approached, in contrast to Sullivan's original theory, which predicts only a second-order transition. The predictions of this computationally convenient theory are in qualitative agreement with a more rigorous theory to be presented in a future publication

Non-commutative gauge Gravity: Second- order Correction and Scalar Particles Creation

International Nuclear Information System (INIS)

Zaim, S.

2009-01-01

A noncommutative gauge theory for a charged scalar field is constructed. The invariance of this model under local Poincare and general coordinate transformations is verified. Using the general modified field equation, a general Klein-Gordon equation up to the second order of the noncommu- tativity parameter is derived. As an application, we choose the Bianchi I universe. Using the Seiberg-Witten maps, the deformed noncommutative metric is obtained and a particle production process is studied. It is shown that the noncommutativity plays the same role as an electric field, gravity and chemical potential.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

Science.gov (United States)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For

Mixed first- and second-order transport method using domain decomposition techniques for reactor core calculations

International Nuclear Information System (INIS)

Girardi, E.; Ruggieri, J.M.

2003-01-01

The aim of this paper is to present the last developments made on a domain decomposition method applied to reactor core calculations. In this method, two kind of balance equation with two different numerical methods dealing with two different unknowns are coupled. In the first part the two balance transport equations (first order and second order one) are presented with the corresponding following numerical methods: Variational Nodal Method and Discrete Ordinate Nodal Method. In the second part, the Multi-Method/Multi-Domain algorithm is introduced by applying the Schwarz domain decomposition to the multigroup eigenvalue problem of the transport equation. The resulting algorithm is then provided. The projection operators used to coupled the two methods are detailed in the last part of the paper. Finally some preliminary numerical applications on benchmarks are given showing encouraging results. (authors)

Second-order nonlinearity induced transparency.

Science.gov (United States)

Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X

2017-04-01

In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.

Temperature dependence of bulk modulus and second-order elastic constants

International Nuclear Information System (INIS)

Singh, P.P.; Kumar, Munish

2004-01-01

A simple theoretical model is developed to investigate the temperature dependence of the bulk modulus and second order elastic constants. The method is based on the two different approaches viz. (i) the theory of thermal expansivity formulated by Suzuki, based on the Mie-Gruneisen equation of state, (ii) the theory of high-pressure-high-temperature equation of state formulated by Kumar, based on thermodynamic analysis. The results obtained for a number of crystals viz. NaCl, KCl, MgO and (Mg, Fe) 2 SiO 4 are discussed and compared with the experimental data. It is concluded that the Kumar formulation is far better that the Suzuki theory of thermal expansivity

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

Science.gov (United States)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Three-dimensional cross-linked carbon network wrapped with ordered polyaniline nanowires for high-performance pseudo-supercapacitors

Science.gov (United States)

Hu, Huan; Liu, Shuwu; Hanif, Muddasir; Chen, Shuiliang; Hou, Haoqing

2014-12-01

The polyaniline (PANI)-based pseudo-supercapacitor has been extensively studied due to its good conductivity, ease of synthesis, low-cost monomer, tunable properties and remarkable specific capacitance. In this work, a three-dimensional cross-linked carbon network (3D-CCN) was used as a contact-resistance-free substrate for PANI-based pseudo-supercapacitors. The ordered PANI nanowires (PaNWs) were grown on the 3D-CCN to form PaNWs/3D-CCN composites by in-situ polymerization. The PaNWs/3D-CCN composites exhibited a specific capacitance (Cs) of 1191.8 F g-1 at a current density of 0.5 A g-1 and a superior rate capability with 66.4% capacitance retention at 100.0 A g-1. The high specific capacitance is attributed to the thin PaNW coating and the spaced PANI nanowire array, which ensure a higher utilization of PANI due to the ease of diffusion of protons through/on the PANI nanowires. In addition, the unique 3D-CCN was used as a high-conductivity platform (or skeleton) with no contact resistance for fast electron transfer and facile charge transport within the composites. Therefore, the binder-free composites can process rapid gains or losses of electrons and ions, even at a high current density. As a result, the specific capacitance and rate capability of our composites are remarkably higher than those of other PANI composites.

Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

International Nuclear Information System (INIS)

Ren Ji; Ruan Hangyu

2008-01-01

We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability

Directory of Open Access Journals (Sweden)

Muhammad Ayub

2013-01-01

the case of k≥3. We discuss the singular invariant representations of canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras. Furthermore, we give an integration procedure for canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras which comprises of two approaches, namely, division into four types I, II, III, and IV and that of integrability of the invariant representations. We prove that if a system of two second-order ODEs has a three-dimensional solvable Lie algebra, then, its general solution can be obtained from a partially linear, partially coupled or reduced invariantly represented system of equations. A natural extension of this result is provided for a system of two kth-order (k≥3 ODEs. We present illustrative examples of familiar integrable physical systems which admit three-dimensional Lie algebras such as the classical Kepler problem and the generalized Ermakov systems that give rise to closed trajectories.

The (G′/G-Expansion Method and Its Application for Higher-Order Equations of KdV (III

Directory of Open Access Journals (Sweden)

Huizhang Yang

2014-01-01

Full Text Available New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G′/G-expansion method, where G=G(ξ satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. The property of this method is that it is quite simple and understandable.

KINETIC AND EQUILIBRIUM STUDIES OF Pb(II) AND Cd(II ...

African Journals Online (AJOL)

and DRK isotherms and the experimental data were found to fit best the Langmuir .... The approximate surface area of the adsorbents was determined using the Sears' method [9]. ... if sorption had occurred by physical or chemical processes. ... Lagergren pseudo-first order equation, pseudo-second order equation, Elovich ...

Removal of Congo Red from Aqueous Solution by Anion Exchange Membrane (EBTAC): Adsorption Kinetics and Themodynamics

Science.gov (United States)

Khan, Muhammad Imran; Akhtar, Shahbaz; Zafar, Shagufta; Shaheen, Aqeela; Khan, Muhammad Ali; Luque, Rafael; ur Rehman, Aziz

2015-01-01

The adsorption behavior of anionic dye congo red (CR) from aqueous solutions using an anion exchange membrane (EBTAC) has been investigated at room temperature. The effect of several factors including contact time, membrane dosage, ionic strength and temperature were studied. Kinetic models, namely pseudo-first-order and pseudo-second-order, liquid film diffusion and Elovich models as well as Bangham and modified freundlich Equations, were employed to evaluate the experimental results. Parameters such as adsorption capacities, rate constant and related correlation coefficients for every model were calculated and discussed. The adsorption of CR on anion exchange membranes followed pseudo-second-order Kinetics. Thermodynamic parameters, namely changes in Gibbs free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) were calculated for the adsorption of congo red, indicating an exothermic process. PMID:28793430

Dye removal from wastewater using activated carbon developed from sawdust: adsorption equilibrium and kinetics.

Science.gov (United States)

Malik, P K

2004-09-10

Mahogany sawdust was used to develop an effective carbon adsorbent. This adsorbent was employed for the removal of direct dyes from spent textile dyeing wastewater. The experimental data were analysed by the Langmuir and Freundlich models of adsorption. Equilibrium data fitted well with the Langmuir model. The rates of adsorption were found to conform to the pseudo-second-order kinetics with good correlation. The equilibrium adsorption capacity of the sawdust carbon was determined with the Langmuir equation as well as the pseudo-second-order rate equation and found to be >300 mg dye per gram of the adsorbent. The most ideal pH for adsorption of direct dyes onto sawdust carbon was found to be 3 and below. The results indicate that the Mahogany sawdust carbon could be employed as a low cost alternative to commercial activated carbon in the removal of dyes from wastewater.

Evaluation of Lagergren Kinetics Equation by Using Novel Kinetics Expression of Sorption of Zn2+ onto Horse Dung Humic Acid (HD-HA

Directory of Open Access Journals (Sweden)

Bambang Rusdiarso

2016-12-01

Full Text Available Extraction and purification of humic acid from dry horse dung powder (HD-HA was performed successfully and the purified HD-HA was then applied as sorbent to adsorb Zn2+. Extraction and purification were performed based on procedure of Stevenson (1994 under atmospheric air. Parameters investigated in this work consist of effect of medium sorption acidity, sorption rate (ka and desorption rate constant (kd, Langmuir (monolayer and Freundlich (multilayer sorption capacities, and energy (E of sorption. The ka and kd were determined according to the kinetic model of second order sorption reaching equilibrium, monolayer sorption capacity (b and energy (E were determined according to Langmuir isotherm model, and multilayer sorption capacity (B was determined based on Freundlich isotherm model. Sorption of Zn2+ on purified HD-HA was maximum at pH 5.0. The novel kinetic expression resulted from proposed kinetic model has been shown to be more applicable than the commonly known Lagergren equation obtained from the pseudo-first order sorption model. The application of the equation revealed that the intercept of Lagergren equation, ln qe was more complex function of initial concentration of Zn2+ (a, Langmuir sorption capacity (b, and sorbed Zn2+ at equilibrium (xe.

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

Science.gov (United States)

Fruhnert, Michael

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time

Hermitian Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds

International Nuclear Information System (INIS)

Popov, Alexander D.

2010-01-01

We consider the Hermitian Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X 6 which is the twistor space of an oriented Riemannian manifold M 4 . Each solution of the HYM equations on such X 6 defines a pseudo-holomorphic structure on the bundle E. It is shown that the pull-back to X 6 of any anti-self-dual gauge field on M 4 is a solution of the HYM equations on X 6 . This correspondence allows us to introduce new twistor actions for bosonic and supersymmetric Yang-Mills theories. As examples of X 6 we consider homogeneous nearly Kaehler and nearly Calabi-Yau manifolds which are twistor spaces of S 4 , CP 2 and B 4 , CB 2 (real 4-ball and complex 2-ball), respectively. Various explicit examples of solutions to the HYM equations on these spaces are provided. Applications in flux compactifications of heterotic strings are briefly discussed.

Observations on the properties of second and general-order kinetics equations describing the thermoluminescence processes

International Nuclear Information System (INIS)

Kitis, G.; Furetta, C.; Azorin, J.

2003-01-01

Synthetic thermoluminescent (Tl) glow peaks, following a second and general kinetics order have been generated by computer. The general properties of the so generated peaks have been investigated over several order of magnitude of simulated doses. Some non usual results which, at the best knowledge of the authors, are not reported in the literature, are obtained and discussed. (Author)

The second-order description of rotational non-equilibrium effects in polyatomic gases

Science.gov (United States)

Myong, Rho Shin

2017-11-01

The conventional description of gases is based on the physical laws of conservation (mass, momentum, and energy) in conjunction with the first-order constitutive laws, the two-century old so-called Navier-Stokes-Fourier (NSF) equation based on a critical assumption made by Stokes in 1845 that the bulk viscosity vanishes. While the Stokes' assumption is certainly legitimate in the case of dilute monatomic gases, ever increasing evidences, however, now indicate that such is not the case, in particular, in the case of polyatomic gases-like nitrogen and carbon dioxide-far-from local thermal equilibrium. It should be noted that, from room temperature acoustic attenuation data, the bulk viscosity for carbon dioxide is three orders of magnitude larger than its shear viscosity. In this study, this fundamental issue in compressible gas dynamics is revisited and the second-order constitutive laws are derived by starting from the Boltzmann-Curtiss kinetic equation. Then the topology of the second-order nonlinear coupled constitutive relations in phase space is investigated. Finally, the shock-vortex interaction problem where the strong interaction of two important thermal (translational and rotational) non-equilibrium phenomena occurs is considered in order to highlight the rotational non-equilibrium effects in polyatomic gases. This work was supported by the National Research Foundation of South Korea (NRF 2017-R1A2B2-007634).

Field Method for Integrating the First Order Differential Equation

Institute of Scientific and Technical Information of China (English)

JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu

2007-01-01

An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.

Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

International Nuclear Information System (INIS)

Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

2011-01-01

In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)

SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD

Science.gov (United States)

Krogh, F. T.

1994-01-01

The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.

Second-order particle-in-cell (PIC) computational method in the one-dimensional variable Eulerian mesh system

International Nuclear Information System (INIS)

Pyun, J.J.

1981-01-01

As part of an effort to incorporate the variable Eulerian mesh into the second-order PIC computational method, a truncation error analysis was performed to calculate the second-order error terms for the variable Eulerian mesh system. The results that the maximum mesh size increment/decrement is limited to be α(Δr/sub i/) 2 where Δr/sub i/ is a non-dimensional mesh size of the ith cell, and α is a constant of order one. The numerical solutions of Burgers' equation by the second-order PIC method in the variable Eulerian mesh system wer compared with its exact solution. It was found that the second-order accuracy in the PIC method was maintained under the above condition. Additional problems were analyzed using the second-order PIC methods in both variable and uniform Eulerian mesh systems. The results indicate that the second-order PIC method in the variable Eulerian mesh system can provide substantial computational time saving with no loss in accuracy

Kinetic Study of Zn2+ and Cd2+ Ions Sorption by Ceric Oxide Powder

International Nuclear Information System (INIS)

Hassan, H.S.; Abd El-Rahman, K.M.; El Sayed, A.A.

2008-01-01

Ceric Oxide powder was chemically synthesized and characterized using infrared spectra and x-ray diffraction. The sorptive removal of Zinc and Cadmium ions from aqueous waste solution using synthetic ceric oxide powder was investigated using batch technique. Experiments were carried out as a function of ph, particle size, solute concentration and temperature. The uptake of zinc was found to be greater than that of cadmium. A comparison of kinetic models applied to the sorption process of each ion was evaluated for the pseudo first order, the pseudo second order, and homogeneous particle diffusion kinetic models, respectively. The results showed that both the pseudo second order and the homogeneous particle diffusion model (HPDM) were found to best correlate the experimental rate data. The numerical values of the rate constants and particle diffusion coefficients were determined from the graphical representation of the proposed models. Activation energy (Ε a ) and entropy (δ S * ) of activation for each sorption process were also calculated from the linearized form of Arrhenius equation

A fast, high-order solver for the Grad–Shafranov equation

International Nuclear Information System (INIS)

Pataki, Andras; Cerfon, Antoine J.; Freidberg, Jeffrey P.; Greengard, Leslie; O’Neil, Michael

2013-01-01

We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented

Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model with second-order field equations.

Science.gov (United States)

Gao, Xian; Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi

2011-11-18

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

Directory of Open Access Journals (Sweden)

Navnit Jha

2014-04-01

Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain

Directory of Open Access Journals (Sweden)

Ruzanna Kh. Makaova

2017-12-01

Full Text Available In this paper we study the boundary value problem for a degenerating third order equation of hyperbolic type in a mixed domain. The equation under consideration in the positive part of the domain coincides with the Hallaire equation, which is a pseudoparabolic type equation. Moreover, in the negative part of the domain it coincides with a degenerating hyperbolic equation of the first kind, the particular case of the Bitsadze–Lykov equation. The existence and uniqueness theorem for the solution is proved. The uniqueness of the solution to the problem is proved with the Tricomi method. Using the functional relationships of the positive and negative parts of the domain on the degeneration line, we arrive at the convolution type Volterra integral equation of the 2nd kind with respect to the desired solution by a derivative trace. With the Laplace transform method, we obtain the solution of the integral equation in its explicit form. At last, the solution to the problem under study is written out explicitly as the solution of the second boundary-value problem in the positive part of the domain for the Hallaire equation and as the solution to the Cauchy problem in the negative part of the domain for a degenerate hyperbolic equation of the first kind.

Semiorders, Intervals Orders and Pseudo Orders Preference Structures in Multiple Criteria Decision Aid Methods

Directory of Open Access Journals (Sweden)

Fernández Barberis, Gabriela

2013-06-01

Full Text Available During the last decades, an important number of Multicriteria Decision Aid Methods (MCDA has been proposed to help the decision maker to select the best compromise alternative. Meanwhile, the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations family of outranking method and their applications has attracted much attention from academics and practitioners. In this paper, an extension of these methods is presented, consisting of analyze its functioning under New Preference Structures (NPS. The preference structures taken into account are, namely: semiorders, intervals orders and pseudo orders. These structures outstandingly improve the modelization as they give more flexibility, amplitude and certainty at the preferences formulation, since they tend to abandon the Complete Transitive Comparability Axiom of Preferences in order to substitute it by the Partial Comparability Axiom of Preferences. It must be remarked the introduction of Incomparability relations to the analysis and the consideration of preference structures that accept the Indifference intransitivity. The NPS incorporation is carried out in three phases that the PROMETHEE Methodology takes in: preference structure enrichment, dominance relation enrichment and outranking relation exploitation for decision aid, in order to finally arrive at solving the alternatives ranking problem through the PROMETHEE I or the PROMETHEE II utilization, according to whether a partial ranking or a complete one, is respectively required under the NPS

Algebra of pseudo-differential C*-operators

International Nuclear Information System (INIS)

Mohammad, N.

1987-11-01

In this paper the algebra of pseudo-differential operators is studied in the framework of C * -algebras. It is proved that every pseudo-differential operator of order m admits an adjoint operator, in this case, which is again a pseudo-differential operator. Consequently, the space of all pseudo-differential operators on a compact manifold is an involutive algebra. 10 refs

On the General Equation of the Second Degree

Indian Academy of Sciences (India)

IAS Admin

On the General Equation of the Second Degree. Keywords. Conics, eigenvalues, eigenvec- tors, pairs of lines. S Kesavan. S Kesavan works at the. Institute for Mathematical. Sciences, Chennai. His area of interest is partial differential equations with specialization in elliptic problems connected to homogenization, control.

Introduction to differential equations

CERN Document Server

Taylor, Michael E

2011-01-01

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

Second- and Higher-Order Virial Coefficients Derived from Equations of State for Real Gases

Science.gov (United States)

Parkinson, William A.

2009-01-01

Derivation of the second- and higher-order virial coefficients for models of the gaseous state is demonstrated by employing a direct differential method and subsequent term-by-term comparison to power series expansions. This communication demonstrates the application of this technique to van der Waals representations of virial coefficients.…

Spectral methods for a nonlinear initial value problem involving pseudo differential operators

International Nuclear Information System (INIS)

Pasciak, J.E.

1982-01-01

Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed

A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem

International Nuclear Information System (INIS)

Pan Shaohua; Chen, J.-S.

2009-01-01

We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

Science.gov (United States)

Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J

2009-11-28

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

Solving Variable Coefficient Fourth-Order Parabolic Equation by ...

African Journals Online (AJOL)

Solving Variable Coefficient Fourth-Order Parabolic Equation by Modified initial guess Variational ... variable coefficient fourth order parabolic partial differential equations. The new method shows rapid convergence to the exact solution.

Second-Order Science of Interdisciplinary Research

DEFF Research Database (Denmark)

Alrøe, Hugo Fjelsted; Noe, Egon

2014-01-01

require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order science in domains where...... there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory...... of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem...

Equilibrium and Kinetic Sorption of Some Heavy Metals from Aqueous Waste Solutions Using p (AAc-HEMA)

International Nuclear Information System (INIS)

El-Sayed, A.H.; Khalil, F.H.; Elnesr, E.; Mansour, T.; El-Gammal, B.; El -Sabbah, M.M.B.

2013-01-01

Removal of heavy metals from aqueous waste solution using poly acrylic acid / 2-hydroxy ethyle methacrylate ( p-AAc/ HEMA) was investigated. Experiments were carried out as function of contact time, initial concentration, ph, particle size and temperature. Adsorption data were modeled using the pseudo-first-order, pseudo-second-order and intra-particle diffusion kinetics equations. It was shown that pseudo-second-order kinetic equation could best describe the adsorption kinetics. The results indicated that poly acrylic acid / 2-hydroxy ethyle methacrylate (p-AAc/ HEMA) is suitable as adsorbent material for adsorption of Sr 2+ , Co 2+ , Cd 2+ , Zn 2+ , Nd 3+ and Eu 3+ radio active nuclei from aqueous solutions.

Robust second-order scheme for multi-phase flow computations

Science.gov (United States)

Shahbazi, Khosro

2017-06-01

A robust high-order scheme for the multi-phase flow computations featuring jumps and discontinuities due to shock waves and phase interfaces is presented. The scheme is based on high-order weighted-essentially non-oscillatory (WENO) finite volume schemes and high-order limiters to ensure the maximum principle or positivity of the various field variables including the density, pressure, and order parameters identifying each phase. The two-phase flow model considered besides the Euler equations of gas dynamics consists of advection of two parameters of the stiffened-gas equation of states, characterizing each phase. The design of the high-order limiter is guided by the findings of Zhang and Shu (2011) [36], and is based on limiting the quadrature values of the density, pressure and order parameters reconstructed using a high-order WENO scheme. The proof of positivity-preserving and accuracy is given, and the convergence and the robustness of the scheme are illustrated using the smooth isentropic vortex problem with very small density and pressure. The effectiveness and robustness of the scheme in computing the challenging problem of shock wave interaction with a cluster of tightly packed air or helium bubbles placed in a body of liquid water is also demonstrated. The superior performance of the high-order schemes over the first-order Lax-Friedrichs scheme for computations of shock-bubble interaction is also shown. The scheme is implemented in two-dimensional space on parallel computers using message passing interface (MPI). The proposed scheme with limiter features approximately 50% higher number of inter-processor message communications compared to the corresponding scheme without limiter, but with only 10% higher total CPU time. The scheme is provably second-order accurate in regions requiring positivity enforcement and higher order in the rest of domain.

Optimization of an intracavity Q-switched solid-state second order Raman laser

Science.gov (United States)

Chen, Zhiqiong; Fu, Xihong; Peng, Hangyu; Zhang, Jun; Qin, Li; Ning, Yongqiang

2017-01-01

In this paper, the model of an intracavity Q-switched second order Raman laser is established, the characteristics of the output 2nd Stokes are simulated. The dynamic balance mechanism among intracavity conversion rates of stimulated emission, first order Raman and second order Raman is obtained. Finally, optimization solutions for increasing output 2nd Stokes pulse energy are proposed.

Adsorption of cationic dye from aqueous solution by clay as an adsorbent: thermodynamic and kinetic studies

International Nuclear Information System (INIS)

Fil, B.A.; Ozmetn, C.

2012-01-01

In the study, montmorillonite was used as an adsorbent for the removal of methylene blue (MB) from aqueous solutions. Batch studies were performed to address various experimental parameters like contact time, pH, temperature, stirring speed, ionic strength, adsorbent dosage and initial concentration for the removal of this dye. Adsorption rate increased with the increase in initial dye concentration, ionic strength, stirring speed, pH and temperature. Kinetic study showed that the adsorption of dye on montmorillonite was a gradual process. Quasi-equilibrium reached in 3 h. Pseudo-first-order, pseudo-second-order, Elovich, Bangham, mass transfer and intra-particle particle diffusion models were used to fit the experimental data. Pseudo-second-order rate equation was able to provide realistic description of adsorption kinetics. Intra-particle diffusion process was identified as the main mechanism controlling the rate of the dye sorption. The diffusion coefficient, D, was found to increase when the stirring speed, ionic strength and temperature were raised. Thermodynamic activation parameters such as delt G, delt S and del H were also calculated. (author)

Second-order wave diffraction by a circular cylinder using scaled boundary finite element method

International Nuclear Information System (INIS)

Song, H; Tao, L

2010-01-01

The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

Science.gov (United States)

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Biosorption of uranium by immobilized cells of Rhodotorula glutinis

International Nuclear Information System (INIS)

Jing Bai; Zhan Li; Fangli Fan; Xiaolei Wu; Xiaojie Yin; Longlong Tian; Zhi Qin; Junsheng Guo

2014-01-01

Biosorption of uranium ions from diluted solution (≤40 mg L -1 ) onto immobilized cells of Rhodotorula glutinis was investigated in a batch system. Equilibrium, kinetic and thermodynamic studies were conducted by considering the effect of initial uranium concentration, contact time and temperature. Non-linear forms of Langmuir, Freundlich and Sips isotherm models were used to fit the equilibrium data, Sips model was designated as the best one. Kinetic data were simulated by non-linear pseudo-first-order, pseudo-second-order and intra-particle diffusion equations. Pseudo-first-order kinetic equation described the experimental data better than pseudo-second-order equation and intra-particle diffusion equation can fit the kinetic data with two independent curves. Thermodynamic parameters, including ∆H 0, ∆G 0 and ∆S 0, were evaluated, the sorption process was determined to be spontaneous and endothermic. Uranium sorption from pure uranium solutions and uranium pit wastewater by immobilized biomass and blank beads, as well as the regeneration results indicated that immobilized R. glutinis can be use to recovery uranium from uranium pit wastewater. (author)

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

Science.gov (United States)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

Oscillation of two-dimensional linear second-order differential systems

International Nuclear Information System (INIS)

Kwong, M.K.; Kaper, H.G.

1985-01-01

This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references

Wavefield Extrapolation in Pseudo-depth Domain

KAUST Repository

Ma, Xuxin

2011-12-11

Wave-equation based seismic migration and inversion tools are widely used by the energy industry to explore hydrocarbon and mineral resources. By design, most of these techniques simulate wave propagation in a space domain with the vertical axis being depth measured from the surface. Vertical depth is popular because it is a straightforward mapping of the subsurface space. It is, however, not computationally cost-effective because the wavelength changes with local elastic wave velocity, which in general increases with depth in the Earth. As a result, the sampling per wavelength also increases with depth. To avoid spatial aliasing in deep fast media, the seismic wave is oversampled in shallow slow media and therefore increase the total computation cost. This issue is effectively tackled by using the vertical time axis instead of vertical depth. This is because in a vertical time representation, the "wavelength" is essentially time period for vertical rays. This thesis extends the vertical time axis to the pseudo-depth axis, which features distance unit while preserving the properties of the vertical time representation. To explore the potentials of doing wave-equation based imaging in the pseudo-depth domain, a Partial Differential Equation (PDE) is derived to describe acoustic wave in this new domain. This new PDE is inherently anisotropic because the use of a constant vertical velocity to convert between depth and vertical time. Such anisotropy results in lower reflection coefficients compared with conventional space domain modeling results. This feature is helpful to suppress the low wavenumber artifacts in reverse-time migration images, which are caused by the widely used cross-correlation imaging condition. This thesis illustrates modeling acoustic waves in both conventional space domain and pseudo-depth domain. The numerical tool used to model acoustic waves is built based on the lowrank approximation of Fourier integral operators. To investigate the potential

Second order approximation for optical polaron in the strong coupling case

International Nuclear Information System (INIS)

Bogolubov, N.N. Jr.

1993-11-01

Here we propose a method of construction second order approximation for ground state energy for class of model Hamiltonian with linear type interaction on Bose operators in strong coupling case. For the application of the above method we have considered polaron model and propose construction set of nonlinear differential equations for definition ground state energy in strong coupling case. We have considered also radial symmetry case. (author). 10 refs

The pseudo-spin orbit interaction and the normal spin orbit interaction

International Nuclear Information System (INIS)

Sugawara-Tanabe, K.

1999-01-01

We found the hidden symmetry of the pseudo-spin approximation which is inherent in the Dirac equation both for the spherical potential and for deformed potential with axially symmetric shape. We found two kinds of conditions for both cases, i.e., the exact conditions and the approximate condition for the pseudo-spin symmetry. The former condition is not always satisfied by the real nuclei, but the latter condition is realistic and applicable to the real nuclei. We found that the LS coupling scheme is restored not only for the parity doublet states by also for the other levels at superdeformation because of strong quadrupole field. The contribution from the unique-parity level to the E1 transition becomes non-negligible order in superdeformation. (author)

Numerical solution of distributed order fractional differential equations

Science.gov (United States)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Application of the graphical unitary group approach to the energy second derivative for CI wave functions via the coupled perturbed CI equations

International Nuclear Information System (INIS)

Fox, D.J.

1983-10-01

Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed

Investigation of Pseudo-Active State in Z-Source Inverter

DEFF Research Database (Denmark)

Schaltz, Erik; Oprea, Octavian; Larsen, Lasse

2005-01-01

This paper introduces a new operating state of the Z-source inverter denoted the pseudo-active state. The pseudoactive state is a state that may boost the output voltage of the Zsource inverter to a level higher than expected. The influence of the pseudo-active state is investigated and an equation...

Higher order field equations. II

International Nuclear Information System (INIS)

Tolhoek, H.A.

1977-01-01

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)

PSpectRe: a pseudo-spectral code for (P)reheating

International Nuclear Information System (INIS)

Easther, Richard; Finkel, Hal; Roth, Nathaniel

2010-01-01

PSpectRe is a C++ program that uses Fourier-space pseudo-spectral methods to evolve interacting scalar fields in an expanding universe. PSpectRe is optimized for the analysis of parametric resonance in the post-inflationary universe and provides an alternative to finite differencing codes, such as Defrost and LatticeEasy. PSpectRe has both second- (Velocity-Verlet) and fourth-order (Runge-Kutta) time integrators. Given the same number of spatial points and/or momentum modes, PSpectRe is not significantly slower than finite differencing codes, despite the need for multiple Fourier transforms at each timestep, and exhibits excellent energy conservation. Further, by computing the post-resonance equation of state, we show that in some circumstances PSpectRe obtains reliable results while using substantially fewer points than a finite differencing code. PSpectRe is designed to be easily extended to other problems in early-universe cosmology, including the generation of gravitational waves during phase transitions and pre-inflationary bubble collisions. Specific applications of this code will be described in future work

Access is mainly a second-order process: SDT models whether phenomenally (first-order) conscious states are accessed by reflectively (second-order) conscious processes.

Science.gov (United States)

Snodgrass, Michael; Kalaida, Natasha; Winer, E Samuel

2009-06-01

Access can either be first-order or second-order. First order access concerns whether contents achieve representation in phenomenal consciousness at all; second-order access concerns whether phenomenally conscious contents are selected for metacognitive, higher order processing by reflective consciousness. When the optional and flexible nature of second-order access is kept in mind, there remain strong reasons to believe that exclusion failure can indeed isolate phenomenally conscious stimuli that are not so accessed. Irvine's [Irvine, E. (2009). Signal detection theory, the exclusion failure paradigm and weak consciousness-Evidence for the access/phenomenal distinction? Consciousness and Cognition.] partial access argument fails because exclusion failure is indeed due to lack of second-order access, not insufficient phenomenally conscious information. Further, the enable account conforms with both qualitative differences and subjective report, and is simpler than the endow account. Finally, although first-order access may be a distinct and important process, second-order access arguably reflects the core meaning of access generally.

Ammonia removal in electrochemical oxidation: Mechanism and pseudo-kinetics

International Nuclear Information System (INIS)

Li Liang; Liu Yan

2009-01-01

This paper investigated the mechanism and pseudo-kinetics for removal of ammonia by electrochemical oxidation with RuO 2 /Ti anode using batch tests. The results show that the ammonia oxidation rates resulted from direct oxidation at electrode-liquid interfaces of the anode by stepwise dehydrogenation, and from indirect oxidation by hydroxyl radicals were so slow that their contribution to ammonia removal was negligible under the condition with Cl - . The oxidation rates of ammonia ranged from 1.0 to 12.3 mg N L -1 h -1 and efficiency reached nearly 100%, primarily due to the indirect oxidation of HOCl, and followed pseudo zero-order kinetics in electrochemical oxidation with Cl - . About 88% ammonia was removed from the solution. The removed one was subsequently found in the form of N 2 in the produced gas. The rate at which Cl - lost electrons at the anode was a major factor in the overall ammonia oxidation. Current density and Cl - concentration affected the constant of the pseudo zero-order kinetics, expressed by k = 0.0024[Cl - ] x j. The ammonia was reduced to less than 0.5 mg N L -1 after 2 h of electrochemical oxidation for the effluent from aerobic or anaerobic reactors which treated municipal wastewater. This result was in line with the strict discharge requirements

Prediction of stably stratified homogeneous shear flows with second-order turbulence models

International Nuclear Information System (INIS)

Pereira, J C F; Rocha, J M P

2010-01-01

The present study investigated the role of pressure-correlation second-order turbulence modelling schemes on the predicted behaviour of stably stratified homogeneous vertical-sheared turbulence. The pressure-correlation terms were modelled with a nonlinear formulation (Craft 1991), which was compared with a linear pressure-strain model and the 'isotropization of production' model for the pressure-scalar correlation. Two additional modelling issues were investigated: the influence of the buoyancy term in the kinetic energy dissipation rate equation and the time scale in the thermal production term in the scalar variance dissipation equation. The predicted effects of increasing the Richardson number on turbulence characteristics were compared against a comprehensive set of direct numerical simulation databases. The linear models provide a broadly satisfactory description of the major effects of the Richardson number on stratified shear flow. The buoyancy term in the dissipation equation of the turbulent kinetic energy generates excessively low levels of dissipation. For moderate and large Richardson numbers, the term yields unrealistic linear oscillations in the shear and buoyancy production terms, and therefore should be dropped in this flow (or at least their coefficient c ε3 should be substantially reduced from its standard value). The mechanical dissipation time scale provides marginal improvements in comparison to the scalar time scale in the production. The observed inaccuracy of the linear model in predicting the magnitude of the effects on the velocity anisotropy was demonstrated to be attributed mainly to the defective behaviour of the pressure-correlation model, especially for stronger stratification. The turbulence closure embodying a nonlinear formulation for the pressure-correlations and specific versions of the dissipation equations failed to predict the tendency of the flow to anisotropy with increasing stratification. By isolating the effects of the

Synthesis of magnetic ordered mesoporous carbon (Fe-OMC) adsorbent and its evaluation for fuel desulfurization

Science.gov (United States)

Farzin Nejad, N.; Shams, E.; Amini, M. K.

2015-09-01

In this work, magnetic ordered mesoporous carbon adsorbent was synthesized using soft templating method to adsorb sulfur from model oil (dibenzothiophene in n-hexane). Through this research, pluronic F-127, resorcinol-formaldehyde and hydrated iron nitrate were respectively used as soft template, carbon source and iron source. The adsorbent was characterized by X-ray diffraction, nitrogen adsorption-desorption isotherm and transmission electron microscopy. Nitrogen adsorption-desorption measurement revealed the high surface area (810 m2 g-1), maxima pore size of 3.3 nm and large pore volume (1.01 cm3 g-1) of the synthesized sample. The adsorbent showed a maximum adsorption capacity of 111 mg dibenzothiophene g-1 of adsorbent. Sorption process was described by the pseudo-second-order rate equation and could be better fitted by the Freundlich model, showing the heterogeneous feature of the adsorption process. In addition, the adsorption capacity of regenerated adsorbent was 78.6% of the initial level, after five regeneration cycles.

First and second order derivatives for optimizing parallel RF excitation waveforms

Science.gov (United States)

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

A Second Look at Second-Order Belief Attribution in Autism.

Science.gov (United States)

Tager-Flusberg, Helen; Sullivan, Kate

1994-01-01

Twelve students with autism and 12 with mental retardation, who had passed a first-order test of false belief, were given a second-order reasoning task. No intergroup performance differences were seen. Findings suggest that the difficulty for both groups with the second-order task lies in information processing demands rather than conceptual…

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

Science.gov (United States)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

Analysis of an Nth-order nonlinear differential-delay equation

Science.gov (United States)

Vallée, Réal; Marriott, Christopher

1989-01-01

The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.

Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

CERN Document Server

Gazzola, Filippo; Sweers, Guido

2010-01-01

This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

On Fractional Order Hybrid Differential Equations

Directory of Open Access Journals (Sweden)

Mohamed A. E. Herzallah

2014-01-01

Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations

Science.gov (United States)

Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan

2016-12-01

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function

Pseudo-differential operators groups, geometry and applications

CERN Document Server

Zhu, Hongmei

2017-01-01

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Second-order gauge-invariant perturbations during inflation

International Nuclear Information System (INIS)

Finelli, F.; Marozzi, G.; Vacca, G. P.; Venturi, G.

2006-01-01

The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second-order gauge-invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second-order gauge-invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections with respect to the first order spectrum. For all scales of interest the amplitude of these spectra depends on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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Pituk Mihály

2007-01-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

MURLI, 1-D Flux, Reaction Rate in Cylindrical Geometry Thermal Reactor Lattice by Transport

International Nuclear Information System (INIS)

Huria, H.C.

1985-01-01

1 - Description of problem or function: MURLI is an integral transport theory code to calculate fluxes and reaction rates in one- dimensional cylindrical geometry lattice cells of a thermal reactor. For a specified buckling, it computes k-effective using few-group diffusion theory and a few-group collapsed set of Cross sections. The code can optionally be used to solve a first order differential equation for the number density of fissile, fertile and fission product nuclei as a function of time, and to recalculate fluxes, reaction rates and k-effective at different stages of burnup. A 27-group cross section data library is included. There are four pseudo-fission products each associated with the decay chains of plutonium and uranium isotopes in addition to Rh-105, Xe-135, Np-239, U-236, Am-241, Am-242 and Am-243. There is also data for one lumped pseudo-fission product. 2 - Method of solution: Multiple collision probabilities and escape probabilities are calculated for each cylindrical shell region assuming protons are born uniformly and isotropically over the entire region volume. The equations of integral transport theory can then be solved for neutron flux. The first order differential burnup equation is solved by a fourth order Runge-Kutta method. 3 - Restrictions on the complexity of the problem: There are maxima of 8 fissionable elements, 8 resonant elements, and 20 spatial regions

Maximum principles for boundary-degenerate second-order linear elliptic differential operators

OpenAIRE

Feehan, Paul M. N.

2012-01-01

We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the smooth subsolutions along this boundary vanishing locus ensures that these maximum principles hold irrespective of the sign of the Fichera function. Boundary conditions need only be prescribed on the complement in th...

Pseudo-extravasation rate constant of dynamic susceptibility contrast-MRI determined from pharmacokinetic first principles.

Science.gov (United States)

Li, Xin; Varallyay, Csanad G; Gahramanov, Seymur; Fu, Rongwei; Rooney, William D; Neuwelt, Edward A

2017-11-01

Dynamic susceptibility contrast-magnetic resonance imaging (DSC-MRI) is widely used to obtain informative perfusion imaging biomarkers, such as the relative cerebral blood volume (rCBV). The related post-processing software packages for DSC-MRI are available from major MRI instrument manufacturers and third-party vendors. One unique aspect of DSC-MRI with low-molecular-weight gadolinium (Gd)-based contrast reagent (CR) is that CR molecules leak into the interstitium space and therefore confound the DSC signal detected. Several approaches to correct this leakage effect have been proposed throughout the years. Amongst the most popular is the Boxerman-Schmainda-Weisskoff (BSW) K 2 leakage correction approach, in which the K 2 pseudo-first-order rate constant quantifies the leakage. In this work, we propose a new method for the BSW leakage correction approach. Based on the pharmacokinetic interpretation of the data, the commonly adopted R 2 * expression accounting for contributions from both intravascular and extravasating CR components is transformed using a method mathematically similar to Gjedde-Patlak linearization. Then, the leakage rate constant (K L ) can be determined as the slope of the linear portion of a plot of the transformed data. Using the DSC data of high-molecular-weight (~750 kDa), iron-based, intravascular Ferumoxytol (FeO), the pharmacokinetic interpretation of the new paradigm is empirically validated. The primary objective of this work is to empirically demonstrate that a linear portion often exists in the graph of the transformed data. This linear portion provides a clear definition of the Gd CR pseudo-leakage rate constant, which equals the slope derived from the linear segment. A secondary objective is to demonstrate that transformed points from the initial transient period during the CR wash-in often deviate from the linear trend of the linearized graph. The inclusion of these points will have a negative impact on the accuracy of the leakage

Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

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Zhi-Wei Lv

2010-06-01

Full Text Available By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

Embedded solitons in the third-order nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Pal, Debabrata; Ali, Sk Golam; Talukdar, B

2008-01-01

We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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Ravi P. Agarwal

2007-04-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials.

Science.gov (United States)

Salehi, Morteza; Jafari, S A

2017-08-15

We suggest that spin-singlet pseudo-scalar s-wave superconducting pairing creates a two dimensional sea of Majorana fermions on the surface of three dimensional Dirac superconductors (3DDS). This pseudo-scalar superconducting order parameter Δ 5 , in competition with scalar Dirac mass m, leads to a topological phase transition due to band inversion. We find that a perfect Andreev-Klein reflection is guaranteed by presence of anomalous Andreev reflection along with the conventional one. This effect manifests itself in a resonant peak of the differential conductance. Furthermore, Josephson current of the Δ 5 |m|Δ 5 junction in the presence of anomalous Andreev reflection is fractional with 4π period. Our finding suggests another search area for condensed matter realization of Majorana fermions which are beyond the vortex-core of p-wave superconductors. The required Δ 5 pairing can be extrinsically induced by a conventional s-wave superconductor into a three dimensional Dirac material (3DDM).

Source of second order chromaticity in RHIC

International Nuclear Information System (INIS)

Luo, Y.; Gu, X.; Fischer, W.; Trbojevic, D.

2011-01-01

In this note we will answer the following questions: (1) what is the source of second order chromaticities in RHIC? (2) what is the dependence of second order chromaticity on the on-momentum β-beat? (3) what is the dependence of second order chromaticity on β* at IP6 and IP8? To answer these questions, we use the perturbation theory to numerically calculate the contributions of each quadrupole and sextupole to the first, second, and third order chromaticities.

On solutions of variable-order fractional differential equations

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Ali Akgül

2017-01-01

solutions to fractional differential equations are compelling to get in real applications, due to the nonlocality and complexity of the fractional differential operators, especially for variable-order fractional differential equations. Therefore, it is significant to enhanced numerical methods for fractional differential equations. In this work, we consider variable-order fractional differential equations by reproducing kernel method. There has been much attention in the use of reproducing kernels for the solutions to many problems in the recent years. We give two examples to demonstrate how efficiently our theory can be implemented in practice.

Exact solutions to two higher order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Xu Liping; Zhang Jinliang

2007-01-01

Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Science.gov (United States)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

A porous flow model of flank eruptions on Mt. Etna: second-order perturbation theory

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N. Cenni

1997-06-01

Full Text Available A porous flow model for magma migration from a deep source within a volcanic edifice is developed. The model is based on the assumption that an isotropic and homogeneous system of fractures allows magma migration from one localized feeding dyke up to the surface of the volcano. The maximum level that magma can reach within the volcano (i.e., the «free surface» of magma, where fluid pressure equals the atmospheric pressure is reproduced through a second-order perturbation approach to the non-linear equations governing the migration of incompressible fluids through a porous medium. The perturbation parameter is found to depend on the ratio of the volumic discharge rate at the source (m3/s divided by the product of the hydraulic conductivity of the medium (m1/s times the square of the source depth. The second-order corrections for the free surface of Mt. Etna are found to be small but not negligible; from the comparison between first-order and second-order free surfaces it appears that the former is higher near the summit, slightly lower at intermediate altitudes and slightly higher far away from the axis of the volcano. Flank eruptions in the southern sector are found to be located in regions where the topography is actually lower than the theoretical free surface of magma. In this sector, modulations in the eruption site density correlate well with even minor differences between free surface and topography. In the northern and western sectors similar good fits are found, while the NE rift and the eastern sector seem to require mechanisms or structures respectively favouring and inhibiting magma migration.

Synchronization from Second Order Network Connectivity Statistics

Science.gov (United States)

Zhao, Liqiong; Beverlin, Bryce; Netoff, Theoden; Nykamp, Duane Q.

2011-01-01

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates. PMID:21779239

An Analysis of Second-Order Autoshaping

Science.gov (United States)

Ward-Robinson, Jasper

2004-01-01

Three mechanisms can explain second-order conditioning: (1) The second-order conditioned stimulus (CS2) could activate a representation of the first-order conditioned stimulus (CS1), thereby provoking the conditioned response (CR); The CS2 could enter into an excitatory association with either (2) the representation governing the CR, or (3) with a…

First and second order vortex dynamics

International Nuclear Information System (INIS)

Kim, Yoonbai; Lee, Kimyeong

2002-01-01

The low energy dynamics of vortices in self-dual Abelian Higgs theory in (2+1)-dimensional spacetime is of second order in vortex velocity and characterized by the moduli space metric. When the Chern-Simons term with a small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provide an additional check of the first and second order terms by studying the angular momentum in field theory

The solutions of second-order linear differential systems with constant delays

Science.gov (United States)

Diblík, Josef; Svoboda, Zdeněk

2017-07-01

The representations of solutions to initial problems for non-homogenous n-dimensional second-order differential equations with delays x″(t )-2 A x'(t -τ )+(A2+B2)x (t -2 τ )=f (t ) by means of special matrix delayed functions are derived. Square matrices A and B are commuting and τ > 0. Derived representations use what is called a delayed exponential of a matrix and results generalize some of known results previously derived for homogenous systems.

A high-order Petrov-Galerkin method for the Boltzmann transport equation

International Nuclear Information System (INIS)

Pain, C.C.; Candy, A.S.; Piggott, M.D.; Buchan, A.; Eaton, M.D.; Goddard, A.J.H.; Oliveira, C.R.E. de

2005-01-01

We describe a new Petrov-Galerkin method using high-order terms to introduce dissipation in a residual-free formulation. The method is developed following both a Taylor series analysis and a variational principle, and the result has much in common with traditional Petrov-Galerkin, Self Adjoint Angular Flux (SAAF) and Even Parity forms of the Boltzmann transport equation. In addition, we consider the subtleties in constructing appropriate boundary conditions. In sub-grid scale (SGS) modelling of fluids the advantages of high-order dissipation are well known. Fourth-order terms, for example, are commonly used as a turbulence model with uniform dissipation. They have been shown to have superior properties to SGS models based upon second-order dissipation or viscosity. Even higher-order forms of dissipation (e.g. 16.-order) can offer further advantages, but are only easily realised by spectral methods because of the solution continuity requirements that these higher-order operators demand. Higher-order operators are more effective, bringing a higher degree of representation to the solution locally. Second-order operators, for example, tend to relax the solution to a linear variation locally, whereas a high-order operator will tend to relax the solution to a second-order polynomial locally. The form of the dissipation is also important. For example, the dissipation may only be applied (as it is in this work) in the streamline direction. While for many problems, for example Large Eddy Simulation (LES), simply adding a second or fourth-order dissipation term is a perfectly satisfactory SGS model, it is well known that a consistent residual-free formulation is required for radiation transport problems. This motivated the consideration of a new Petrov-Galerkin method that is residual-free, but also benefits from the advantageous features that SGS modelling introduces. We close with a demonstration of the advantages of this new discretization method over standard Petrov

Solutions to second order non-homogeneous multi-point BVPs using a fixed-point theorem

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Yuji Liu

2008-07-01

Full Text Available In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs of second order differential equations with the one-dimensional p-Laplacian. These problems have a common equation (in different function domains and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several known ones and are illustrated by examples. It is also shown that the approach for getting three positive solutions by using multi-fixed-point theorems can be extended to nonhomogeneous BVPs. The emphasis is on the nonhomogeneous boundary conditions and the nonlinear term involving first order derivative of the unknown. Some open problems are also proposed.

Removal of Disperse Blue 56 and Disperse Red 135 dyes from aqueous dispersions by modified montmorillonite nanoclay

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Ahmadishoar Javad

2017-01-01

Full Text Available In this study modified montmorillonite was used as an adsorbent for the removal of two selected disperse dyes i.e., Disperse Blue 56 (DB and Disperse Red 135 (DR from dye dispersions. The adsorption equilibrium data of dyes adsorption were investigated by using Nernst, Freundlich and Langmuir isotherm models. The adsorption kinetics was analyzed by using different models including pseudo-first-order, pseudo-second-order, Elovich and Intraparticle diffusion model. The Freundlich isotherm was found to be the most appropriate model for describing the sorption of the dyes on modified nanoclay. The best fit to the experimental results was obtained by using the pseudo-second-order kinetic equation, which satisfactorily described the process of dye adsorption. Although different kinetic models may control the rate of the adsorption process, the results indicated that the main rate limiting step was the intraparticle diffusion. The results showed that the proposed modified montmorillonite could be used as an effective adsorbent for the removal of disperse dyes even from highly concentrated dispersions.

Kinetic study of Cs+ and Eu3+ ions sorption by zirconium oxide powder

International Nuclear Information System (INIS)

Hanafi, H.A.; Hassan, H.S.; Hamed, M.M.

2009-01-01

Full text: Zirconium oxide powder was chemically synthesized by sol-gel method and characterized using infrared spectra and x-ray diffraction. The sorptive removal of cesium and europium ions from aqueous waste solution using synthetic zirconium oxide powder was investigated using batch technique. Experiments were carried out as a function of pH, time and temperature. The uptake of europium was found to be greater than that of cesium. A comparison of kinetic models applied to the sorption process of each ion was evaluated for the pseudo first order, the pseudo second order, and homogeneous particle diffusion kinetic models, respectively. The results showed that both the pseudo second order and the homogeneous particle diffusion models (HPDM) were found to best correlate the experimental rate data. The numerical values of the rate constants and particle diffusion coefficients were determined from the graphical representation of the proposed models. Activation energy (Ea) and entropy (Δ S*) of activation for each sorption process were also calculated from the linearized form of Arrhenius equation. (author)

Studies of wheel-running reinforcement: parameters of Herrnstein's (1970) response-strength equation vary with schedule order.

Science.gov (United States)

Belke, T W

2000-05-01

Six male Wistar rats were exposed to different orders of reinforcement schedules to investigate if estimates from Herrnstein's (1970) single-operant matching law equation would vary systematically with schedule order. Reinforcement schedules were arranged in orders of increasing and decreasing reinforcement rate. Subsequently, all rats were exposed to a single reinforcement schedule within a session to determine within-session changes in responding. For each condition, the operant was lever pressing and the reinforcing consequence was the opportunity to run for 15 s. Estimates of k and R(O) were higher when reinforcement schedules were arranged in order of increasing reinforcement rate. Within a session on a single reinforcement schedule, response rates increased between the beginning and the end of a session. A positive correlation between the difference in parameters between schedule orders and the difference in response rates within a session suggests that the within-session change in response rates may be related to the difference in the asymptotes. These results call into question the validity of parameter estimates from Herrnstein's (1970) equation when reinforcer efficacy changes within a session.

A natural sorbent, Luffa cylindrica for the removal of a model basic dye

International Nuclear Information System (INIS)

Altinisik, Aylin; Guer, Emel; Seki, Yoldas

2010-01-01

In this work, application of Luffa cylindrica in malachite green (MG) removal from aqueous solution was studied in a batch system. The effect of contact time, pH and temperature on removal of malachite green was also investigated. By the time pH was increased from 3 to 5, the amount of sorbed malachite green also increased. Beyond the pH value of 5, the amount of sorbed malachite green remains constant. The fits of equilibrium sorption data to Langmuir, Freundlich and Dubinin-Radushkevich equations were investigated. Langmuir isotherm exhibited best fit with the experimental data. Monolayer sorption capacity increased with the increasing of temperature. Sorption kinetic was evaluated by pseudo-first-order, pseudo-second-order, Elovich rate equations and intraparticle diffusion models. It was inferred that sorption follows pseudo-second-order kinetic model. Thermodynamic parameters for sorption process were also found out. Spontaneous and endothermic nature of sorption was obtained due to negative value of free energy (ΔG o ) and positive value of enthalpy (ΔH o ) changes. FTIR analyses were also conducted to confirm the sorption of malachite green onto L. cylindrica.

International conference Fourier Analysis and Pseudo-Differential Operators

CERN Document Server

Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations

2014-01-01

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”

First and second order derivatives for optimizing parallel RF excitation waveforms.

Science.gov (United States)

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. Copyright © 2015 Elsevier Inc. All rights reserved.

Generalized Second-Order Parametric Optimality Conditions in Semiinfinite Discrete Minmax Fractional Programming and Second-Order Univexity

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Ram Verma

2016-02-01

Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions. 

Initial-value problems for first-order differential recurrence equations with auto-convolution

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Mircea Cirnu

2011-01-01

Full Text Available A differential recurrence equation consists of a sequence of differential equations, from which must be determined by recurrence a sequence of unknown functions. In this article, we solve two initial-value problems for some new types of nonlinear (quadratic first order homogeneous differential recurrence equations, namely with discrete auto-convolution and with combinatorial auto-convolution of the unknown functions. In both problems, all initial values form a geometric progression, but in the second problem the first initial value is exempted and has a prescribed form. Some preliminary results showing the importance of the initial conditions are obtained by reducing the differential recurrence equations to algebraic type. Final results about solving the considered initial value problems, are shown by mathematical induction. However, they can also be shown by changing the unknown functions, or by the generating function method. So in a remark, we give a proof of the first theorem by the generating function method.

A new implementation of the second-order polarization propagator approximation (SOPPA)

DEFF Research Database (Denmark)

Packer, Martin J.; Dalskov, Erik K.; Enevoldsen, Thomas

1996-01-01

We present a new implementation of the second-order polarization propagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear...... and triplet transitions for benzene and naphthalene. The results compare well with experiment and CASPT2 values, calculated with identical basis sets and molecular geometries. This indicates that SOPPA can provide reliable values for excitation energies and response properties for relatively large molecular...

Wavefield extrapolation in pseudo-depth domain

KAUST Repository

Ma, Xuxin; Alkhalifah, Tariq Ali

2012-01-01

Extrapolating seismic waves in Cartesian coordinate is prone to uneven spatial sampling, because the seismic wavelength tends to grow with depth, as velocity increase. We transform the vertical depth axis to a pseudo one using a velocity weighted mapping, which can effectively mitigate this wavelength variation. We derive acoustic wave equations in this new domain based on the direct transformation of the Laplacian derivatives, which admits solutions that are more accurate and stable than those derived from the kinematic transformation. The anisotropic versions of these equations allow us to isolate the vertical velocity influence and reduce its impact on modeling and imaging. The major benefit of extrapolating wavefields in pseudo-depth space is its near uniform wavelength as opposed to the normally dramatic change of wavelength with the conventional approach. Time wavefield extrapolation on a complex velocity shows some of the features of this approach.

A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains

Science.gov (United States)

Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.

2012-08-01

We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.

Second order gauge invariant measure of a tidally deformed black hole

Energy Technology Data Exchange (ETDEWEB)

Ahmadi, Nahid, E-mail: nahmadi@ut.ac.ir [Department of Physics, University of Tehran, Kargar Avenue North, Tehran 14395-547 (Iran, Islamic Republic of)

2012-08-01

In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in [1], in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A generally non-vanishing expression for this observable, which accomodates tidal perturbations and implies nonlinear response of the horizon, is also presented.

Higher-order stochastic differential equations and the positive Wigner function

Science.gov (United States)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Sorption kinetics of diuron on volcanic ash derived soils.

Science.gov (United States)

Cáceres-Jensen, Lizethly; Rodríguez-Becerra, Jorge; Parra-Rivero, Joselyn; Escudey, Mauricio; Barrientos, Lorena; Castro-Castillo, Vicente

2013-10-15

Diuron sorption kinetic was studied in Andisols, Inceptisol and Ultisols soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Two types of kinetic models were used to fit the experimental dates: those that allow to establish principal kinetic parameters and modeling of sorption process (pseudo-first-order, pseudo-second-order), and some ones frequently used to describe solute transport mechanisms of organic compounds on different sorbents intended for remediation purposes (Elovich equation, intraparticle diffusion, Boyd, and two-site nonequilibrium models). The best fit was obtained with the pseudo-second-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the behavior of Diuron in each soil, in Andisols were observed the highest values for both parameters. The application of the models to describe solute transport mechanisms allowed establishing that in all soils the mass transfer controls the sorption kinetic across the boundary layer and intraparticle diffusion into macropores and micropores. The slowest sorption rate was observed on Ultisols, behavior which must be taken into account when the leaching potential of Diuron is considered. Copyright © 2013 Elsevier B.V. All rights reserved.

Second-order splitting schemes for a class of reactive systems

International Nuclear Information System (INIS)

Ren Zhuyin; Pope, Stephen B.

2008-01-01

We consider the numerical time integration of a class of reaction-transport systems that are described by a set of ordinary differential equations for primary variables. In the governing equations, the terms involved may require the knowledge of secondary variables, which are functions of the primary variables. Specifically, we consider the case where, given the primary variables, the evaluation of the secondary variables is computationally expensive. To solve this class of reaction-transport equations, we develop and demonstrate several computationally efficient splitting schemes, wherein the portions of the governing equations containing chemical reaction terms are separated from those parts containing the transport terms. A computationally efficient solution to the transport sub-step is achieved through the use of linearization or predictor-corrector methods. The splitting schemes are applied to the reactive flow in a continuously stirred tank reactor (CSTR) with the Davis-Skodjie reaction model, to the CO+H 2 oxidation in a CSTR with detailed chemical kinetics, and to a reaction-diffusion system with an extension of the Oregonator model of the Belousov-Zhabotinsky reaction. As demonstrated in the test problems, the proposed splitting schemes, which yield efficient solutions to the transport sub-step, achieve second-order accuracy in time

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

OpenAIRE

Kihara, Hironobu

2008-01-01

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations; Projet N3S. Methode en temps d`ordre eleve par decomposition d`operateurs. Application aux equations de Navier-Stokes

Energy Technology Data Exchange (ETDEWEB)

Boukir, K

1994-06-01

This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs.

Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

Science.gov (United States)

Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)

1999-01-01

Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

W-transform for exponential stability of second order delay differential equations without damping terms.

Science.gov (United States)

Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid

2017-01-01

In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.

A Special Variant of the Moment Method for Fredholm Integral Equations of the Second Kind

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S. A. Solov’eva

2015-01-01

Full Text Available We consider the linear Fredholm integral equation of the second kind, where the kernel and the free term are smooth functions. We find the unknown function in this class as well.Exact and approximate methods for the solution of linear Fredholm integral equations of the second kind are well developed. However, classical methods do not take into account the structural properties of the kernel and the free term of equation.In this paper we develop and justify a special variant of the moment method to solve this equation, which takes into account the differential properties of initial data. The proposed paper furthers studies of N.S Gabbasov, I.P. Kasakina, and S.A Solov’eva. We use approximation theory, version of the general theory of approximate methods of analysis that Gabdulkhayev B.G suggested, and methods of functional analysis to prove theorems. In addition, we use N.S. Gabbasov’s ideas and methods in papers that are devoted to the Fredholm equations of the first kind, as well as N.S. Gabbasov and S.A Solov’eva’s investigations on the Fredholm equations of the third kind in the space of distributions.The first part of the paper provides a description of the basic function space and elements of the theory of approximation in it.In the second part we propose and theoretically justify a generalized moment method. We have demonstrated that the improvement of differential properties of the initial data improves the approximation accuracy. Since, in practice, the approximate equations are solved, as a rule, only approximately, we prove the stability and causality of the proposed method. The resulting estimate of the paper is in good agreement with the estimate for the ordinary moment method for equations of the second kind in the space of continuous functions.In the final section we have shown that a developed method is optimal in order of accuracy among all polynomial projection methods to solve Fredholm integral equations of the second

Systemic Design for Second-Order Effects

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Evan Barba

2017-04-01

Full Text Available Second-order effects refer to changes within a system that are the result of changes made somewhere else in the system (the first-order effects. Second-order effects can occur at different spatial, temporal, or organizational scales from the original interventions, and are difficult to control. Some organizational theorists suggest that careful management of feedback processes can facilitate controlled change from one organizational configuration to another. Recognizing that skill in managing feedback processes is a core competency of design suggests that design skills are potentially useful tools in achieving organizational change. This paper describes a case study in which a co-design methodology was used to control the second-order effects resulting from a classroom intervention to create organizational change. This approach is then theorized as the Instigator Systems approach.

The multi-order envelope periodic solutions to the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Xiao Yafeng; Xue Haili; Zhang Hongqing

2011-01-01

Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)

The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE

Directory of Open Access Journals (Sweden)

Man Kam Kwong

2006-06-01

Full Text Available Within the last decade, there has been growing interest in the study of multiple solutions of two- and multi-point boundary value problems of nonlinear ordinary differential equations as fixed points of a cone mapping. Undeniably many good results have emerged. The purpose of this paper is to point out that, in the special case of second-order equations, the shooting method can be an effective tool, sometimes yielding better results than those obtainable via fixed point techniques.

Direct determination of the rate constant of propagation by pseudo-stationary polymerization technique: screening investigation for the (implicit) penultimate effect

International Nuclear Information System (INIS)

Schnoll-Bitai, I.; Friedrich Olaj, O.; Liu Song Yu

1999-01-01

The systems styrene-p-methylstyrene, styrene-p-chlorostyrene, methyl methacrylate-p-methylstyrene and methyl methacrylate-p-chlorostyrene were polymerized under pseudo-stationary conditions (rotating sector or pulsed laser) at 25 degree C, 40 degree C and 50 degree C. The respective molecular weight distributions measured by GPC were analysed in order to derive directly the phenomenological rate constant of propagation, κ sub ρ. Copolymer compositions as a function of monomer feed could be described by the terminal model, whereas the kinetic results could only be interpreted in terms of the restricted penultimate model

Adsorption of phenolic compound by aged-refuse

Energy Technology Data Exchange (ETDEWEB)

Chai Xiaoli [State Key Laboratory of Pollution Control and Resource Reuse, School of Enviromental Science and Engineering, Tongji University, Siping Road 1239, Shanghai 200092 (China)]. E-mail: xlchai@mail.tongji.edu.cn; Zhao Youcai [State Key Laboratory of Pollution Control and Resource Reuse, School of Enviromental Science and Engineering, Tongji University, Siping Road 1239, Shanghai 200092 (China)

2006-09-01

The adsorption of phenol, 2-chlorophenol, 4-chlorophenol and 2,4-dichlorophenol by aged-refuse has been studied. Adsorption isotherms have been determined for phenol, 2-chlorophenol, 4-chlorophenol and 2,4-dichlorophenol and the data fits well to the Freundlich equation. The chlorinated phenols are absorbed more strongly than the phenol and the adsorption capacity has an oblivious relationship with the numbers and the position of chlorine subsistent. The experiment data suggests that both the partition function and the chemical adsorption involve in the adsorption process. Pseudo-first-order and pseudo-second-order model were applied to investigate the kinetics of the adsorption and the results show that it fit the pseudo-second-order model. More than one step involves in the adsorption process and the overall rate of the adsorption process appears to be controlled by the chemical reaction. The thermodynamic analysis indicates that the adsorption is spontaneous and endothermic.

Adsorption of phenolic compound by aged-refuse

International Nuclear Information System (INIS)

Chai Xiaoli; Zhao Youcai

2006-01-01

The adsorption of phenol, 2-chlorophenol, 4-chlorophenol and 2,4-dichlorophenol by aged-refuse has been studied. Adsorption isotherms have been determined for phenol, 2-chlorophenol, 4-chlorophenol and 2,4-dichlorophenol and the data fits well to the Freundlich equation. The chlorinated phenols are absorbed more strongly than the phenol and the adsorption capacity has an oblivious relationship with the numbers and the position of chlorine subsistent. The experiment data suggests that both the partition function and the chemical adsorption involve in the adsorption process. Pseudo-first-order and pseudo-second-order model were applied to investigate the kinetics of the adsorption and the results show that it fit the pseudo-second-order model. More than one step involves in the adsorption process and the overall rate of the adsorption process appears to be controlled by the chemical reaction. The thermodynamic analysis indicates that the adsorption is spontaneous and endothermic

Pseudo-spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

KAUST Repository

Zou, Peng

2017-05-10

Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.

Hojman's theorem of the third-order ordinary differential equation

International Nuclear Information System (INIS)

Hong-Sheng, Lü; Hong-Bin, Zhang; Shu-Long, Gu

2009-01-01

This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results. (general)

A high order solver for the unbounded Poisson equation

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

2013-01-01

. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied......A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field...... and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain....

A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

OpenAIRE

Ngwane, F. F.; Jator, S. N.

2017-01-01

In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one...

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

KAUST Repository

Abdulle, Assyr

2012-01-01

© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

First- and second-order processing in transient stereopsis.

Science.gov (United States)

Edwards, M; Pope, D R; Schor, C M

2000-01-01

Large-field stimuli were used to investigate the interaction of first- and second-order pathways in transient-stereo processing. Stimuli consisted of sinewave modulations in either the mean luminance (first-order stimulus) or the contrast (second-order stimulus) of a dynamic-random-dot field. The main results of the present study are that: (1) Depth could be extracted with both the first-order and second-order stimuli; (2) Depth could be extracted from dichoptically mixed first- and second-order stimuli, however, the same stimuli, when presented as a motion sequence, did not result in a motion percept. Based upon these findings we conclude that the transient-stereo system processes both first- and second-order signals, and that these two signals are pooled prior to the extraction of transient depth. This finding of interaction between first- and second-order stereoscopic processing is different from the independence that has been found with the motion system.

Analog computing for a new nuclear reactor dynamic model based on a time-dependent second order form of the neutron transport equation

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal; Suh, Kune Y.

2011-01-01

This paper considers the concept of analog computing based on a cellular neural network (CNN) paradigm to simulate nuclear reactor dynamics using a time-dependent second order form of the neutron transport equation. Instead of solving nuclear reactor dynamic equations numerically, which is time-consuming and suffers from such weaknesses as vulnerability to transient phenomena, accumulation of round-off errors and floating-point overflows, use is made of a new method based on a cellular neural network. The state-of-the-art shows the CNN as being an alternative solution to the conventional numerical computation method. Indeed CNN is an analog computing paradigm that performs ultra-fast calculations and provides accurate results. In this study use is made of the CNN model to simulate the space-time response of scalar flux distribution in steady state and transient conditions. The CNN model also is used to simulate step perturbation in the core. The accuracy and capability of the CNN model are examined in 2D Cartesian geometry for two fixed source problems, a mini-BWR assembly, and a TWIGL Seed/Blanket problem. We also use the CNN model concurrently for a typical small PWR assembly to simulate the effect of temperature feedback, poisons, and control rods on the scalar flux distribution

Nonlocal higher order evolution equations

KAUST Repository

Rossi, Julio D.; Schö nlieb, Carola-Bibiane

2010-01-01

In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove

Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

OpenAIRE

Li, Xiaowang; Deng, Zhongmin

2016-01-01

A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white no...

Modulation masking produced by second-order modulators

DEFF Research Database (Denmark)

Füllgrabe, Christian; Moore, Brian C.J.; Demany, Laurent

2005-01-01

Recent studies suggest that an auditory nonlinearity converts second-order sinusoidal amplitude modulation (SAM) (i.e., modulation of SAM depth) into a first-order SAM component, which contributes to the perception of second-order SAM. However, conversion may also occur in other ways such as coch...

Adsorption kinetics of Rhodamine-B on used black tea leaves

Directory of Open Access Journals (Sweden)

Hossain Mohammad

2012-08-01

Full Text Available Abstract Rhodamine B (Rh-B is one of the most common pollutants in the effluents of textile industries effluents in developing countries. This study was carried out to evaluate the applicability of used black tea leaves (UBTL for the adsorptive removal of Rh-B from aqueous system by investigating the adsorption kinetics in batch process. The effects of concentration and temperature on adsorption kinetics were examined. First-, second- and pseudo-second order kinetic equations were used to investigate the adsorption mechanism. The adsorption of Rh-B on UBTL followed pseudo-second order kinetics. The equilibrium amount adsorbed and the equilibrium concentration were calculated from pseudo-second-order kinetic plots for different initial concentrations of Rh-B to construct the adsorption isotherm. The adsorption isotherm was well expressed by Langmuir equation. The maximum adsorption capacity of UBTL to Rh-B was found to be 53.2 mg/g at pH = 2.0. The equilibrium amount adsorbed, calculated from pseudo-second-order kinetic plots, increased with temperature increase. The positive value of enthalpy of adsorption, ΔHads = 31.22 kJ/mol, suggested that the adsorption of Rh-B on UBTL at pH = 2.0 is an endothermic process.

Kinetic equation for spin-polarized plasmas

International Nuclear Information System (INIS)

Cowley, S.C.; Kulsrud, R.M.; Valeo, E.

1984-07-01

The usual kinetic description of a plasma is extended to include variables to describe the spin. The distribution function, over phase-space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution equation for the distribution function is given. The equations derived are used to calculate depolarization due to four processes, inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10 -4 S -1 for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small amplitude magnetic fluctuations (of order one gauss) resonant with the spin precession frequency can lead to significant depolarization (depolarises triton in ten seconds and deuteron in a hundred seconds.)

Automatic estimation of pressure-dependent rate coefficients.

Science.gov (United States)

Allen, Joshua W; Goldsmith, C Franklin; Green, William H

2012-01-21

A general framework is presented for accurately and efficiently estimating the phenomenological pressure-dependent rate coefficients for reaction networks of arbitrary size and complexity using only high-pressure-limit information. Two aspects of this framework are discussed in detail. First, two methods of estimating the density of states of the species in the network are presented, including a new method based on characteristic functional group frequencies. Second, three methods of simplifying the full master equation model of the network to a single set of phenomenological rates are discussed, including a new method based on the reservoir state and pseudo-steady state approximations. Both sets of methods are evaluated in the context of the chemically-activated reaction of acetyl with oxygen. All three simplifications of the master equation are usually accurate, but each fails in certain situations, which are discussed. The new methods usually provide good accuracy at a computational cost appropriate for automated reaction mechanism generation.

Automatic estimation of pressure-dependent rate coefficients

KAUST Repository

Allen, Joshua W.; Goldsmith, C. Franklin; Green, William H.

2012-01-01

A general framework is presented for accurately and efficiently estimating the phenomenological pressure-dependent rate coefficients for reaction networks of arbitrary size and complexity using only high-pressure-limit information. Two aspects of this framework are discussed in detail. First, two methods of estimating the density of states of the species in the network are presented, including a new method based on characteristic functional group frequencies. Second, three methods of simplifying the full master equation model of the network to a single set of phenomenological rates are discussed, including a new method based on the reservoir state and pseudo-steady state approximations. Both sets of methods are evaluated in the context of the chemically-activated reaction of acetyl with oxygen. All three simplifications of the master equation are usually accurate, but each fails in certain situations, which are discussed. The new methods usually provide good accuracy at a computational cost appropriate for automated reaction mechanism generation. This journal is © the Owner Societies.

On bifurcations of a system of cubic differential equations with an integrating multiplier singular along a second-order curve

Directory of Open Access Journals (Sweden)

Aleksandr Alekseev

2015-07-01

Full Text Available We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.

An implicit second order numerical method for two-fluid models

International Nuclear Information System (INIS)

Toumi, I.

1995-01-01

We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)

Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II

Directory of Open Access Journals (Sweden)

Akira Shirai

2015-01-01

Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \\[f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

Science.gov (United States)

Gao, Peng

2018-04-01

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

Science.gov (United States)

Gao, Peng

2018-06-01

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

On a generalized fifth order KdV equations

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter, we dealt with finding the solutions of a generalized fifth order KdV equation (for short, gfKdV) by using the Adomian decomposition method (for short, ADM). We prove the convergence of ADM applied to the gfKdV equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the gfKdV equation

On the relation between elementary partial difference equations and partial differential equations

NARCIS (Netherlands)

van den Berg, I.P.

1998-01-01

The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential

An eco-friendly dyeing of woolen yarn by Terminalia chebula extract with evaluations of kinetic and adsorption characteristics.

Science.gov (United States)

Shabbir, Mohd; Rather, Luqman Jameel; Shahid-Ul-Islam; Bukhari, Mohd Nadeem; Shahid, Mohd; Ali Khan, Mohd; Mohammad, Faqeer

2016-05-01

In the present study Terminalia chebula was used as an eco-friendly natural colorant for sustainable textile coloration of woolen yarn with primary emphasis on thermodynamic and kinetic adsorption aspects of dyeing processes. Polyphenols and ellagitannins are the main coloring components of the dye extract. Assessment of the effect of pH on dye adsorption showed an increase in adsorption capacity with decreasing pH. Effect of temperature on dye adsorption showed 80 °C as optimum temperature for wool dyeing with T. chebula dye extract. Two kinetic equations, namely pseudo first-order and pseudo second-order equations, were employed to investigate the adsorption rates. Pseudo second-order model provided the best fit (R (2) = 0.9908) to the experimental data. The equilibrium adsorption data were fitted by Freundlich and Langmuir isotherm models. The adsorption behavior accorded well (R (2) = 0.9937) with Langmuir isotherm model. Variety of eco-friendly and sustainable shades were developed in combination with small amount of metallic mordants and assessed in terms of colorimetric (CIEL(∗) a (∗) b (∗) and K/S) properties measured using spectrophotometer under D65 illuminant (10° standard observer). The fastness properties of dyed woolen yarn against light, washing, dry and wet rubbing were also evaluated.

An eco-friendly dyeing of woolen yarn by Terminalia chebula extract with evaluations of kinetic and adsorption characteristics

Science.gov (United States)

Shabbir, Mohd; Rather, Luqman Jameel; Shahid-ul-Islam; Bukhari, Mohd Nadeem; Shahid, Mohd; Ali Khan, Mohd; Mohammad, Faqeer

2016-01-01

In the present study Terminalia chebula was used as an eco-friendly natural colorant for sustainable textile coloration of woolen yarn with primary emphasis on thermodynamic and kinetic adsorption aspects of dyeing processes. Polyphenols and ellagitannins are the main coloring components of the dye extract. Assessment of the effect of pH on dye adsorption showed an increase in adsorption capacity with decreasing pH. Effect of temperature on dye adsorption showed 80 °C as optimum temperature for wool dyeing with T. chebula dye extract. Two kinetic equations, namely pseudo first-order and pseudo second-order equations, were employed to investigate the adsorption rates. Pseudo second-order model provided the best fit (R2 = 0.9908) to the experimental data. The equilibrium adsorption data were fitted by Freundlich and Langmuir isotherm models. The adsorption behavior accorded well (R2 = 0.9937) with Langmuir isotherm model. Variety of eco-friendly and sustainable shades were developed in combination with small amount of metallic mordants and assessed in terms of colorimetric (CIEL∗a∗b∗ and K/S) properties measured using spectrophotometer under D65 illuminant (10° standard observer). The fastness properties of dyed woolen yarn against light, washing, dry and wet rubbing were also evaluated. PMID:27222752

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

Science.gov (United States)

Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

From differential to difference equations for first order ODEs

Science.gov (United States)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

International Nuclear Information System (INIS)

Bokhari, Ashfaque H.; Zaman, F. D.; Mahomed, F. M.

2010-01-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

Convective boundary layer flow and heat transfer in a nanofluid in the presence of second order slip, constant heat flux and zero nanoparticles flux

Energy Technology Data Exchange (ETDEWEB)

Rahman, M.M., E-mail: mansurdu@yahoo.com [Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, PC 123 Al-Khod, Muscat (Oman); Al-Rashdi, Maryam H. [Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, PC 123 Al-Khod, Muscat (Oman); Pop, I. [Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca 400084 (Romania)

2016-02-15

Highlights: • Convective boundary layer flow and heat transfer in a nanofluid is investigated. • Second order slip increases the rate of shear stress and decreases the rate of heat transfer in a nanofluid. • In nanofluid flow zero normal flux of the nanoparticles at the surface is realistic to apply. • Multiple solutions are identified for certain values of the parameter space. • The upper branch solution is found to be stable, hence physically realizable. - Abstract: In this work, the effects of the second order slip, constant heat flux, and zero normal flux of the nanoparticles due to thermophoresis on the convective boundary layer flow and heat transfer characteristics in a nanofluid using Buongiorno's model over a permeable shrinking sheet is studied theoretically. The nonlinear coupled similarity equations are solved using the function bvp4c using Matlab. Similarity solutions of the flow, heat transfer and nanoparticles volume fraction are presented graphically for several values of the model parameters. The results show that the application of second order slip at the interface is found to be increased the rate of shear stress and decreased the rate of heat transfer in a nanofluid, so need to be taken into account in nanofluid modeling. The results further indicate that multiple solutions exist for certain values of the parameter space. The stability analysis provides guarantee that the lower branch solution is unstable, while the upper branch solution is stable and physically realizable.

Determination of the absolute second-order rate constant for the reaction Na + O3 → NaO + O2

International Nuclear Information System (INIS)

Husain, David; Marshall, Paul; Plane, J.M.C.

1985-01-01

The absolute second-order rate constant for the reaction Na + O 3 -> NaO + O 2 (k 1 ) has been determined by time-resolved atomic resonance absorption spectroscopy at lambda = 589 nm [Na(3 2 Psub(j)) 2 Ssub(1/2))] following pulsed irradiation, coupled with monitoring of O 3 by light absorption in the ultra-violet; this yields k 1 (500 K) = 4(+4,-2) x 10 -10 cm 3 molecule -1 s -1 , resolving large differences for various estimates of this important quantity used in modelling the sodium layer in the mesosphere. (author)

Soliton and periodic solutions for higher order wave equations of KdV type (I)

International Nuclear Information System (INIS)

Khuri, S.A.

2005-01-01

The aim of the paper is twofold. First, a new ansaetze is introduced for the construction of exact solutions for higher order wave equations of KdV type (I). We show the existence of a class of discontinuous soliton solutions with infinite spikes. Second, the projective Riccati technique is implemented as an alternate approach for obtaining new exact solutions, solitary solutions, and periodic wave solutions

Relaxation approximations to second-order traffic flow models by high-resolution schemes

International Nuclear Information System (INIS)

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-01-01

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers

On realization of nonlinear systems described by higher-order differential equations

NARCIS (Netherlands)

van der Schaft, Arjan

1987-01-01

We consider systems of smooth nonlinear differential and algebraic equations in which some of the variables are distinguished as “external variables.” The realization problem is to replace the higher-order implicit differential equations by first-order explicit differential equations and the

Theory of a higher-order Sturm-Liouville equation

CERN Document Server

Kozlov, Vladimir

1997-01-01

This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

Representing Rate Equations for Enzyme-Catalyzed Reactions

Science.gov (United States)

Ault, Addison

2011-01-01

Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…

Kinetics of diuron and amitrole adsorption from aqueous solution on activated carbons.

Science.gov (United States)

Fontecha-Cámara, M A; López-Ramón, M V; Pastrana-Martínez, L M; Moreno-Castilla, C

2008-08-15

A study was conducted on the adsorption kinetics of diuron and amitrole from aqueous solutions on activated carbons of different particle sizes and on an activated carbon fiber. Different kinetic models were applied to the experimental results obtained. A pseudo-second-order rate equation fitted the adsorption kinetics data better than a pseudo-first-order rate equation. Amitrole showed faster adsorption kinetics compared with diuron because of the smaller size of the former herbicide, despite its lower driving force for adsorption. Both reaction rate constants increased when the particle size decreased. The activated carbon fiber and the activated carbon of smallest particle size (0.03 mm) showed similar adsorption kinetics. The intraparticle diffusion rate constant increased with higher initial concentration of herbicides in solution and with lower particle size of the adsorbent. This is because the rise in initial concentration increased the amount adsorbed at equilibrium, and the reduction in particle size increased the number of collisions between adsorbate and adsorbent particles. Demineralization of the activated carbon with particle size of 0.5mm had practically no effect on the adsorption kinetics.

Recursive belief manipulation and second-order false-beliefs

DEFF Research Database (Denmark)

Braüner, Torben; Blackburn, Patrick Rowan; Polyanskaya, Irina

2016-01-01

it indicate that a more fundamental *conceptual change* has taken place? In this paper we extend Braüner's hybrid-logical analysis of first-order false-belief tasks to the second-order case, and argue that our analysis supports a version of the conceptual change position.......The literature on first-order false-belief is extensive, but less is known about the second-order case. The ability to handle second-order false-beliefs correctly seems to mark a cognitively significant step, but what is its status? Is it an example of *complexity only* development, or does...

Higher order harmonics of reactor neutron equation

International Nuclear Information System (INIS)

Li Fu; Hu Yongming; Luo Zhengpei

1996-01-01

The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out

From ordinary to partial differential equations

CERN Document Server

Esposito, Giampiero

2017-01-01

This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities

DEFF Research Database (Denmark)

Khare, A.; Rasmussen, Kim Ø; Salerno, M.

2006-01-01

-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...

The mixed BVP for second order nonlinear ordinary differential equation at resonance

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan

2017-01-01

Roč. 290, 2-3 (2017), s. 393-400 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : mixed problem at resonance * nonlinear ordinary differencial equation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.742, year: 2016

Calculating Second-Order Effects in MOSFET's

Science.gov (United States)

Benumof, Reuben; Zoutendyk, John A.; Coss, James R.

1990-01-01

Collection of mathematical models includes second-order effects in n-channel, enhancement-mode, metal-oxide-semiconductor field-effect transistors (MOSFET's). When dimensions of circuit elements relatively large, effects neglected safely. However, as very-large-scale integration of microelectronic circuits leads to MOSFET's shorter or narrower than 2 micrometer, effects become significant in design and operation. Such computer programs as widely-used "Simulation Program With Integrated Circuit Emphasis, Version 2" (SPICE 2) include many of these effects. In second-order models of n-channel, enhancement-mode MOSFET, first-order gate-depletion region diminished by triangular-cross-section deletions on end and augmented by circular-wedge-cross-section bulges on sides.

Waste Plant Material as a Potential Adsorbent of a Selected Azo Dye

Directory of Open Access Journals (Sweden)

Tomczak Elwira

2017-06-01

Full Text Available This paper discusses the adsorption of Direct Orange 26 azo dye on sunflower husk - an agricultural waste product. During the study, sorption kinetics and equilibrium as well as sorption capacity of the husk were investigated. The adsorption kinetics was analyzed using pseudo-first and pseudo-second order equations, which indicated a chemical sorption mechanism. The sorption equilibrium was approximated with the two-parameter Freundlich and Langmuir equations and the three-parameter Redlich-Peterson equation. The main experiments were carried out in a laboratory adsorption column under different process conditions. Experimental data were interpreted with the Thomas model, based on the volumetric flow rate, initial composition of the feed solution and mass of the adsorbent. The results of modeling the adsorption equilibrium, adsorption kinetics and adsorption dynamics were evaluated statistically.

Pseudo-populations a basic concept in statistical surveys

CERN Document Server

Quatember, Andreas

2015-01-01

This book emphasizes that artificial or pseudo-populations play an important role in statistical surveys from finite universes in two manners: firstly, the concept of pseudo-populations may substantially improve users’ understanding of various aspects in the sampling theory and survey methodology; an example of this scenario is the Horvitz-Thompson estimator. Secondly, statistical procedures exist in which pseudo-populations actually have to be generated. An example of such a scenario can be found in simulation studies in the field of survey sampling, where close-to-reality pseudo-populations are generated from known sample and population data to form the basis for the simulation process. The chapters focus on estimation methods, sampling techniques, nonresponse, questioning designs and statistical disclosure control.This book is a valuable reference in understanding the importance of the pseudo-population concept and applying it in teaching and research.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

Science.gov (United States)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

New exact solutions of sixth-order thin-film equation

Directory of Open Access Journals (Sweden)

Wafaa M. Taha

2014-01-01

Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.

Second-Order Risk Constraints in Decision Analysis

Directory of Open Access Journals (Sweden)

Love Ekenberg

2014-01-01

Full Text Available Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities are associated with distributions over them (second-order representations have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.