WorldWideScience

Sample records for simple approximate solutions

  1. A simple approximation for the current-voltage characteristics of high-power, relativistic diodes

    Energy Technology Data Exchange (ETDEWEB)

    Ekdahl, Carl, E-mail: cekdahl@lanl.gov [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

    2016-06-15

    A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. The approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.

  2. An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon

    International Nuclear Information System (INIS)

    Jiang, R.

    2009-01-01

    It is difficult to find the optimal solution of the sequential age replacement policy for a finite-time horizon. This paper presents an accurate approximation to find an approximate optimal solution of the sequential replacement policy. The proposed approximation is computationally simple and suitable for any failure distribution. Their accuracy is illustrated by two examples. Based on the approximate solution, an approximate estimate for the total cost is derived.

  3. Inverse kinematic solution for near-simple robots and its application to robot calibration

    Science.gov (United States)

    Hayati, Samad A.; Roston, Gerald P.

    1986-01-01

    This paper provides an inverse kinematic solution for a class of robot manipulators called near-simple manipulators. The kinematics of these manipulators differ from those of simple-robots by small parameter variations. Although most robots are by design simple, in practice, due to manufacturing tolerances, every robot is near-simple. The method in this paper gives an approximate inverse kinematics solution for real time applications based on the nominal solution for these robots. The validity of the results are tested both by a simulation study and by applying the algorithm to a PUMA robot.

  4. Generalized Gradient Approximation Made Simple

    International Nuclear Information System (INIS)

    Perdew, J.P.; Burke, K.; Ernzerhof, M.

    1996-01-01

    Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society

  5. A trigonometric approximation for the tension in the string of a simple pendulum accurate for all amplitudes

    International Nuclear Information System (INIS)

    Lima, F M S

    2009-01-01

    In a previous work, O'Connell (Phys. Teach. 40, 24 (2002)) investigated the time dependence of the tension in the string of a simple pendulum oscillating within the small-angle regime. In spite of the approximation sin θ ∼ θ being accurate only for amplitudes below 7 deg., his experimental results are for a pendulum oscillating with an amplitude of about 18 deg., therefore beyond the small-angle regime. This lapse may also be found in some textbooks, laboratory manuals and internet. By noting that the exact analytical solution for this problem involves the so-called Jacobi elliptic functions, which are unknown to most students (even instructors), I take into account a sinusoidal approximate solution for the pendulum equation I introduced in a recent work (Eur. J. Phys. 29 1091 (2008)) for deriving a simple trigonometric approximation for the tension valid for all possible amplitudes. This approximation is compared to both the O'Connell and the exact results, revealing that it is accurate enough for analysing large-angle pendulum experiments. (letters and comments)

  6. Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

    KAUST Repository

    Younis, Mohammad I.

    2014-01-01

    We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions

  7. The soliton solution of the PHI24 field theory in the Hartree approximation

    International Nuclear Information System (INIS)

    Altenbokum, M.

    1984-01-01

    In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de

  8. Approximative solutions of stochastic optimization problem

    Czech Academy of Sciences Publication Activity Database

    Lachout, Petr

    2010-01-01

    Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf

  9. A simple approximation method for dilute Ising systems

    International Nuclear Information System (INIS)

    Saber, M.

    1996-10-01

    We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs

  10. Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

    International Nuclear Information System (INIS)

    Kotler, Z.; Neria, E.; Nitzan, A.

    1991-01-01

    The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.)

  11. Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

    Energy Technology Data Exchange (ETDEWEB)

    Kotler, Z.; Neria, E.; Nitzan, A. (Tel Aviv Univ. (Israel). School of Chemistry)

    1991-02-01

    The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.).

  12. A method for the approximate solutions of the unsteady boundary layer equations

    International Nuclear Information System (INIS)

    Abdus Sattar, Md.

    1990-12-01

    The approximate integral method proposed by Bianchini et al. to solve the unsteady boundary layer equations is considered here with a simple modification to the scale function for the similarity variable. This is done by introducing a time dependent length scale. The closed form solutions, thus obtained, give satisfactory results for the velocity profile and the skin friction to a limiting case in comparison with the results of the past investigators. (author). 7 refs, 2 figs

  13. Simple approximations for the batch-arrival MX/G/1 queue

    NARCIS (Netherlands)

    van Ommeren, Jan C.W.

    1990-01-01

    In this paper we consider the MX/G/I queueing system with batch arrivals. We give simple approximations for the waiting-time probabilities of individual customers. These approximations are checked numerically and they are found to perform very well for a wide variety of batch-size and service-timed

  14. Simple Lie groups without the approximation property

    DEFF Research Database (Denmark)

    Haagerup, Uffe; de Laat, Tim

    2013-01-01

    For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...

  15. Approximated solutions to Born-Infeld dynamics

    International Nuclear Information System (INIS)

    Ferraro, Rafael; Nigro, Mauro

    2016-01-01

    The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

  16. Approximated solutions to Born-Infeld dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)

    2016-02-01

    The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

  17. Rational approximations to solutions of linear differential equations.

    Science.gov (United States)

    Chudnovsky, D V; Chudnovsky, G V

    1983-08-01

    Rational approximations of Padé and Padé type to solutions of differential equations are considered. One of the main results is a theorem stating that a simultaneous approximation to arbitrary solutions of linear differential equations over C(x) cannot be "better" than trivial ones implied by the Dirichlet box principle. This constitutes, in particular, the solution in the linear case of Kolchin's problem that the "Roth's theorem" holds for arbitrary solutions of algebraic differential equations. Complete effective proofs for several valuations are presented based on the Wronskian methods and graded subrings of Picard-Vessiot extensions.

  18. An approximate JKR solution for a general contact, including rough contacts

    Science.gov (United States)

    Ciavarella, M.

    2018-05-01

    In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is δ =δ1 -√{ 2 wA‧ /P″ } where w is surface energy, δ1 is the adhesiveless indentation, A‧ is the first derivative of contact area and P‧‧ the second derivative of the load with respect to δ1. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts, but also sinusoidal waves contact and correctly predicts some features of an ideal asperity model used as a test case and not as a real description of a rough contact problem. The solution permits therefore an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The result turns out to depend only on rms amplitude and slopes of the surface, and as in the fractal limit, slopes would grow without limit, tends to the adhesiveless result - although in this limit the JKR model is inappropriate. The solution would also go to adhesiveless result for large rms amplitude of roughness hrms, irrespective of the small scale details, and in agreement with common sense, well known experiments and previous models by the author.

  19. Approximate solutions of common fixed-point problems

    CERN Document Server

    Zaslavski, Alexander J

    2016-01-01

    This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal...

  20. Simple Solutions for Dry Eye

    Science.gov (United States)

    Patient Education Sheet Simple Solutions for Dry Eye The SSF thanks J. Daniel Nelson, MD, Associate Medical Director, Specialty Care HealthPartners Medical Group & Clinics, and Professor of Ophthalmology, University of ...

  1. Comment on 'Approximation for a large-angle simple pendulum period'

    International Nuclear Information System (INIS)

    Yuan Qingxin; Ding Pei

    2009-01-01

    In a recent letter, Belendez et al (2009 Eur. J. Phys. 30 L25-8) proposed an alternative of approximation for the period of a simple pendulum suggested earlier by Hite (2005 Phys. Teach. 43 290-2) who set out to improve on the Kidd and Fogg formula (2002 Phys. Teach. 40 81-3). As a response to the approximation scheme, we obtain another analytical approximation for the large-angle pendulum period, which owns the simplicity and accuracy in evaluating the exact period, and moreover, for amplitudes less than 144 deg. the analytical approximate expression is more accurate than others in the literature. (letters and comments)

  2. Approximation of entropy solutions to degenerate nonlinear parabolic equations

    Science.gov (United States)

    Abreu, Eduardo; Colombeau, Mathilde; Panov, Evgeny Yu

    2017-12-01

    We approximate the unique entropy solutions to general multidimensional degenerate parabolic equations with BV continuous flux and continuous nondecreasing diffusion function (including scalar conservation laws with BV continuous flux) in the periodic case. The approximation procedure reduces, by means of specific formulas, a system of PDEs to a family of systems of the same number of ODEs in the Banach space L^∞, whose solutions constitute a weak asymptotic solution of the original system of PDEs. We establish well posedness, monotonicity and L^1-stability. We prove that the sequence of approximate solutions is strongly L^1-precompact and that it converges to an entropy solution of the original equation in the sense of Carrillo. This result contributes to justify the use of this original method for the Cauchy problem to standard multidimensional systems of fluid dynamics for which a uniqueness result is lacking.

  3. Simple approximation for estimating centerline gamma absorbed dose rates due to a continuous Gaussian plume

    International Nuclear Information System (INIS)

    Overcamp, T.J.; Fjeld, R.A.

    1987-01-01

    A simple approximation for estimating the centerline gamma absorbed dose rates due to a continuous Gaussian plume was developed. To simplify the integration of the dose integral, this approach makes use of the Gaussian cloud concentration distribution. The solution is expressed in terms of the I1 and I2 integrals which were developed for estimating long-term dose due to a sector-averaged Gaussian plume. Estimates of tissue absorbed dose rates for the new approach and for the uniform cloud model were compared to numerical integration of the dose integral over a Gaussian plume distribution

  4. Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation

    Directory of Open Access Journals (Sweden)

    G. H. Gudmundsson

    2008-07-01

    Full Text Available New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.

  5. Approximate variational solutions of the Grad-Shafranov equation

    International Nuclear Information System (INIS)

    Ludwig, G.O.

    2001-01-01

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

  6. A simple approximation of productivity scores of fuzzy production plans

    DEFF Research Database (Denmark)

    Hougaard, Jens Leth

    2005-01-01

    This paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans. The procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational...

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

    International Nuclear Information System (INIS)

    Bouaziz, M.N.; Aziz, Abdul

    2010-01-01

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

  8. Approximate solution fuzzy pantograph equation by using homotopy perturbation method

    Science.gov (United States)

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

    2017-09-01

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

  9. Approximate solution for the reactor neutron probability distribution

    International Nuclear Information System (INIS)

    Ruby, L.; McSwine, T.L.

    1985-01-01

    Several authors have studied the Kolmogorov equation for a fission-driven chain-reacting system, written in terms of the generating function G(x,y,z,t) where x, y, and z are dummy variables referring to the neutron, delayed neutron precursor, and detector-count populations, n, m, and c, respectively. Pal and Zolotukhin and Mogil'ner have shown that if delayed neutrons are neglected, the solution is approximately negative binomial for the neutron population. Wang and Ruby have shown that if the detector effect is neglected, the solution, including the effect of delayed neutrons, is approximately negative binomial. All of the authors assumed prompt-neutron emission not exceeding two neutrons per fission. An approximate method of separating the detector effect from the statistics of the neutron and precursor populations has been proposed by Ruby. In this weak-coupling limit, it is assumed that G(x,y,z,t) = H(x,y)I(z,t). Substitution of this assumption into the Kolmogorov equation separates the latter into two equations, one for H(x,y) and the other for I(z,t). Solution of the latter then gives a generating function, which indicates that in the weak-coupling limit, the detector counts are Poisson distributed. Ruby also showed that if the detector effect is neglected in the equation for H(x,y), i.e., the detector efficiency is set to zero, then the resulting equation is identical with that considered by Wang and Ruby. The authors present here an approximate solution for H(x,y) that does not set the detector efficiency to zero

  10. Approximate solutions of the Wei Hua oscillator using the Pekeris ...

    Indian Academy of Sciences (India)

    The approximate analytical bound-state solutions of the Schrödinger equation for the. Wei Hua oscillator are carried out in N-dimensional space by taking Pekeris approximation scheme to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov ...

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

    International Nuclear Information System (INIS)

    Matausek, M.V.; Milosevic, M.

    1981-01-01

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

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

    International Nuclear Information System (INIS)

    Matausek, M.V.; Milosevic, M.

    1981-01-01

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

  13. An approximate analytical solution for describing surface runoff and sediment transport over hillslope

    Science.gov (United States)

    Tao, Wanghai; Wang, Quanjiu; Lin, Henry

    2018-03-01

    Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

  14. Analytical approximate solutions for a general class of nonlinear delay differential equations.

    Science.gov (United States)

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

    We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

  15. Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation

    International Nuclear Information System (INIS)

    Ye, Caier; Zhang, Weiguo

    2015-01-01

    Highlights: • Analyze the dynamical behavior of the planar dynamical system corresponding to the perturbed Klein–Gordon equation. • Present the relations between the properties of traveling wave solutions and the perturbation coefficient. • Obtain all explicit expressions of approximate damped oscillatory solutions. • Investigate error estimates between exact damped oscillatory solutions and the approximate solutions and give some numerical simulations. - Abstract: The influence of perturbation on traveling wave solutions of the perturbed Klein–Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis

  16. Approximate solutions to Mathieu's equation

    Science.gov (United States)

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  17. The neutron's Dirac-equation: Its rigorous solution at slab-like magnetic fields, non-relativistic approximation, energy spectra and statistical characteristics

    International Nuclear Information System (INIS)

    Zhang Yongde.

    1987-03-01

    In this paper, the neutron Dirac-equation is presented. After decoupling it into two equations of the simple spinors, the rigorous solution of this equation is obtained in the case of slab-like uniform magnetic fields at perpendicular incidence. At non-relativistic approximation and first order approximation of weak field (NRWFA), our results have included all results that have been obtained in references for this case up to now. The corresponding transformations of the neutron's spin vectors are given. The single particle spectrum and its approximate expression are obtained. The characteristics of quantum statistics with the approximate expression of energy spectrum are studied. (author). 15 refs

  18. Approximated solutions to the Schroedinger equation

    International Nuclear Information System (INIS)

    Rico, J.F.; Fernandez-Alonso, J.I.

    1977-01-01

    The authors are currently working on a couple of the well-known deficiencies of the variation method and present here some of the results that have been obtained so far. The variation method does not give information a priori on the trial functions best suited for a particular problem nor does it give information a posteriori on the degree of precision attained. In order to clarify the origin of both difficulties, a geometric interpretation of the variation method is presented. This geometric interpretation is the starting point for the exact formal solution to the fundamental state and for the step-by-step approximations to the exact solution which are also given. Some comments on these results are included. (Auth.)

  19. Solution of a simple inelastic scattering problem

    International Nuclear Information System (INIS)

    Knudson, S.K.

    1975-01-01

    Simple examples of elastic scattering, typically from square wells, serve as important pedagogical tools in discussion of the concepts and processes involved in elastic scattering events. An analytic solution of a model inelastic scattering system is presented here to serve in this role for inelastic events. The model and its solution are simple enough to be of pedagogical utility, but also retain enough of the important physical features to include most of the special characteristics of inelastic systems. The specific model chosen is the collision of an atom with a harmonic oscillator, interacting via a repulsive square well potential. Pedagogically important features of inelastic scattering, including its multistate character, convergence behavior, and dependence on an ''inelastic potential'' are emphasized as the solution is determined. Results are presented for various energies and strengths of inelastic scattering, which show that the model is capable of providing an elementary representation of vibrationally inelastic scattering

  20. Solution of the Chew-Low equations in the quadratic approximation

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Zharkov, A.Yu.

    1982-01-01

    Within the framework of the iteration scheme for constructing the general solution of the Chew-Low equations as suggested earlier the second order power contributions are found. In contrast to the linear approximation obtained before the quadratic approximation includes an infinite number of poles on the complex plane of the uniformizing variable w. It is shown that taking into account the second order corrections in the general solution allows us to select the class of solutions possessing the Born pole at w=0. The most cumbersome part of analytical computations has been carried out by computer using the algebraic system REDUCE-2

  1. A multi scale approximation solution for the time dependent Boltzmann-transport equation

    International Nuclear Information System (INIS)

    Merk, B.

    2004-03-01

    The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

  2. A simple approach to nonlinear oscillators

    International Nuclear Information System (INIS)

    Ren Zhongfu; He Jihuan

    2009-01-01

    A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.

  3. Approximate design theory for a simple block design with random block effects

    OpenAIRE

    Christof, Karin

    1985-01-01

    Approximate design theory for a simple block design with random block effects / K. Christof ; F. Pukelsheim. - In: Linear statistical inference / ed. by T. Calinski ... - Berlin u. a. : Springer, 1985. - S. 20-28. - (Lecture notes in statistics ; 35)

  4. Solutions of simple dual bootstrap models satisfying Lee--Veneziano relation and the smallness of cut discontinuities

    International Nuclear Information System (INIS)

    Chiu, C.B.; Hossain, M.; Tow, D.M.

    1977-07-01

    To investigate the t-dependent solutions of simple dual bootstrap models, two general formulations are discussed, one without and one with cut cancellation at the planar level. The possible corresponding production mechanisms are discussed. In contrast to Bishari's formulation, both models recover the Lee-Veneziano relation, i.e., in the peak approximation the Pomeron intercept is unity. The solutions based on an exponential form for the reduced triple-Reggeon vertex for both models are discussed in detail. Also calculated are the cut discontinuities for both models and for Bishari's and it is shown that at both the planar and cylinder levels they are small compared with the corresponding pole residues. Precocious asymptotic planarity is also found in the solutions

  5. Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary

    Science.gov (United States)

    Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing

    2016-04-01

    An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.

  6. Scattering in particle-hole space: simple approximations to nuclear RPA calculations in the continuum

    International Nuclear Information System (INIS)

    Toledo Piza, A.F.R. de.

    1987-01-01

    The Random Phase Approximation (RPA) treatment of nuclear small amplitude vibrations including particle-hole continua is handled in terms of previously developed techniques to treat single-particle resonances in a reaction theoretical framework. A hierarchy of interpretable approximations is derived and a simple working approximation is proposed which involves a numerical effort no larger than that involved in standard, discrete RPA calculations. (Author) [pt

  7. Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations

    Science.gov (United States)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2013-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad

  8. Efficient solution of parabolic equations by Krylov approximation methods

    Science.gov (United States)

    Gallopoulos, E.; Saad, Y.

    1990-01-01

    Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

  9. A simple method to approximate liver size on cross-sectional images using living liver models

    International Nuclear Information System (INIS)

    Muggli, D.; Mueller, M.A.; Karlo, C.; Fornaro, J.; Marincek, B.; Frauenfelder, T.

    2009-01-01

    Aim: To assess whether a simple. diameter-based formula applicable to cross-sectional images can be used to calculate the total liver volume. Materials and methods: On 119 cross-sectional examinations (62 computed tomography and 57 magnetic resonance imaging) a simple, formula-based method to approximate the liver volume was evaluated. The total liver volume was approximated measuring the largest craniocaudal (cc), ventrodorsal (vd), and coronal (cor) diameters by two readers and implementing the equation: Vol estimated =ccxvdxcorx0.31. Inter-rater reliability, agreement, and correlation between liver volume calculation and virtual liver volumetry were analysed. Results: No significant disagreement between the two readers was found. The formula correlated significantly with the volumetric data (r > 0.85, p < 0.0001). In 81% of cases the error of the approximated volume was <10% and in 92% of cases <15% compared to the volumetric data. Conclusion: Total liver volume can be accurately estimated on cross-sectional images using a simple, diameter-based equation.

  10. On the WKBJ approximation

    International Nuclear Information System (INIS)

    El Sawi, M.

    1983-07-01

    A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)

  11. Approximate radiative solutions of the Einstein equations

    International Nuclear Information System (INIS)

    Kuusk, P.; Unt, V.

    1976-01-01

    In this paper the external field of a bounded source emitting gravitational radiation is considered. A successive approximation method is used to integrate the Einstein equations in Bondi's coordinates (Bondi et al, Proc. R. Soc.; A269:21 (1962)). A method of separation of angular variables is worked out and the approximate Einstein equations are reduced to key equations. The losses of mass, momentum, and angular momentum due to gravitational multipole radiation are found. It is demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In an appendix Bondi's new function is given in terms of sources. (author)

  12. Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

    KAUST Repository

    Younis, Mohammad I.

    2014-08-17

    We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

  13. Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion

    Science.gov (United States)

    Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi

    2011-01-01

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…

  14. Solving Simple Kinetics without Integrals

    Science.gov (United States)

    de la Pen~a, Lisandro Herna´ndez

    2016-01-01

    The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

  15. Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

    Directory of Open Access Journals (Sweden)

    Berenguer MI

    2010-01-01

    Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .

  16. Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

    Directory of Open Access Journals (Sweden)

    Daniel Olvera

    2014-01-01

    Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

  17. Physical Applications of a Simple Approximation of Bessel Functions of Integer Order

    Science.gov (United States)

    Barsan, V.; Cojocaru, S.

    2007-01-01

    Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

  18. Quantum theory of atom-surface scattering: exact solutions and evaluation of approximations

    International Nuclear Information System (INIS)

    Chiroli, C.; Levi, A.C.

    1976-01-01

    In a recent article a hard corrugated surface was proposed as a simple model for atom-surface scattering. The problem was not solved exactly, however, but several alternative approximations were considered. Since these three similar, but inequivalent, approximations were proposed, the problem arose to evaluate these approximations in order to choose between them. In the present letter some exact calculations are presented which make this choice rationally possible. (Auth.)

  19. The Pathwise Numerical Approximation of Stationary Solutions of Semilinear Stochastic Evolution Equations

    International Nuclear Information System (INIS)

    Caraballo, T.; Kloeden, P.E.

    2006-01-01

    Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions. A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations. Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions

  20. Approximating the physical inner product of loop quantum cosmology

    International Nuclear Information System (INIS)

    Bahr, Benjamin; Thiemann, Thomas

    2007-01-01

    In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity

  1. Accuracy analysis of automodel solutions for Lévy flight-based transport: from resonance radiative transfer to a simple general model

    Science.gov (United States)

    Kukushkin, A. B.; Sdvizhenskii, P. A.

    2017-12-01

    The results of accuracy analysis of automodel solutions for Lévy flight-based transport on a uniform background are presented. These approximate solutions have been obtained for Green’s function of the following equations: the non-stationary Biberman-Holstein equation for three-dimensional (3D) radiative transfer in plasma and gases, for various (Doppler, Lorentz, Voigt and Holtsmark) spectral line shapes, and the 1D transport equation with a simple longtailed step-length probability distribution function with various power-law exponents. The results suggest the possibility of substantial extension of the developed method of automodel solution to other fields far beyond physics.

  2. Loglinear Approximate Solutions to Real-Business-Cycle Models: Some Observations

    Science.gov (United States)

    Lau, Sau-Him Paul; Ng, Philip Hoi-Tak

    2007-01-01

    Following the analytical approach suggested in Campbell, the authors consider a baseline real-business-cycle (RBC) model with endogenous labor supply. They observe that the coefficients in the loglinear approximation of the dynamic equations characterizing the equilibrium are related to the fundamental parameters in a relatively simple manner.…

  3. Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

    International Nuclear Information System (INIS)

    Basak, K C; Ray, P C; Bera, R K

    2009-01-01

    The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

  4. Determinant formula for solutions of the Garnier system and Padé approximation

    International Nuclear Information System (INIS)

    Mano, Toshiyuki

    2012-01-01

    It is known that a class of special solutions of the Garnier system is expressed by a determinant formula in terms of a certain specialization of the Schur functions with rectangular-shape partitions. Y Yamada showed that such a determinant formula for rational solutions of Riccati type can be derived by making use of the Padé approximation. In this paper, we extend Yamada’s method. We derive a determinant formula for transcendental solutions of Riccati type by showing that the Padé approximation can be utilized in order to construct a Schlesinger transformation between isomonodromic deformations. In addition, we show that this method is effective in generic solutions of the Garnier system and derive a determinant structure of them. (paper)

  5. Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

    Directory of Open Access Journals (Sweden)

    Xiao-Ying Qin

    2014-01-01

    Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

  6. Trigonometric solutions of triangle equations. Simple Lie superalgebras

    International Nuclear Information System (INIS)

    Bazhanov, V.V.; Shadrikov, A.G.

    1988-01-01

    Trigonometric solutions of the graded triangle equation are constructed for the fundamental representations of all simple (nonexceptional) Lie superalgebras with nondegenerate metric. In Sec. 1, we introduce the concept of Z 2 graded spaces and give the basic definitions. In Sec. 2, we determine fundamental representations of the Lie superalgebras sl(mn) and osp(2rs) and give explicit realizations of the Coxeter automorphisms. In secs. 3 and 4, we give the trigonometric solutions of the graded triangle equation (quantum R matrices)

  7. Approximate solutions of some problems of scattering of surface ...

    Indian Academy of Sciences (India)

    A Choudhary

    Abstract. A class of mixed boundary value problems (bvps), occurring in the study of scattering of surface water waves by thin vertical rigid barriers placed in water of finite depth, is examined for their approximate solutions. Two different placings of vertical barriers are analyzed, namely, (i) a partially immersed barrier and.

  8. Approximate expressions for the period of a simple pendulum using a Taylor series expansion

    International Nuclear Information System (INIS)

    Belendez, Augusto; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi; Arribas, Enrique

    2011-01-01

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be performed which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the Kidd-Fogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.

  9. Approximate expressions for the period of a simple pendulum using a Taylor series expansion

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, Augusto; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Arribas, Enrique, E-mail: a.belendez@ua.es [Departamento de Fisica Aplicada, Escuela Superior de IngenierIa Informatica, Universidad de Castilla-La Mancha, Avda de Espana, s/n, E-02071 Albacete (Spain)

    2011-09-15

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be performed which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the Kidd-Fogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.

  10. Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

    Science.gov (United States)

    Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.

    1987-01-01

    The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

  11. A Simple Solution to Type Specialization

    DEFF Research Database (Denmark)

    Danvy, Olivier

    1998-01-01

    Partial evaluation specializes terms, but traditionally this specialization does not apply to the type of these terms. As a result, specializing, e.g., an interpreter written in a typed language, which requires a “universal” type to encode expressible values, yields residual programs with type tags...... all over. Neil Jones has stated that getting rid of these type tags was an open problem, despite possible solutions such as Torben Mogensen's “constructor specialization.” To solve this problem, John Hughes has proposed a new paradigm for partial evaluation, “Type Specialization”, based on type...... inference instead of being based on symbolic interpretation. Type Specialization is very elegant in principle but it also appears non-trivial in practice. Stating the problem in terms of types instead of in terms of type encodings suggests a very simple type-directed solution, namely, to use a projection...

  12. Approximate Solution of LR Fuzzy Sylvester Matrix Equations

    Directory of Open Access Journals (Sweden)

    Xiaobin Guo

    2013-01-01

    Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

  13. Approximate solution to the Kolmogorov equation for a fission chain-reacting system

    International Nuclear Information System (INIS)

    Ruby, L.; McSwine, T.L.

    1986-01-01

    An approximate solution has been obtained for the Kolmogorov equation describing a fission chain-reacting system. The method considers the population of neutrons, delayed-neutron precursors, and detector counts. The effect of the detector is separated from the statistics of the chain reaction by a weak coupling assumption that predicts that the detector responds to the average rather than to the instantaneous neutron population. An approximate solution to the remaining equation, involving the populations of neutrons and precursors, predicts a negative-binomial behaviour for the neutron probability distribution

  14. Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

    Directory of Open Access Journals (Sweden)

    Yaobing Zhao

    2014-01-01

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

  15. The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

    Science.gov (United States)

    Gai, Litao; Bilige, Sudao; Jie, Yingmo

    2016-01-01

    In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

  16. Higher-Order Approximation of Cubic-Quintic Duffing Model

    DEFF Research Database (Denmark)

    Ganji, S. S.; Barari, Amin; Babazadeh, H.

    2011-01-01

    We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations...

  17. Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

    Science.gov (United States)

    Finster, Felix; Smoller, Joel

    2010-09-01

    A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.

  18. Enhancement accuracy of approximated solutions of the nonlinear singular integral equations of Chew-Low type

    International Nuclear Information System (INIS)

    Zhidkov, E.P.; Nguen Mong; Khoromskij, B.N.

    1979-01-01

    The ways of enhancement of the accuracy of approximate solutions of the Chew-Low type equation are considered. Difference schemes are proposed which allow one to obtain solution expansion in degrees of lattice step. On the basis of the expansion by the Richardson method the refinement of approximated solutions is made. Besides, the iteration process is constructed which reduces immediately to the solution of enhanced accuracy. The efficiency of the methods proposed is illustrated by numerical examples

  19. Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods

    International Nuclear Information System (INIS)

    Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T

    2008-01-01

    A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient

  20. Numerical solution of the ekpyrotic scenario in the moduli space approximation

    International Nuclear Information System (INIS)

    Soerensen, Torquil MacDonald

    2005-01-01

    A numerical solution to the equations of motion for the ekpyrotic bulk brane scenario in the moduli space approximation is presented. The visible universe brane has positive tension, and we use a potential that goes to zero exponentially at large distance, and also goes to zero at small distance. In the case considered, no bulk brane, visible brane collision occurs in the solution. This property and the general behavior of the solution is qualitatively the same when the visible brane tension is negative, and for many different parameter choices

  1. Approximate Solution of Dam-break Flow of Low Viscosity Bingham Fluid

    Science.gov (United States)

    Puay, How Tion; Hosoda, Takashi

    In this study, we investigate the characteristics of dam-break flow of low viscosity Bingham fluid by deriving an approximate solution for the time development of the front position and depth at the origin of the flow. The asymptotic solutions representing the characteristic of Bingham fluid in the limit of low plastic viscosity are verified with a depth-averaged numerical model. Numerical simulations showed that with the decrease of plastic viscosity, the time development of the front position and depth at the origin approach to the theoretical asymptotic solution.

  2. About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

    International Nuclear Information System (INIS)

    Dubrovsky, V. G.; Topovsky, A. V.

    2013-01-01

    New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

  3. A simple approximative procedure for taking into account low cycle fatigue loads

    Energy Technology Data Exchange (ETDEWEB)

    Larsen, G; Thomsen, K

    1996-09-01

    In this paper a simple approximative algorithm for taking into account low cycle fatigue loads is presented. Traditionally, the fatigue life consumption of a wind turbine is estimated by considering a number of (independent) load cases and performing a rainflow counting analysis on each of those. These results are then subsequently synthesized into a total load spectrum by performing a weighed sum of the number of individual load case ranges. The fatigue life consumption is thus obtained by applying the Palmgren-Miner rule on the total load spectrum. However, due to the assumption of isolated basic load cases, the above procedure fail to represent the low-frequency contributions related to the transition between those load cases. The procedure to be described in the following aims at taking the fatigue contribution, related to the transitions between the defined load cases, into account in an approximative manner. (au)

  4. Approximate solution to neutron transport equation with linear anisotropic scattering

    International Nuclear Information System (INIS)

    Coppa, G.; Ravetto, P.; Sumini, M.

    1983-01-01

    A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)

  5. A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mazhar Iqbal

    2014-01-01

    Full Text Available Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.

  6. An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method

    International Nuclear Information System (INIS)

    Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.

    2009-01-01

    The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.

  7. Approximate solution of the Saha equation - temperature as an explicit function of particle densities

    International Nuclear Information System (INIS)

    Sato, M.

    1991-01-01

    The Saha equation for a plasma in thermodynamic equilibrium (TE) is approximately solved to give the temperature as an explicit function of population densities. It is shown that the derived expressions for the Saha temperature are valid approximations to the exact solution. An application of the approximate temperature to the calculation of TE plasma parameters is also described. (orig.)

  8. Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Palacios, Sergio L.

    2004-01-01

    We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

  9. About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

    Energy Technology Data Exchange (ETDEWEB)

    Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

    2013-03-15

    New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

  10. Approximate solution of the transport equation by methods of Galerkin type

    International Nuclear Information System (INIS)

    Pitkaranta, J.

    1977-01-01

    Questions of the existence, uniqueness, and convergence of approximate solutions of transport equations by methods of the Galerkin type (where trial and weighting functions are the same) are discussed. The results presented do not exclude the infinite-dimensional case. Two strategies can be followed in the variational approximation of the transport operator: one proceeds from the original form of the transport equation, while the other is based on the partially symmetrized equation. Both principles are discussed in this paper. The transport equation is assumed in a discretized multigroup form

  11. On Approximate Solutions of Functional Equations in Vector Lattices

    Directory of Open Access Journals (Sweden)

    Bogdan Batko

    2014-01-01

    Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.

  12. Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

    Science.gov (United States)

    Ito, Kazufumi

    1987-01-01

    The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

  13. Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method

    Directory of Open Access Journals (Sweden)

    S. Das

    2013-12-01

    Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.

  14. A Simple General Solution for Maximal Horizontal Range of Projectile Motion

    OpenAIRE

    Busic, Boris

    2005-01-01

    A convenient change of variables in the problem of maximizing the horizontal range of the projectile motion, with an arbitrary initial vertical position of the projectile, provides a simple, straightforward solution.

  15. New family of simple solutions of relativistic perfect fluid hydrodynamics

    International Nuclear Information System (INIS)

    Csoergo, T.; Nagy, M.I.; Csanad, M.

    2008-01-01

    A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is found-more than 50 years after the previous similar result, the Landau-Khalatnikov solution. Surprisingly, the new solutions have a simple form, that generalizes the renowned, but accelerationless, Hwa-Bjorken solution. These new solutions take into account the work done by the fluid elements on each other, and work not only in one temporal and one spatial dimensions, but also in arbitrary number of spatial dimensions. They are applied here for an advanced estimation of initial energy density and life-time of the reaction in ultra-relativistic heavy ion collisions. New formulas are also conjectured, that yield further important increase of the initial energy density estimate and the measured life-time of the reaction if the value of the speed of sound is in the realistic range

  16. Structural stability of solutions to the Riemann problem for a non-strictly hyperbolic system with flux approximation

    Directory of Open Access Journals (Sweden)

    Meina Sun

    2016-05-01

    Full Text Available We study the Riemann problem for a non-strictly hyperbolic system of conservation laws under the linear approximations of flux functions with three parameters. The approximated system also belongs to the type of triangular systems of conservation laws and this approximation does not change the structure of Riemann solutions to the original system. Furthermore, it is proven that the Riemann solutions to the approximated system converge to the corresponding ones to the original system as the perturbation parameter tends to zero.

  17. Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method

    Energy Technology Data Exchange (ETDEWEB)

    Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)

    2010-04-15

    Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)

  18. Some approximating formulae to the solution of an abstract evolution problem

    International Nuclear Information System (INIS)

    Ngongo, M.E.

    1991-12-01

    We consider discrete semigroups of operators associated with the first two primary sub-families of A-acceptable Norsett's rational approximations to e q , S 1 (γ;q) and S 2 (γ;q) with q is an element of C and γ a real parameter, and construct approximating formulae to the solution of an abstract evolution problem. The study of convergence is reduced to exploiting previous fundamental results of the author for this class of semigroups and this results, for associated numerical schemes, in a convergence independent of the regularity of the data of the problem. (author). 17 refs, 3 tabs

  19. Approximation properties of haplotype tagging

    Directory of Open Access Journals (Sweden)

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  20. Solution of two-dimensional equations of neutron transport in 4P0-approximation of spherical harmonics method

    International Nuclear Information System (INIS)

    Polivanskij, V.P.

    1989-01-01

    The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs

  1. Exact and approximate solutions for the decades-old Michaelis-Menten equation: Progress-curve analysis through integrated rate equations.

    Science.gov (United States)

    Goličnik, Marko

    2011-01-01

    The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.

  2. Approximate solutions of dual fuzzy polynomials by feed-back neural networks

    Directory of Open Access Journals (Sweden)

    Ahmad Jafarian

    2012-11-01

    Full Text Available Recently, artificial neural networks (ANNs have been extensively studied and used in different areas such as pattern recognition, associative memory, combinatorial optimization, etc. In this paper, we investigate the ability of fuzzy neural networks to approximate solution of a dual fuzzy polynomial of the form $a_{1}x+ ...+a_{n}x^n =b_{1}x+ ...+b_{n}x^n+d,$ where $a_{j},b_{j},d epsilon E^1 (for j=1,...,n.$ Since the operation of fuzzy neural networks is based on Zadeh's extension principle. For this scope we train a fuzzified neural network by back-propagation-type learning algorithm which has five layer where connection weights are crisp numbers. This neural network can get a crisp input signal and then calculates its corresponding fuzzy output. Presented method can give a real approximate solution for given polynomial by using a cost function which is defined for the level sets of fuzzy output and target output. The simulation results are presented to demonstrate the efficiency and effectiveness of the proposed approach.

  3. Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

    International Nuclear Information System (INIS)

    Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

    2009-01-01

    A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

  4. Asymptotic shape of solutions to the perturbed simple pendulum problems

    Directory of Open Access Journals (Sweden)

    Tetsutaro Shibata

    2007-05-01

    Full Text Available We consider the positive solution of the perturbed simple pendulum problem $$ u''(r + frac{N-1}{r}u'(r - g(u(t + lambda sin u(r = 0, $$ with $0 < r < R$, $ u'(0 = u(R = 0$. To understand well the shape of the solution $u_lambda$ when $lambda gg 1$, we establish the leading and second terms of $Vert u_lambdaVert_q$ ($1 le q < infty$ with the estimate of third term as $lambda o infty$. We also obtain the asymptotic formula for $u_lambda'(R$ as $lambda o infty$.

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

    Directory of Open Access Journals (Sweden)

    Shaheed N. Huseen

    2013-01-01

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

  6. Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

    Science.gov (United States)

    Johnson, Marcus; Kamalapurkar, Rushikesh; Bhasin, Shubhendu; Dixon, Warren E

    2015-08-01

    An approximate online equilibrium solution is developed for an N -player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics. A Lyapunov-based stability analysis shows that uniformly ultimately bounded tracking is achieved, and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions. The actor, critic, and identifier structures are implemented in real time continuously and simultaneously. Simulations on two and three player games illustrate the performance of the developed method.

  7. Approximate solutions: ramps and periodic variations. Chapter 5

    International Nuclear Information System (INIS)

    1998-01-01

    The aim of reactor regulation is generally to maintain reactor power at the demand power, or to vary it slowly to attain a new demand power. On the other hand, the purpose of reactor shutdown systems (SDS) is to insert rapidly, on actuation, a large negative reactivity in order to minimize an overpower, or limit the energy released during a transient, so that fuel failure is improbable. Control mechanisms are therefore characterized by: their reactivity worth (mk), which must exceed the reactivity effect which the mechanism is designed to compensate; and their insertion rate (mk/s), which must be at least as fast as the effect to be controlled. Table 5.1 gives a summary of the various control mechanisms in a CANDU 6 reactor. The reactivity worth shown for each mechanism is the static reactivity change associated with full movement of the device. In reality, the dynamic reactivity will vary in a continuous manner, not suddenly, as assumed in the previous chapter. The realistic simulation of a reactivity insertion in the reactor must then take into account the rate of insertion of reactivity, which is governed by the insertion speed of the mechanism. We have seen in the previous chapter that it is possible to solved analytically the point-kinetics equations for constant reactivity. We could generalize these solutions to step-wise reactivity variations by linking together the analytic solutions to for a sequence of step changes. This approach is not necessarily the best from a numerical point of view. By introducing one or more simplifying assumptions, it will be possible to obtain an analytical solution of arbitrary variations in reactivity or in the external source. These assumptions will undoubtedly limit the applicability of the results, but the approximate solutions obtained will allow us to describe the reactor behaviour analytically. (author)

  8. Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

    International Nuclear Information System (INIS)

    Chen Changyuan; Sun Dongsheng; Lu Falin

    2007-01-01

    Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

  9. Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

    Science.gov (United States)

    Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

    2018-03-01

    In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

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

    Science.gov (United States)

    Singh, Brajesh K; Srivastava, Vineet K

    2015-04-01

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

  11. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2016-01-01

    Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

  12. Application of simple approximate system analysis methods for reliability and availability improvement of reactor WWER-1000

    International Nuclear Information System (INIS)

    Manchev, B.; Marinova, B.; Nenkova, B.

    2001-01-01

    The method described on this report provides a set of simple, easily understood 'approximate' models applicable to a large class of system architectures. Constructing a Markov model of each redundant subsystem and its replacement after that by a pseudo-component develops the approximation models. Of equal importance, the models can be easily understood even of non-experts, including managers, high-level decision-makers and unsophisticated consumers. A necessary requirement for their application is the systems to be repairable and the mean time to repair to be much smaller than the mean time to failure. This ia a case most often met in the real practice. Results of the 'approximate' model application on a technological system of Kozloduy NPP are also presented. The results obtained can be compared quite favorably with the results obtained by using SAPHIRE software

  13. Approximate analytic theory of the multijunction grill

    International Nuclear Information System (INIS)

    Hurtak, O.; Preinhaelter, J.

    1991-03-01

    An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs

  14. Analysis of a Cartesian PML approximation to acoustic scattering problems in and

    KAUST Repository

    Bramble, James H.

    2013-08-01

    We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.

  15. Fall with linear drag and Wien's displacement law: approximate solution and Lambert function

    International Nuclear Information System (INIS)

    Vial, Alexandre

    2012-01-01

    We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms. (paper)

  16. Polarographic behaviour and determination of selenite and tellurite in simple solutions or in a binary mixture

    International Nuclear Information System (INIS)

    Hassan, A.

    1991-01-01

    The polarographic behaviour of simple solutions of selenite and tellurite in 1 M ammonium salts of formate, acetate, tartrate, oxalate, and benzoate solutions in absence and in presence of Triton X-100 as a maximum suppressor and a temperature of 25 O C has been investigated. Schemes for the mechanism of reductions occuring at the DME have been deduced. A method for analytical determination of selenite and tellurite in simple solutions as well as in a binary mixture in the presence of 4-14 . 10 -3 % Triton X-100 is reported. (author)

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

    KAUST Repository

    Domínguez, Luis F.

    2012-06-25

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

  18. Approximate and analytical solutions for solute transport from an injection well into a single fracture

    International Nuclear Information System (INIS)

    Chen, C.S.; Yates, S.R.

    1989-01-01

    In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. It has been reported that by treating the radioactive decay constant as the appropriate first-order rate constant, these solutions can also be used to study injection problems of a similar nature subject to first-order chemical or biological reactions. The fracture is idealized by a pair of parallel, smooth plates separated by an aperture of constant thickness. Groundwater was assumed to be immobile in the underlying and overlying porous formations due to their low permeabilities. However, the injected radionuclides were able to move from the fracture into the porous matrix by molecular diffusion (the matrix diffusion) due to possible concentration gradients across the interface between the fracture and the porous matrix. Calculation of the transient solutions is not straightforward, and the paper documents a contained Fortran program, which computes the Stehfest inversion, the Airy functions, and gives the concentration distributions in the fracture as well as in the porous matrix for both transient and steady-state cases

  19. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  20. Application of the probabilistic approximate analysis method to a turbopump blade analysis. [for Space Shuttle Main Engine

    Science.gov (United States)

    Thacker, B. H.; Mcclung, R. C.; Millwater, H. R.

    1990-01-01

    An eigenvalue analysis of a typical space propulsion system turbopump blade is presented using an approximate probabilistic analysis methodology. The methodology was developed originally to investigate the feasibility of computing probabilistic structural response using closed-form approximate models. This paper extends the methodology to structures for which simple closed-form solutions do not exist. The finite element method will be used for this demonstration, but the concepts apply to any numerical method. The results agree with detailed analysis results and indicate the usefulness of using a probabilistic approximate analysis in determining efficient solution strategies.

  1. Approximate solutions for the two-dimensional integral transport equation. Solution of complex two-dimensional transport problems

    International Nuclear Information System (INIS)

    Sanchez, Richard.

    1980-11-01

    This work is divided into two parts: the first part deals with the solution of complex two-dimensional transport problems, the second one (note CEA-N-2166) treats the critically mixed methods of resolution. A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the interface current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding, and water, or homogenized structural material. The cells are divided into zones that are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is effected by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: CALLIOPE uses a cylindrical cell model and one or three terms for the flux expansion, and NAUSICAA uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes, one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark problems and by calculations performed in the APOLLO multigroup code [fr

  2. NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics

    CERN Document Server

    Goldstein, M; Haussmann, W; Hayman, W; Rogge, L

    1992-01-01

    This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In ...

  3. Solution of multigroup diffusion equations in cylindrical configuration by local polynomial approximation

    International Nuclear Information System (INIS)

    Jakab, J.

    1979-05-01

    Local approximations of neutron flux density by 2nd degree polynomials are used in calculating light water reactors. The calculations include spatial kinetics tasks for the models of two- and three-dimensional reactors in the Cartesian geometry. The resulting linear algebraic equations are considered to be formally identical to the results of the differential method of diffusion equation solution. (H.S.)

  4. The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

    Science.gov (United States)

    Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

    2018-04-01

    We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

  5. Approximation of the Doppler broadening function by Frobenius method

    International Nuclear Information System (INIS)

    Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C.

    2005-01-01

    An analytical approximation of the Doppler broadening function ψ(x,ξ) is proposed. This approximation is based on the solution of the differential equation for ψ(x,ξ) using the methods of Frobenius and the parameters variation. The analytical form derived for ψ(x,ξ) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)

  6. Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

    Science.gov (United States)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2012-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.

  7. A Simple Harmonic Universe

    Energy Technology Data Exchange (ETDEWEB)

    Graham, Peter W.; /Stanford U., ITP; Horn, Bart; Kachru, Shamit; /Stanford U., ITP /SLAC; Rajendran, Surjeet; /Johns Hopkins U. /Stanford U., ITP; Torroba, Gonzalo; /Stanford U., ITP /SLAC

    2011-12-14

    We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k = +1, and are supported by a negative cosmological term and matter with -1 < w < -1 = 3. In the case of moderate bounces (where the ratio of the maximal scale factor a{sub +} to the minimal scale factor a{sub -} is {Omicron}(1)), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a{sub +} = a{sub -}, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.

  8. Magnetic analysis of tokamak plasma with approximate MHD equilibrium solution

    International Nuclear Information System (INIS)

    Moriyama, Shin-ichi; Hiraki, Naoji

    1993-01-01

    A magnetic analysis method for determining equilibrium configuration parameters (plasma shape, poloidal beta and internal inductance) on a non-circular tokamak is described. The feature is to utilize an approximate MHD equilibrium solution which explicitly relates the configuration parameters with the magnetic fields picked up by magnetic sensors. So this method is suitable for the real-time analysis performed during a tokamak discharge. A least-squares fitting procedure is added to the analytical algorithm in order to reduce the errors in the magnetic analysis. The validity is investigated through the numerical calculation for a tokamak equilibrium model. (author)

  9. A Simple Model for Nonlinear Confocal Ultrasonic Beams

    Science.gov (United States)

    Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

    2007-01-01

    A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

  10. Anion bridges drive salting out of a simple amphiphile from aqueous solution

    International Nuclear Information System (INIS)

    Bowron, D.T.; Finney, J.L.

    2002-01-01

    Neutron diffraction with isotope substitution has been used to determine the structural changes that occur on the addition of a simple salting-out agent to a dilute aqueous alcohol solution. The striking results obtained demonstrate a relatively simple process occurs in which interamphiphile anionic salt bridges are formed between the polar groups of the alcohol molecules. These ion bridges drive an increase in the exposure of the alcohol molecule nonpolar surface to the solvent water and hence point the way to their eventual salting out by the hydrophobic effect

  11. A Closed-Form Approximation Solution for an Inventory Model with Supply Disruptions and Non-ZIO Reorder Policy

    Directory of Open Access Journals (Sweden)

    David Heimann

    2007-08-01

    Full Text Available In supply chains, domestic and global, a producer must decide on an optimal quantity of items to order from suppliers and at what inventory level to place this order (the EOQ problem. We discuss how to modify the EOQ in the face of failures and recoveries by the supplier. This is the EOQ with disruption problem (EOQD. The supplier makes transitions between being capable and not being capable of filling an order in a Markov failure and recovery process. The producer adjusts the reorder point and the inventories to provide a margin of safety. Numerical solutions to the EOQD problem have been developed. In addition, a closed-form approximate solution has been developed for the zero inventory option (ZIO, where the inventory level on reordering is set to be zero. This paper develops a closed-form approximate solution for the EOQD problem when the reorder point can be non-zero, obtaining for that situation an optimal reorder quantity and optimal reorder point that represents an improvement on the optimal ZIO solution. The paper also supplies numerical examples demonstrating the cost savings against the ZIO situation, as well as the accuracy of the approximation technique.

  12. Simple Machines Forum, a Solution for Dialogue Optimization between Physicians

    Directory of Open Access Journals (Sweden)

    Laura SÎNGIORZAN

    2013-02-01

    Full Text Available We developed an instrument which can ensure a quick and easy dialogue between the physicians of the Oncology Institute and family physicians. The platform we chose was Simple Machines Forum (abbreviated as SMF, a free Internet forum (BBS - Bulletin Board System application. The purpose of this article is not to detail the software platform, but to emphasize the facilities and advantages of using this solution in the medical community.

  13. Using trees to compute approximate solutions to ordinary differential equations exactly

    Science.gov (United States)

    Grossman, Robert

    1991-01-01

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

  14. Novel surgical performance evaluation approximates Standardized Incidence Ratio with high accuracy at simple means.

    Science.gov (United States)

    Gabbay, Itay E; Gabbay, Uri

    2013-01-01

    Excess adverse events may be attributable to poor surgical performance but also to case-mix, which is controlled through the Standardized Incidence Ratio (SIR). SIR calculations can be complicated, resource consuming, and unfeasible in some settings. This article suggests a novel method for SIR approximation. In order to evaluate a potential SIR surrogate measure we predefined acceptance criteria. We developed a new measure - Approximate Risk Index (ARI). "Number Needed for Event" (NNE) is the theoretical number of patients needed "to produce" one adverse event. ARI is defined as the quotient of the group of patients needed for no observed events Ge by total patients treated Ga. Our evaluation compared 2500 surgical units and over 3 million heterogeneous risk surgical patients that were induced through a computerized simulation. Surgical unit's data were computed for SIR and ARI to evaluate compliance with the predefined criteria. Approximation was evaluated by correlation analysis and performance prediction capability by Receiver Operating Characteristics (ROC) analysis. ARI strongly correlates with SIR (r(2) = 0.87, p 0.9) 87% sensitivity and 91% specificity. ARI provides good approximation of SIR and excellent prediction capability. ARI is simple and cost-effective as it requires thorough risk evaluation of only the adverse events patients. ARI can provide a crucial screening and performance evaluation quality control tool. The ARI method may suit other clinical and epidemiological settings where relatively small fraction of the entire population is affected. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.

  15. Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

    Science.gov (United States)

    Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

    2002-01-01

    Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

  16. Simple solution-processed titanium oxide electron transport layer for efficient inverted polymer solar cells

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Liang [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Shen, Wenfei [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); Institute of Hybrid Materials, Laboratory of New Fiber Materials and Modern Textile—The Growing Base for State Key Laboratory, Qingdao University, Qingdao 266071 (China); Chen, Weichao [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); Bao, Xichang, E-mail: baoxc@qibebt.ac.cn [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); Wang, Ning; Dou, Xiaowei; Han, Liangliang; Wen, Shuguang [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China)

    2014-12-31

    Titanium oxide (TiO{sub X}) is an effective electron transport layer (ETL) in polymer solar cells (PSCs). We report efficient inverted PSCs with a simple solution-processed amorphous TiO{sub X} (s-TiO{sub X}) film as an ETL. The s-TiO{sub X} film with high light transmittance was prepared by spin-coating titanium (IV) isopropoxide isopropanol solution on indium tin oxide coated glass in inert and then placed in air under room temperature for 60 min. The introduction of s-TiO{sub X} ETL greatly improved the short circuit current density of the devices. PSCs based on poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester and poly(4,8-bis-alkyloxy-benzo[1,2-b:4,5-b′]dithiophene-alt-alkylcarbonyl -thieno[3,4-b]thiophene):[6,6]-phenyl- C71-butyric acid methyl ester using s-TiO{sub X} film as ETL shows high power conversion efficiency of 4.29% and 6.7% under the illumination of AM 1.5G, 100 mW/cm{sup 2}, which shows enhancements compared to the conventional PSCs with poly(styrenesulfonate)-doped poly(ethylenedioxythiophene) as anode buffer layer. In addition, the device exhibits good stability in a humid ambient atmosphere without capsulation. The results indicate that the annealing-free, simple solution processed s-TiO{sub X} film is an efficient ETL for high-performance PSCs. - Highlights: • High quality s-TiO{sub X} films were prepared by a simple, solution method without thermal treatment. • The s-TiO{sub X} films with high transmittance are very smooth. • The organic photovoltaic performance with s-TiO{sub X} film improved greatly and exhibited good stability. • The annealing-free, simple prepared s-TiO{sub X} film will be much compatible with flexible substrates.

  17. High energy approximations in quantum field theory

    International Nuclear Information System (INIS)

    Orzalesi, C.A.

    1975-01-01

    New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt

  18. The triangular density to approximate the normal density: decision rules-of-thumb

    International Nuclear Information System (INIS)

    Scherer, William T.; Pomroy, Thomas A.; Fuller, Douglas N.

    2003-01-01

    In this paper we explore the approximation of the normal density function with the triangular density function, a density function that has extensive use in risk analysis. Such an approximation generates a simple piecewise-linear density function and a piecewise-quadratic distribution function that can be easily manipulated mathematically and that produces surprisingly accurate performance under many instances. This mathematical tractability proves useful when it enables closed-form solutions not otherwise possible, as with problems involving the embedded use of the normal density. For benchmarking purposes we compare the basic triangular approximation with two flared triangular distributions and with two simple uniform approximations; however, throughout the paper our focus is on using the triangular density to approximate the normal for reasons of parsimony. We also investigate the logical extensions of using a non-symmetric triangular density to approximate a lognormal density. Several issues associated with using a triangular density as a substitute for the normal and lognormal densities are discussed, and we explore the resulting numerical approximation errors for the normal case. Finally, we present several examples that highlight simple decision rules-of-thumb that the use of the approximation generates. Such rules-of-thumb, which are useful in risk and reliability analysis and general business analysis, can be difficult or impossible to extract without the use of approximations. These examples include uses of the approximation in generating random deviates, uses in mixture models for risk analysis, and an illustrative decision analysis problem. It is our belief that this exploratory look at the triangular approximation to the normal will provoke other practitioners to explore its possible use in various domains and applications

  19. Accuracy of approximations of solutions to Fredholm equations by kernel methods

    Czech Academy of Sciences Publication Activity Database

    Gnecco, G.; Kůrková, Věra; Sanguineti, M.

    2012-01-01

    Roč. 218, č. 14 (2012), s. 7481-7497 ISSN 0096-3003 R&D Projects: GA ČR GAP202/11/1368; GA MŠk OC10047 Grant - others:CNR-AV ČR(CZ-IT) Project 2010–2012 “Complexity of Neural -Network and Kernel Computational Models Institutional research plan: CEZ:AV0Z10300504 Keywords : approximate solutions to integral equations * radial and kernel-based networks * Gaussian kernels * model complexity * analysis of algorithms Subject RIV: IN - Informatics, Computer Science Impact factor: 1.349, year: 2012

  20. Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

    Science.gov (United States)

    Cummings, Patrick

    We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

  1. Modeling Rocket Flight in the Low-Friction Approximation

    Directory of Open Access Journals (Sweden)

    Logan White

    2014-09-01

    Full Text Available In a realistic model for rocket dynamics, in the presence of atmospheric drag and altitude-dependent gravity, the exact kinematic equation cannot be integrated in closed form; even when neglecting friction, the exact solution is a combination of elliptic functions of Jacobi type, which are not easy to use in a computational sense. This project provides a precise analysis of the various terms in the full equation (such as gravity, drag, and exhaust momentum, and the numerical ranges for which various approximations are accurate to within 1%. The analysis leads to optimal approximations expressed through elementary functions, which can be implemented for efficient flight prediction on simple computational devices, such as smartphone applications.

  2. Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

    Directory of Open Access Journals (Sweden)

    De-Gang Wang

    2012-01-01

    Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

  3. An approximate stationary solution for multi-allele neutral diffusion with low mutation rates.

    Science.gov (United States)

    Burden, Conrad J; Tang, Yurong

    2016-12-01

    We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K-1)(K-2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra. Copyright © 2016 Elsevier Inc. All rights reserved.

  4. Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

    OpenAIRE

    Theinchai, Ratchata; Chankan, Siriwan; Yukunthorn, Weera

    2016-01-01

    We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

  5. Zeolites as alcohol adsorbents from aqueous solutions

    Directory of Open Access Journals (Sweden)

    Cekova Blagica

    2006-01-01

    Full Text Available The potential usage of zeolites as adsorbents for the removal of organic molecules from water was investigated in a series of experiments with aqueous solutions of lower alcohols. This could represent a simple solution to the problem of cleaning up industrial wastewater as well as recovering valuable chemicals at relatively low costs. Adsorption isotherms of the Langmuir type were applied, and calculations showed that the amount of propanol adsorbed on silicalite corresponded to approximately 70% of the pore volume. The adsorption process is simple, and recovery of the more concentrated products is easily done by heat treatment and/or at lowered pressures. Adsorption experiments with aqueous acetone showed that silicalite had approximately the same adsorption capacity for acetone as for n-propanol. Heats of adsorption were determined calorimetrically.

  6. Approximate solution of space and time fractional higher order phase field equation

    Science.gov (United States)

    Shamseldeen, S.

    2018-03-01

    This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

  7. Solutions stability of one-dimensional parametric superconducting magnetic levitation model analysis by the first approximation

    International Nuclear Information System (INIS)

    Shvets', D.V.

    2009-01-01

    By the first approximation analyzing stability conditions of unperturbed solution of one-dimensional dynamic model with magnetic interaction between two superconducting rings obtained. The stability region in the frozen magnetic flux parameters space was constructed.

  8. Solutions to the linearized Navier-Stokes equations for channel flow via the WKB approximation

    Science.gov (United States)

    Leonard, Anthony

    2017-11-01

    Progress on determining semi-analytical solutions to the linearized Navier-Stokes equations for incompressible channel flow, laminar and turbulent, is reported. Use of the WKB approximation yields, e.g., solutions to initial-value problem for the inviscid Orr-Sommerfeld equation in terms of the Bessel functions J+ 1 / 3 ,J- 1 / 3 ,J1 , and Y1 and their modified counterparts for any given wave speed c = ω /kx and k⊥ ,(k⊥2 =kx2 +kz2) . Of particular note to be discussed is a sequence i = 1 , 2 , . . . of homogeneous inviscid solutions with complex k⊥ i for each speed c, (0 < c <=Umax), in the downstream direction. These solutions for the velocity component normal to the wall v are localized in the plane parallel to the wall. In addition, for limited range of negative c, (- c * <= c <= 0) , we have found upstream-traveling homogeneous solutions with real k⊥(c) . In both cases the solutions for v serve as a source for corresponding solutions to the inviscid Squire equation for the vorticity component normal to the wall ωy.

  9. Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

    Science.gov (United States)

    Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

    2016-02-01

    The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

  10. Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching

    Directory of Open Access Journals (Sweden)

    Hua Yang

    2012-01-01

    Full Text Available We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs. Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.

  11. Estimating the approximation error when fixing unessential factors in global sensitivity analysis

    Energy Technology Data Exchange (ETDEWEB)

    Sobol' , I.M. [Institute for Mathematical Modelling of the Russian Academy of Sciences, Moscow (Russian Federation); Tarantola, S. [Joint Research Centre of the European Commission, TP361, Institute of the Protection and Security of the Citizen, Via E. Fermi 1, 21020 Ispra (Italy)]. E-mail: stefano.tarantola@jrc.it; Gatelli, D. [Joint Research Centre of the European Commission, TP361, Institute of the Protection and Security of the Citizen, Via E. Fermi 1, 21020 Ispra (Italy)]. E-mail: debora.gatelli@jrc.it; Kucherenko, S.S. [Imperial College London (United Kingdom); Mauntz, W. [Department of Biochemical and Chemical Engineering, Dortmund University (Germany)

    2007-07-15

    One of the major settings of global sensitivity analysis is that of fixing non-influential factors, in order to reduce the dimensionality of a model. However, this is often done without knowing the magnitude of the approximation error being produced. This paper presents a new theorem for the estimation of the average approximation error generated when fixing a group of non-influential factors. A simple function where analytical solutions are available is used to illustrate the theorem. The numerical estimation of small sensitivity indices is discussed.

  12. Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam

    Directory of Open Access Journals (Sweden)

    Ratchata Theinchai

    2016-01-01

    Full Text Available We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM. The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.

  13. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  14. Bessel collocation approach for approximate solutions of Hantavirus infection model

    Directory of Open Access Journals (Sweden)

    Suayip Yuzbasi

    2017-11-01

    Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

  15. Finite element approximation to the even-parity transport equation

    International Nuclear Information System (INIS)

    Lewis, E.E.

    1981-01-01

    This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

  16. Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

    International Nuclear Information System (INIS)

    Yildirim, A.; Gökdoğan, A.; Merdan, M.; Lakshminarayanan, V.

    2012-01-01

    An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge—Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms. (fundamental areas of phenomenology(including applications))

  17. Analytical approximations for wide and narrow resonances

    International Nuclear Information System (INIS)

    Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

    2005-01-01

    This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U 238 were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)

  18. Analytical approximations for wide and narrow resonances

    Energy Technology Data Exchange (ETDEWEB)

    Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br

    2005-07-01

    This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U{sup 238} were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)

  19. Simple analytical approximation for rotationally inelastic rate constants based on the energy corrected sudden scaling law

    International Nuclear Information System (INIS)

    Smith, N.; Pritchard, D.E.

    1981-01-01

    We have recently demonstrated that the energy corrected sudden (ECS) scaling law of De Pristo et al. when conbined with the power law assumption for the basis rates k/sub l/→0proportional[l(l+1)]/sup -g/ can accurately fit a wide body of rotational energy transfer data. We develop a simple and accurate approximation to this fitting law, and in addition mathematically show the connection between it and our earlier proposed energy based law which also has been successful in describing both theoretical and experimental data on rotationally inelastic collisions

  20. Criteria for the reliability of numerical approximations to the solution of fluid flow problems

    International Nuclear Information System (INIS)

    Foias, C.

    1986-01-01

    The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs

  1. On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra

    Energy Technology Data Exchange (ETDEWEB)

    Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)

    2017-10-15

    A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q{sub s}, s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ{sup s} over a proper 2d submanifold are finite and obey the relations q{sub s} Φ{sup s} = 4πn{sub s}h{sub s}, where the h{sub s} > 0 are certain constants (related to dilatonic coupling vectors) and the n{sub s} are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A{sub 1}, A{sub 2}, A{sub 3}, C{sub 2}, G{sub 2} and A{sub 1} + A{sub 1} are presented. (orig.)

  2. The KASY synthesis programme for the approximative solution of the 3-dimensional neutron diffusion equation

    International Nuclear Information System (INIS)

    Buckel, G.; Wouters, R. de; Pilate, S.

    1977-01-01

    The synthesis code KASY for an approximate solution of the three-dimensional neutron diffusion equation is described; the state of the art as well as envisaged program extensions and the application to tasks from the field of reactor designing are dealt with. (RW) [de

  3. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  4. Contribution of the ''simple solutions'' concept to estimate density of actinides concentrated solutions

    International Nuclear Information System (INIS)

    Sorel, C.; Moisy, Ph.; Dinh, B.; Blanc, P.

    2000-01-01

    In order to calculate criticality parameters of nuclear fuel solution systems, number density of nuclides are needed and they are generally estimated from density equations. Most of the relations allowing the calculation of the density of aqueous solutions containing the electrolytes HNO 3 -UO 2 (NO 3 ) 2 -Pu(NO 3 ) 4 , usually called 'nitrate dilution laws' are strictly empirical. They are obtained from a fit of assumed polynomial expressions on experimental density data. Out of their interpolation range, such mathematical expressions show discrepancies between calculated and experimental data appearing in the high concentrations range. In this study, a physico-chemical approach based on the isopiestic mixtures rule is suggested. The behaviour followed by these mixtures was first observed in 1936 by Zdanovskii and expressed as: 'Binary solutions (i.e. one electrolyte in water) having a same water activity are mixed without variation of this water activity value'. With regards to this behaviour, a set of basic thermodynamic expressions has been pointed out by Ryazanov and Vdovenko in 1965 concerning enthalpy, entropy, volume of mixtures, activity and osmotic coefficient of the components. In particular, a very simple relation for the density is obtained from the volume mixture expression depending on only two physico-chemical variables: i) concentration of each component in the mixture and in their respectively binary solutions having the same water activity as the mixture and ii), density of each component respectively in the binary solution having the same water activity as the mixture. Therefore, the calculation needs the knowledge of binary data (water activity, density and concentration) of each component at the same temperature as the mixture. Such experimental data are largely published in the literature and are available for nitric acid and uranyl nitrate. Nevertheless, nitric acid binary data show large discrepancies between the authors and need to be

  5. SPORTS - a simple non-linear thermalhydraulic stability code

    International Nuclear Information System (INIS)

    Chatoorgoon, V.

    1986-01-01

    A simple code, called SPORTS, has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers. (orig.)

  6. Born approximation to a perturbative numerical method for the solution of the Schrodinger equation

    International Nuclear Information System (INIS)

    Adam, Gh.

    1978-05-01

    A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)

  7. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  8. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-01

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  9. A variational solution of transport equation based on spherical geometry

    International Nuclear Information System (INIS)

    Liu Hui; Zhang Ben'ai

    2002-01-01

    A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods

  10. Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

    Directory of Open Access Journals (Sweden)

    Norhasimah Mahiddin

    2014-01-01

    Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

  11. On-the-energy-shell approximation for the heavy ion couple-channels problems

    International Nuclear Information System (INIS)

    Carlson, B.V.; Hussein, M.S.

    Starting with the coupled channels equations describing multiple Coulomb excitations in heavy ion collisions an approximation scheme is developed based on replacing the channel Green's functions by their on-the-energy shell forms, which permits an exact analytic solution for the scattering matrix. The trivially equivalent Coulomb polarization potential valid for strong coupling and small energy loss in the excitation processes is constructed. This potential is seen to have a very simple r-dependence. A simple formula for the sub-barrier elastic scattering cross section is then derived both by using the WRB approximation and by summing the Born series for the T-matrix. Comparison of the two forms for the elastic cross section shows that they give almost identical numerical results in the small coupling limit only. The results are also compared with the predictions of the Alder-Winther theory. (Author) [pt

  12. The quasi-diffusive approximation in transport theory: Local solutions

    International Nuclear Information System (INIS)

    Celaschi, M.; Montagnini, B.

    1995-01-01

    The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

  13. Strong pairing approximation in comparison with the exact solutions to the pairing Hamiltonian

    Directory of Open Access Journals (Sweden)

    Lunyov A.V.

    2016-01-01

    Full Text Available Results of the Strong Pairing Approximation (SPA as a method with the exact particle number conservation are compared with those of the quasiparticle method (QM. It is shown that SPA comes to the same equations as QM for the gap parameter, chemical potential and one- and two-quasiparticle states. Calculations are performed for 14864Gd84 as an example, and compared with the exact solutions to the pairing Hamiltonian.

  14. Fast multigrid solution of the advection problem with closed characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Yavneh, I. [Israel Inst. of Technology, Haifa (Israel); Venner, C.H. [Univ. of Twente, Enschede (Netherlands); Brandt, A. [Weizmann Inst. of Science, Rehovot (Israel)

    1996-12-31

    The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation-ordering and appropriate residual weighting in a simple multigrid V cycle produces an efficient solution process. We also derive upstream finite-difference approximations to the advection operator, whose truncation terms approximate {open_quotes}physical{close_quotes} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity.

  15. Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

    International Nuclear Information System (INIS)

    Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

    2015-01-01

    Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

  16. Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

    DEFF Research Database (Denmark)

    Nielsen, Søren R.K.; Sørensen, John Dalsgaard

    Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before...... passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response....... outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first...

  17. Simple thermodynamic model of the extension of solid solution of Cu-Mo alloys processed by mechanical alloying

    International Nuclear Information System (INIS)

    Aguilar, C.; Guzman, D.; Rojas, P.A.; Ordonez, Stella; Rios, R.

    2011-01-01

    Highlights: → Extension of solid solution in Cu-Mo systems achieved by mechanical alloying. → Simple thermodynamic model to explain extension of solid solution of Mo in Cu. → Model gives results that are consistent with the solubility limit extension reported in other works. - Abstract: The objective of this work is proposing a simple thermodynamic model to explain the increase in the solubility limit of the powders of the Cu-Mo systems or other binary systems processed by mechanical alloying. In the regular solution model, the effects of crystalline defects, such as; dislocations and grain boundary produced during milling were introduced. The model gives results that are consistent with the solubility limit extension reported in other works for the Cu-Cr, Cu-Nb and Cu-Fe systems processed by mechanical alloying.

  18. Approximate solutions to the deep bed filtration problem; Solucoes aproximadas para o problema de deposicao profunda

    Energy Technology Data Exchange (ETDEWEB)

    Silva, Julio M.; Marchesin, Dan [Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil)

    2008-07-01

    The deep bed filtration problem is closely related to secondary oil recovery. In this work we derive explicit solutions to two filtration problems. The filtration function varies non-linearly with the Darcy speed and linearly with the deposition, but very little. The first solution is built by the method of perturbations and although it is only an approximation it is available in multiple symmetries, including the radial geometry used in the field. The main motivation is the validation of numerical methods. The second solution is exact but it is only available in the linear symmetry, i.e., laboratory geometry. We use it to verify the accuracy of the first solution, but it can also be used to simulate the deposition in experiments. (author)

  19. Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

    Science.gov (United States)

    Ford, Neville J.; Connolly, Joseph A.

    2009-07-01

    We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.

  20. Approximate solutions for radial travel time and capture zone in unconfined aquifers.

    Science.gov (United States)

    Zhou, Yangxiao; Haitjema, Henk

    2012-01-01

    Radial time-of-travel (TOT) capture zones have been evaluated for unconfined aquifers with and without recharge. The solutions of travel time for unconfined aquifers are rather complex and have been replaced with much simpler approximate solutions without significant loss of accuracy in most practical cases. The current "volumetric method" for calculating the radius of a TOT capture zone assumes no recharge and a constant aquifer thickness. It was found that for unconfined aquifers without recharge, the volumetric method leads to a smaller and less protective wellhead protection zone when ignoring drawdowns. However, if the saturated thickness near the well is used in the volumetric method a larger more protective TOT capture zone is obtained. The same is true when the volumetric method is used in the presence of recharge. However, for that case it leads to unreasonableness over the prediction of a TOT capture zone of 5 years or more. © 2011, The Author(s). Ground Water © 2011, National Ground Water Association.

  1. Reduced-Contrast Approximations for High-Contrast Multiscale Flow Problems

    KAUST Repository

    Chung, Eric T.; Efendiev, Yalchin

    2010-01-01

    In this paper, we study multiscale methods for high-contrast elliptic problems where the media properties change dramatically. The disparity in the media properties (also referred to as high contrast in the paper) introduces an additional scale that needs to be resolved in multiscale simulations. First, we present a construction that uses an integral equation to represent the highcontrast component of the solution. This representation involves solving an integral equation along the interface where the coefficients are discontinuous. The integral representation suggests some multiscale approaches that are discussed in the paper. One of these approaches entails the use of interface functions in addition to multiscale basis functions representing the heterogeneities without high contrast. In this paper, we propose an approximation for the solution of the integral equation using the interface problems in reduced-contrast media. Reduced-contrast media are obtained by lowering the variance of the coefficients. We also propose a similar approach for the solution of the elliptic equation without using an integral representation. This approach is simpler to use in the computations because it does not involve setting up integral equations. The main idea of this approach is to approximate the solution of the high-contrast problem by the solutions of the problems formulated in reduced-contrast media. In this approach, a rapidly converging sequence is proposed where only problems with lower contrast are solved. It was shown that this sequence possesses the convergence rate that is inversely proportional to the reduced contrast. This approximation allows choosing the reduced-contrast problem based on the coarse-mesh size as discussed in this paper. We present a simple application of this approach to homogenization of elliptic equations with high-contrast coefficients. The presented approaches are limited to the cases where there are sharp changes in the contrast (i.e., the high

  2. Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

    Directory of Open Access Journals (Sweden)

    D. Olvera

    2015-01-01

    Full Text Available We expand the application of the enhanced multistage homotopy perturbation method (EMHPM to solve delay differential equations (DDEs with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.

  3. Simple solution-processed CuOX as anode buffer layer for efficient organic solar cells

    International Nuclear Information System (INIS)

    Shen, Wenfei; Yang, Chunpeng; Bao, Xichang; Sun, Liang; Wang, Ning; Tang, Jianguo; Chen, Weichao; Yang, Renqiang

    2015-01-01

    Graphical abstract: - Highlights: • Simple solution-processed CuO X hole transport layer for efficient organic solar cell. • Good photovoltaic performances as hole transport layer in OSCs with P3HT and PBDTTT-C as donor materials. • The device with CuO X as hole transport layer shows great improved stability compared with that of device with PEDOT:PSS as hole transport layer. - Abstract: A simple, solution-processed ultrathin CuO X anode buffer layer was fabricated for high performance organic solar cells (OSCs). XPS measurement demonstrated that the CuO X was the composite of CuO and Cu 2 O. The CuO X modified ITO glass exhibit a better surface contact with the active layer. The photovoltaic performance of the devices with CuO X layer was optimized by varying the thickness of CuO X films through changing solution concentration. With P3HT:PC 61 BM as the active layer, we demonstrated an enhanced PCE of 4.14% with CuO X anode buffer layer, compared with that of PEDOT:PSS layer. The CuO X layer also exhibits efficient photovoltaic performance in devices with PBDTTT-C:PC 71 BM as the active layer. The long-term stability of CuO X device is better than that of PEDOT:PSS device. The results indicate that the easy solution-processed CuO X film can act as an efficient anode buffer layer for high-efficiency OSCs

  4. Simple polynomial approximation to modified Bethe formula low-energy electron stopping powers data

    Energy Technology Data Exchange (ETDEWEB)

    Taborda, A., E-mail: ana.taborda@irsn.fr [Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-HOM/SDI/LEDI, BP-17, 92262 Fontenay-aux-Roses (France); Desbrée, A. [Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-HOM/SDI/LEDI, BP-17, 92262 Fontenay-aux-Roses (France); Reis, M.A. [C" 2TN, Campus Tecnológico e Nuclear, Instituto Superior Técnico, Universidade de Lisboa, EN10 km139.7, 2685-066 Bobadela LRS (Portugal)

    2015-08-01

    A recently published detailed and exhaustive paper on cross-sections for ionisation induced by keV electrons clearly shows that electron phenomena occurring in parallel with X-ray processes may have been dramatically overlooked for many years, mainly when low atomic number species are involved since, in these cases, the fluorescence coefficient is smaller than the Auger yield. An immediate problem is encountered while attempting to tackle the issue. Accounting for electron phenomena requires the knowledge of the stopping power of electrons within, at least, a reasonably small error. Still, the Bethe formula for stopping powers is known to not be valid for electron energies below 30 keV, and its use leads to values far off experimental ones. Recently, a few authors have addressed this problem and both detailed tables of electron stopping powers for various atomic species and attempts to simplify the calculations, have emerged. Nevertheless, its implementation in software routines to efficiently calculate keV electron effects in materials quickly becomes a bit cumbersome. Following a procedure already used to establish efficient methods to calculate ionisation cross-sections by protons and alpha particles, it became clear that a simple polynomial approximation could be set, which allows retrieving the electronic stopping powers with errors of less than 20% for energies above 500 eV and less than 50% for energies between 50 eV and 500 eV. In this work, we present this approximation which, based on just six parameters, allows to recover electron stopping power values that are less than 20% different from recently published experimentally validated tabulated data.

  5. Numerical approximations of difference functional equations and applications

    Directory of Open Access Journals (Sweden)

    Zdzisław Kamont

    2005-01-01

    Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.

  6. Iterative approximation of the solution of a monotone operator equation in certain Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1988-01-01

    Let X=L p (or l p ), p ≥ 2. The solution of the equation Ax=f, f is an element of X is approximated in X by an iteration process in each of the following two cases: (i) A is a bounded linear mapping of X into itself which is also bounded below; and, (ii) A is a nonlinear Lipschitz mapping of X into itself and satisfies ≥ m |x-y| 2 , for some constant m > 0 and for all x, y in X, where j is the single-valued normalized duality mapping of X into X* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X. (author). 12 refs

  7. Solución aproximada de sistemas diferenciales mixtos Approximated solution of differentials mixed systems

    Directory of Open Access Journals (Sweden)

    Jorge I. Castaño–Bedoya

    2009-12-01

    Full Text Available En este artículo se propone encontrar una solución aproximada para problemas de valor en la frontera y problemas de valor inicial de un sistema diferencial utilizando el método de los desarrollos de Fer.In this paper we propose to find an approximate solution to boundary value problems and initial value differential system problems using the method of Fer developments.

  8. Water-Reflected 233U Uranyl Nitrate Solutions in Simple Geometry

    International Nuclear Information System (INIS)

    Elam, K.R.

    2001-01-01

    A number of critical experiments involving 233 U were performed in the Oak Ridge National Laboratory Building 9213 Critical Experiments Facility during the years 1952 and 1953. These experiments, reported in Reference 1, were directed toward determining bounding values for the minimum critical mass, minimum critical volume, and maximum safe pipe size of water-moderated solutions of 233 U. Additional information on the critical experiments was found in the experimental logbooks. Two experiments utilizing uranyl nitrate (UO 2 (NO 3 ) 2 ) solutions in simple geometry are evaluated in this report. Experiment 37 is in a 10.4-inch diameter sphere, and Experiment 39 is in a 10-inch diameter cylinder. The 233 U concentration ranges from 49 to 62 g 233 U/l. Both experiments were reflected by at least 6 inches of water in all directions. Paraffin-reflected uranyl nitrate experiments, also reported in Reference 1, are evaluated elsewhere. Experiments with smaller paraffin reflected 5-, 6-, and 7.5-inch diameter cylinders are evaluated in U233-SOL-THERM-004. Experiments with paraffin reflected 8-, 8.5-, 9-, 10-, and 12-inch diameter cylinders are evaluated in U233-SOL-THERM-002. Later experiments with highly-enriched 235 U uranyl fluoride solution in the same 10.4-inch diameter sphere are reported in HEU-SOL-THERM-010. Both experiments were judged acceptable for use as criticality-safety benchmark experiments

  9. ABOUT SOME APPROXIMATIONS TO THE CLOSED SET OF NOT TRIVIAL SOLUTIONS OF THE EQUATIONS OF GINZBURG - LANDAU

    Directory of Open Access Journals (Sweden)

    A. A. Fonarev

    2014-01-01

    Full Text Available Possibility of use of a projective iterative method for search of approximations to the closed set of not trivial generalised solutions of a boundary value problem for Ginzburg - Landau's equations of the phenomenological theory of superconduction is investigated. The projective iterative method combines a projective method and iterative process. The generalised solutions of a boundary value problem for Ginzburg - Landau's equations are critical points of a functional of a superconductor free energy.

  10. A functional-type a posteriori error estimate of approximate solutions for Reissner-Mindlin plates and its implementation

    Science.gov (United States)

    Frolov, Maxim; Chistiakova, Olga

    2017-06-01

    Paper is devoted to a numerical justification of the recent a posteriori error estimate for Reissner-Mindlin plates. This majorant provides a reliable control of accuracy of any conforming approximate solution of the problem including solutions obtained with commercial software for mechanical engineering. The estimate is developed on the basis of the functional approach and is applicable to several types of boundary conditions. To verify the approach, numerical examples with mesh refinements are provided.

  11. Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme

    Directory of Open Access Journals (Sweden)

    Şuayip Yüzbaşı

    2015-02-01

    Full Text Available The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic Rössler system. For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method is based on taking the truncated Bessel expansions of the functions in the hyperchaotic Rössler systems. The suggested secheme converts the problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy and efficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code written in Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions.

  12. A simple semi-empirical approximation for bond energy

    International Nuclear Information System (INIS)

    Jorge, F.E.; Giambiagi, M.; Giambiagi, M.S. de.

    1985-01-01

    A simple semi-empirical expression for bond energy, related with a generalized bond index, is proposed and applied within the IEH framework. The correlation with experimental data is good for the intermolecular bond energy of base pairs of nucleic acids and other hydrogen bonded systems. The intramolecular bond energies for a sample of molecules containing typical bonds and for hydrides are discussed. The results are compared with those obtained by other methods. (Author) [pt

  13. Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Alsaedi Ahmed

    2009-01-01

    Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

  14. The comparison of DYNA3D to approximate solutions for a partially- full waste storage tank subjected to seismic loading

    International Nuclear Information System (INIS)

    Zaslawsky, M.; Kennedy, W.N.

    1992-01-01

    Mathematical solutions to the problem consisting of a partially-full waste tank subjected to seismic loading, embedded in soil, is classically difficult in that one has to address: soil-structure interaction, fluid-structure interaction, non-linear behavior of material, dynamic effects. Separating the problem and applying numerous assumptions will yield approximate solutions. This paper explores methods for generating these solutions accurately

  15. A simple low-computation-intensity model for approximating the distribution function of a sum of non-identical lognormals for financial applications

    Science.gov (United States)

    Messica, A.

    2016-10-01

    The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.

  16. Generalized synthetic kernel approximation for elastic moderation of fast neutrons

    International Nuclear Information System (INIS)

    Yamamoto, Koji; Sekiya, Tamotsu; Yamamura, Yasunori.

    1975-01-01

    A method of synthetic kernel approximation is examined in some detail with a view to simplifying the treatment of the elastic moderation of fast neutrons. A sequence of unified kernel (fsub(N)) is introduced, which is then divided into two subsequences (Wsub(n)) and (Gsub(n)) according to whether N is odd (Wsub(n)=fsub(2n-1), n=1,2, ...) or even (Gsub(n)=fsub(2n), n=0,1, ...). The W 1 and G 1 kernels correspond to the usual Wigner and GG kernels, respectively, and the Wsub(n) and Gsub(n) kernels for n>=2 represent generalizations thereof. It is shown that the Wsub(n) kernel solution with a relatively small n (>=2) is superior on the whole to the Gsub(n) kernel solution for the same index n, while both converge to the exact values with increasing n. To evaluate the collision density numerically and rapidly, a simple recurrence formula is derived. In the asymptotic region (except near resonances), this recurrence formula allows calculation with a relatively coarse mesh width whenever hsub(a)<=0.05 at least. For calculations in the transient lethargy region, a mesh width of order epsilon/10 is small enough to evaluate the approximate collision density psisub(N) with an accuracy comparable to that obtained analytically. It is shown that, with the present method, an order of approximation of about n=7 should yield a practically correct solution diviating not more than 1% in collision density. (auth.)

  17. Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

    OpenAIRE

    Fagioli, Simone; Radici, Emanuela

    2018-01-01

    We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegative initial data in $L^{\\infty} \\cap BV$ away from vacuum and supported in a closed interval with zero-velocity boundary conditions. The main novelti...

  18. A simple and effective solution to the constrained QM/MM simulations

    Science.gov (United States)

    Takahashi, Hideaki; Kambe, Hiroyuki; Morita, Akihiro

    2018-04-01

    It is a promising extension of the quantum mechanical/molecular mechanical (QM/MM) approach to incorporate the solvent molecules surrounding the QM solute into the QM region to ensure the adequate description of the electronic polarization of the solute. However, the solvent molecules in the QM region inevitably diffuse into the MM bulk during the QM/MM simulation. In this article, we developed a simple and efficient method, referred to as the "boundary constraint with correction (BCC)," to prevent the diffusion of the solvent water molecules by means of a constraint potential. The point of the BCC method is to compensate the error in a statistical property due to the bias potential by adding a correction term obtained through a set of QM/MM simulations. The BCC method is designed so that the effect of the bias potential completely vanishes when the QM solvent is identical with the MM solvent. Furthermore, the desirable conditions, that is, the continuities of energy and force and the conservations of energy and momentum, are fulfilled in principle. We applied the QM/MM-BCC method to a hydronium ion(H3O+) in aqueous solution to construct the radial distribution function (RDF) of the solvent around the solute. It was demonstrated that the correction term fairly compensated the error and led the RDF in good agreement with the result given by an ab initio molecular dynamics simulation.

  19. A Simple Approach to Derive a Novel N-Soliton Solution for a (3+1)-Dimensional Nonlinear Evolution Equation

    International Nuclear Information System (INIS)

    Wu Jianping

    2010-01-01

    Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a (3+1)-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica. (general)

  20. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  1. Approximate self-consistent potentials for density-functional-theory exchange-correlation functionals

    International Nuclear Information System (INIS)

    Cafiero, Mauricio; Gonzalez, Carlos

    2005-01-01

    We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials

  2. The simple solutions concept: a useful approach to estimate deviation from ideality in solvent extraction

    International Nuclear Information System (INIS)

    Sorel, C.; Pacary, V.

    2010-01-01

    The solvent extraction systems devoted to uranium purification from crude ore to spent fuel involve concentrated solutions in which deviation from ideality can not be neglected. The Simple Solution Concept based on the behaviour of isopiestic solutions has been applied to quantify the activity coefficients of metals and acids in the aqueous phase in equilibrium with the organic phase. This approach has been validated on various solvent extraction systems such as trialkylphosphates, malonamides or acidic extracting agents both on batch experiments and counter-current tests. Moreover, this concept has been successfully used to estimate the aqueous density which is useful to quantify the variation of volume and to assess critical parameters such as the number density of nuclides. (author)

  3. Thin-wall approximation in vacuum decay: A lemma

    Science.gov (United States)

    Brown, Adam R.

    2018-05-01

    The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.

  4. Approximation in two-stage stochastic integer programming

    NARCIS (Netherlands)

    W. Romeijnders; L. Stougie (Leen); M. van der Vlerk

    2014-01-01

    htmlabstractApproximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value.

  5. Approximation in two-stage stochastic integer programming

    NARCIS (Netherlands)

    Romeijnders, W.; Stougie, L.; van der Vlerk, M.H.

    2014-01-01

    Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value. However,

  6. Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

    Energy Technology Data Exchange (ETDEWEB)

    Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)

    2016-09-15

    Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the

  7. Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

    International Nuclear Information System (INIS)

    Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

    2017-01-01

    Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics. (topical review)

  8. Approximate solution methods in engineering mechanics

    International Nuclear Information System (INIS)

    Boresi, A.P.; Cong, K.P.

    1991-01-01

    This is a short book of 147 pages including references and sometimes bibliographies at the end of each chapter, and subject and author indices at the end of the book. The test includes an introduction of 3 pages, 29 pages explaining approximate analysis, 41 pages on finite differences, 36 pages on finite elements, and 17 pages on specialized methods

  9. Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method

    International Nuclear Information System (INIS)

    Song Lina; Wang Weiguo

    2010-01-01

    In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.

  10. Phase diagram of the Blume-Emery-Griffiths model on the simple cubic lattice calculated by the linear chain approximation

    International Nuclear Information System (INIS)

    Albayrak, Erhan; Keskin, Mustafa

    2000-01-01

    The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made

  11. Phase diagram of the Blume-Emery-Griffiths model on the simple cubic lattice calculated by the linear chain approximation

    CERN Document Server

    Albayrak, E

    2000-01-01

    The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made.

  12. Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

    International Nuclear Information System (INIS)

    Yang Pei; Li Zhibin; Chen Yong

    2010-01-01

    In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)

  13. Higher-Order Approximations of Motion of a Nonlinear Oscillator Using the Parameter Expansion Technique

    Science.gov (United States)

    Ganji, S. S.; Domairry, G.; Davodi, A. G.; Babazadeh, H.; Seyedalizadeh Ganji, S. H.

    The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt-Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the solutions. In particular, APL-PM works well for the whole range of oscillation amplitudes and excellent agreement of the approximate frequency with the exact one has been demonstrated. The approximate period derived here is accurate and close to the exact solution. This method has a distinguished feature which makes it simple to use, and also it agrees with the exact solutions for various parameters.

  14. Approximate solutions of the two-dimensional integral transport equation by collision probability methods

    International Nuclear Information System (INIS)

    Sanchez, Richard

    1977-01-01

    A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the Interface Current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding and water, or homogenized structural material. The cells are divided into zones which are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is made by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: the first uses a cylindrical cell model and one or three terms for the flux expansion; the second uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark pr

  15. Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

    International Nuclear Information System (INIS)

    Wei Gaofeng; Dong Shihai

    2008-01-01

    In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential

  16. Analytical solution for the electrical properties of a radio-frequency quadrupole (RFQ) with simple vanes

    International Nuclear Information System (INIS)

    Lancaster, H.

    1982-01-01

    Although the SUPERFISH program is used for calculating the design parameters of an RFQ structure with complex vanes, an analytical solution for electrical properties of an RFQ with simple vanes provides insight into the parametric behavior of these more complicated resonators. The fields in an inclined plane wave guide with proper boundary conditions match those in one quadrant of an RFQ. The principle of duality is used to exploit the solutions to a radial transmission line in solving the field equations. Calculated are the frequency equation, frequency sensitivity factors, electric field, magnetic field, stored energy (U), power dissipation, and quality factor

  17. On the use of the Lie group technique for differential equations with a small parameter: Approximate solutions and integrable equations

    International Nuclear Information System (INIS)

    Burde, G.I.

    2002-01-01

    A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given

  18. Experimental Investigation of Triplet Correlation Approximations for Fluid Water.

    Science.gov (United States)

    Pallewela, Gayani N; Ploetz, Elizabeth A; Smith, Paul E

    2018-08-25

    Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.

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

    International Nuclear Information System (INIS)

    Adam, Gh.

    1978-01-01

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

  20. Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

    Science.gov (United States)

    Rao, T. R. Ramesh

    2018-04-01

    In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

  1. Simple detection of residual enrofloxacin in meat products using microparticles and biochips.

    Science.gov (United States)

    Ha, Mi-Sun; Chung, Myung-Sub; Bae, Dong-Ho

    2016-05-01

    A simple and sensitive method for detecting enrofloxacin, a major veterinary fluoroquinolone, was developed. Monoclonal antibody specific for enrofloxacin was immobilised on a chip and fluorescent dye-labelled microparticles were covalently bound to the enrofloxacin molecules. Enrofloxacin in solution competes with the microparticle-immobilised enrofloxacin (enroMPs) to bind to the antibody on the chip. The presence of enrofloxacin was verified by detecting the fluorescence of enrofloxacin-bound microparticles. Under optimum conditions, a high dynamic range was achieved at enrofloxacin concentrations ranging from 1 to 1000 μg kg(-1). The limits of detection and quantification for standard solutions were 5 and 20 μg kg(-1) respectively, which are markedly lower than the maximum residue limit. Using simple extraction methods, recoveries from fortified beef, pork and chicken samples were 43.4-62.3%. This novel method also enabled approximate quantification of enrofloxacin concentration: the enroMP signal intensity decreased with increasing enrofloxacin concentration. Because of its sensitivity, specificity, simplicity and rapidity, the method described herein will facilitate the detection and approximate quantification of enrofloxacin residues in foods in a high-throughput manner.

  2. Excess Gibbs energy for six binary solid solutions of molecularly simple substances

    Energy Technology Data Exchange (ETDEWEB)

    Lobo, L J; Staveley, L A.K.

    1985-01-01

    In this paper we apply the method developed in a previous study of Ar + CH/sub 4/ to the evaluation of the excess Gibbs energy G /SUP E.S/ for solid solutions of two molecularly simple components. The method depends on combining information on the excess Gibbs energy G /SUP E.L/ for the liquid mixture of the two components with a knowledge of the (T, x) solid-liquid phase diagram. Certain thermal properties o the pure substances are also needed. G /SUP E.S/ has been calculated for binary mixtures of Ar + Kr, Kr + CH/sub 4/, CO + N/sub 2/, Kr + Xe, Ar + N/sub 2/, and Ar + CO. In general, but not always, the solid mixtures are more non-ideal than the liquid mixtures of the same composition at the same temperature. Except for the Kr + CH/sub 4/ system, the ratio r = G /SUP E.S/ /G /SUP E.L/ is larger the richer the solution in the component with the smaller molecules.

  3. Numerical solution of singularity-perturbed two-point boundary-value problems

    International Nuclear Information System (INIS)

    Masenge, R.W.P.

    1993-07-01

    Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

  4. Application of thermodynamics to silicate crystalline solutions

    Science.gov (United States)

    Saxena, S. K.

    1972-01-01

    A review of thermodynamic relations is presented, describing Guggenheim's regular solution models, the simple mixture, the zeroth approximation, and the quasi-chemical model. The possibilities of retrieving useful thermodynamic quantities from phase equilibrium studies are discussed. Such quantities include the activity-composition relations and the free energy of mixing in crystalline solutions. Theory and results of the study of partitioning of elements in coexisting minerals are briefly reviewed. A thermodynamic study of the intercrystalline and intracrystalline ion exchange relations gives useful information on the thermodynamic behavior of the crystalline solutions involved. Such information is necessary for the solution of most petrogenic problems and for geothermometry. Thermodynamic quantities for tungstates (CaWO4-SrWO4) are calculated.

  5. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

    2016-01-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  6. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti

    2016-02-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  7. Substep methods for burnup calculations with Bateman solutions

    International Nuclear Information System (INIS)

    Isotalo, A.E.; Aarnio, P.A.

    2011-01-01

    Highlights: → Bateman solution based depletion requires constant microscopic reaction rates. → Traditionally constant approximation is used for each depletion step. → Here depletion steps are divided to substeps which are solved sequentially. → This allows piecewise constant, rather than constant, approximation for each step. → Discretization errors are almost completely removed with only minor slowdown. - Abstract: When material changes in burnup calculations are solved by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates, one has to first predict the development of the reaction rates during the step and then further approximate these predictions with their averages in the depletion calculation. Representing the continuously changing reaction rates with their averages results in some error regardless of how accurately their development was predicted. Since neutronics solutions tend to be computationally expensive, steps in typical calculations are long and the resulting discretization errors significant. In this paper we present a simple solution to reducing these errors: the depletion steps are divided to substeps that are solved sequentially, allowing finer discretization of the reaction rates without additional neutronics solutions. This greatly reduces the discretization errors and, at least when combined with Monte Carlo neutronics, causes only minor slowdown as neutronics dominates the total running time.

  8. Approximate solution of oil film load-carrying capacity of turbulent journal bearing with couple stress flow

    Science.gov (United States)

    Zhang, Yongfang; Wu, Peng; Guo, Bo; Lü, Yanjun; Liu, Fuxi; Yu, Yingtian

    2015-01-01

    The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.

  9. Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

    Science.gov (United States)

    Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

    2016-01-01

    Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

  10. Simple electrolyte solutions: Comparison of DRISM and molecular dynamics results for alkali halide solutions

    Science.gov (United States)

    Joung, In Suk; Luchko, Tyler; Case, David A.

    2013-01-01

    Using the dielectrically consistent reference interaction site model (DRISM) of molecular solvation, we have calculated structural and thermodynamic information of alkali-halide salts in aqueous solution, as a function of salt concentration. The impact of varying the closure relation used with DRISM is investigated using the partial series expansion of order-n (PSE-n) family of closures, which includes the commonly used hypernetted-chain equation (HNC) and Kovalenko-Hirata closures. Results are compared to explicit molecular dynamics (MD) simulations, using the same force fields, and to experiment. The mean activity coefficients of ions predicted by DRISM agree well with experimental values at concentrations below 0.5 m, especially when using the HNC closure. As individual ion activities (and the corresponding solvation free energies) are not known from experiment, only DRISM and MD results are directly compared and found to have reasonably good agreement. The activity of water directly estimated from DRISM is nearly consistent with values derived from the DRISM ion activities and the Gibbs-Duhem equation, but the changes in the computed pressure as a function of salt concentration dominate these comparisons. Good agreement with experiment is obtained if these pressure changes are ignored. Radial distribution functions of NaCl solution at three concentrations were compared between DRISM and MD simulations. DRISM shows comparable water distribution around the cation, but water structures around the anion deviate from the MD results; this may also be related to the high pressure of the system. Despite some problems, DRISM-PSE-n is an effective tool for investigating thermodynamic properties of simple electrolytes. PMID:23387564

  11. On numerical solution of Burgers' equation by homotopy analysis method

    International Nuclear Information System (INIS)

    Inc, Mustafa

    2008-01-01

    In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

  12. A new approximation of the dispersion relations occurring in the sound-attenuation problem of turbofan aircraft engines

    Directory of Open Access Journals (Sweden)

    Robert SZABO

    2011-12-01

    Full Text Available The dispersion relations, appearing in the analysis of the stability of a gas flow in a straight acoustically-lined duct with respect to perturbations produced by a time harmonic source, beside the wave number and complex frequency contain the solution of a boundary value problem of the Pridmore-Brown equation depending on the wave number and frequency. For this reason, in practice the dispersion relations are rarely simple enough for carried out the zeros. The determination of zeros of these dispersion relations is crucial for the prediction of the perturbation attenuation or amplification. In this paper an approximation of the dispersion relations is given. Our approach preserves the general character of the mean flow, the general Pridmore-Brown equation and it’s only in the shear flow that we replace the exact solution of the boundary value problem with its Taylor polynomial approximate. In this way new approximate dispersion relations are obtained which zero’s can be found by computer.

  13. Exact solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED

    International Nuclear Information System (INIS)

    Kernemann, A.; Stefanis, N.G.

    1989-01-01

    A set of new closed-form solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED is presented. A manifestly covariant phase-space path-integral method is applied for calculating the n-fermion Green's function in a classical external field. In the case of one and two fermions, explicit expressions for the full Green's functions are analytically obtained, with renormalization carried out in the modified minimal subtraction scheme. The renormalization constants and the corresponding anomalous dimensions are determined. The mass-shell behavior of the two-fermion Green's function is investigated in detail. No assumptions are made concerning the structure of asymptotic states and no IR cutoff is used in the calculations

  14. Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling

    Science.gov (United States)

    Yudovsky, Dmitry; Durkin, Anthony J.

    2011-07-01

    Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.

  15. Efficient electroluminescence from a perylenediimide fluorophore obtained from a simple solution processed OLED

    International Nuclear Information System (INIS)

    Cespedes-Guirao, F J; Fernandez-Lazaro, F; Sastre-Santos, A; Garcia-Santamaria, S; Bolink, H J

    2009-01-01

    Simple solution processed organic light emitting diodes are used to screen the performance of two types of highly efficient, narrow band red emitting fluorescent perylenediimides (PDIs). PDIs substituted at the diimide positions seem to form aggregates in the thin film architecture as evidenced by the shifted electroluminescent spectrum. When substituted on the bay position and when used both as the emitting and the electron transporting specie, bright electroluminescence with a narrow width around 610 nm reaching 500 cd m -2 at moderate voltages was observed, demonstrating the usefulness of these fluorophores for OLED applications.

  16. Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Chi-Chang Wang

    2013-09-01

    Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

  17. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  18. Simple solution-processed CuO{sub X} as anode buffer layer for efficient organic solar cells

    Energy Technology Data Exchange (ETDEWEB)

    Shen, Wenfei [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, 189 Songling Road, Qingdao 266101 (China); Institute of Hybrid Materials, The Growing Base for State Key Laboratory, Qingdao University, 308 Ningxia Road, Qingdao 266071 (China); Yang, Chunpeng [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, 189 Songling Road, Qingdao 266101 (China); Bao, Xichang, E-mail: baoxc@qibebt.ac.cn [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, 189 Songling Road, Qingdao 266101 (China); Sun, Liang; Wang, Ning [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, 189 Songling Road, Qingdao 266101 (China); Tang, Jianguo [Institute of Hybrid Materials, The Growing Base for State Key Laboratory, Qingdao University, 308 Ningxia Road, Qingdao 266071 (China); Chen, Weichao [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, 189 Songling Road, Qingdao 266101 (China); Yang, Renqiang, E-mail: yangrq@qibebt.ac.cn [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, 189 Songling Road, Qingdao 266101 (China)

    2015-10-15

    Graphical abstract: - Highlights: • Simple solution-processed CuO{sub X} hole transport layer for efficient organic solar cell. • Good photovoltaic performances as hole transport layer in OSCs with P3HT and PBDTTT-C as donor materials. • The device with CuO{sub X} as hole transport layer shows great improved stability compared with that of device with PEDOT:PSS as hole transport layer. - Abstract: A simple, solution-processed ultrathin CuO{sub X} anode buffer layer was fabricated for high performance organic solar cells (OSCs). XPS measurement demonstrated that the CuO{sub X} was the composite of CuO and Cu{sub 2}O. The CuO{sub X} modified ITO glass exhibit a better surface contact with the active layer. The photovoltaic performance of the devices with CuO{sub X} layer was optimized by varying the thickness of CuO{sub X} films through changing solution concentration. With P3HT:PC{sub 61}BM as the active layer, we demonstrated an enhanced PCE of 4.14% with CuO{sub X} anode buffer layer, compared with that of PEDOT:PSS layer. The CuO{sub X} layer also exhibits efficient photovoltaic performance in devices with PBDTTT-C:PC{sub 71}BM as the active layer. The long-term stability of CuO{sub X} device is better than that of PEDOT:PSS device. The results indicate that the easy solution-processed CuO{sub X} film can act as an efficient anode buffer layer for high-efficiency OSCs.

  19. A solution to nonlinearity problems

    International Nuclear Information System (INIS)

    Neuffer, D.V.

    1989-01-01

    New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab

  20. Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

    Science.gov (United States)

    Liu, Longcheng; Neretnieks, Ivars; Shahkarami, Pirouz; Meng, Shuo; Moreno, Luis

    2018-02-01

    A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.

  1. Legendre-tau approximations for functional differential equations

    Science.gov (United States)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  2. Green-Ampt approximations: A comprehensive analysis

    Science.gov (United States)

    Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.

    2016-04-01

    Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.

  3. Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

    Science.gov (United States)

    Barrett, Steven R. H.; Britter, Rex E.

    Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean

  4. Prediction of thermodynamic instabilities of protein solutions from simple protein–protein interactions

    International Nuclear Information System (INIS)

    D’Agostino, Tommaso; Solana, José Ramón; Emanuele, Antonio

    2013-01-01

    Highlights: ► We propose a model of effective protein–protein interaction embedding solvent effects. ► A previous square-well model is enhanced by giving to the interaction a free energy character. ► The temperature dependence of the interaction is due to entropic effects of the solvent. ► The validity of the original SW model is extended to entropy driven phase transitions. ► We get good fits for lysozyme and haemoglobin spinodal data taken from literature. - Abstract: Statistical thermodynamics of protein solutions is often studied in terms of simple, microscopic models of particles interacting via pairwise potentials. Such modelling can reproduce the short range structure of protein solutions at equilibrium and predict thermodynamics instabilities of these systems. We introduce a square well model of effective protein–protein interaction that embeds the solvent’s action. We modify an existing model [45] by considering a well depth having an explicit dependence on temperature, i.e. an explicit free energy character, thus encompassing the statistically relevant configurations of solvent molecules around proteins. We choose protein solutions exhibiting demixing upon temperature decrease (lysozyme, enthalpy driven) and upon temperature increase (haemoglobin, entropy driven). We obtain satisfactory fits of spinodal curves for both the two proteins without adding any mean field term, thus extending the validity of the original model. Our results underline the solvent role in modulating or stretching the interaction potential

  5. The choice of optimal Discrete Interaction Approximation to the kinetic integral for ocean waves

    Directory of Open Access Journals (Sweden)

    V. G. Polnikov

    2003-01-01

    Full Text Available A lot of discrete configurations for the four-wave nonlinear interaction processes have been calculated and tested by the method proposed earlier in the frame of the concept of Fast Discrete Interaction Approximation to the Hasselmann's kinetic integral (Polnikov and Farina, 2002. It was found that there are several simple configurations, which are more efficient than the one proposed originally in Hasselmann et al. (1985. Finally, the optimal multiple Discrete Interaction Approximation (DIA to the kinetic integral for deep-water waves was found. Wave spectrum features have been intercompared for a number of different configurations of DIA, applied to a long-time solution of kinetic equation. On the basis of this intercomparison the better efficiency of the configurations proposed was confirmed. Certain recommendations were given for implementation of new approximations to the wave forecast practice.

  6. Low-complexity computation of plate eigenmodes with Vekua approximations and the method of particular solutions

    Science.gov (United States)

    Chardon, Gilles; Daudet, Laurent

    2013-11-01

    This paper extends the method of particular solutions (MPS) to the computation of eigenfrequencies and eigenmodes of thin plates, in the framework of the Kirchhoff-Love plate theory. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the finite element method, at reduced complexity, and with large flexibility in the implementation choices.

  7. An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

    Science.gov (United States)

    Alam Khan, Najeeb; Razzaq, Oyoon Abdul

    2016-03-01

    In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

  8. Optimal solutions for a bio mathematical model for the evolution of smoking habit

    Science.gov (United States)

    Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

    In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

  9. A simple model for low energy ion-solid interactions

    International Nuclear Information System (INIS)

    Mohajerzadeh, S.; Selvakumar, C.R.

    1997-01-01

    A simple analytical model for ion-solid interactions, suitable for low energy beam depositions, is reported. An approximation for the nuclear stopping power is used to obtain the analytic solution for the deposited energy in the solid. The ratio of the deposited energy in the bulk to the energy deposited in the surface yields a ceiling for the beam energy above which more defects are generated in the bulk resulting in defective films. The numerical evaluations agree with the existing results in the literature. copyright 1997 American Institute of Physics

  10. A simple approximation to the bivariate normal distribution with large correlation coefficient

    NARCIS (Netherlands)

    Albers, Willem/Wim; Kallenberg, W.C.M.

    1994-01-01

    The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the

  11. Simple model for the dynamics towards metastable states

    International Nuclear Information System (INIS)

    Meijer, P.H.E.; Keskin, M.; Bodegom, E.

    1986-01-01

    Circumstances under which a quenched system will freeze in a metastable state are studied in simple systems with long-range order. The model used is the time-dependent pair approximation, based on the most probable path (MPP) method. The time dependence of the solution is shown by means of flow diagrams. The fixed points and other features of the differential equations in time are independent of the choice of the rate constants. It is explained qualitatively how the system behaves under varying descending temperatures: the role of the initial conditions, the dependence on the quenching rate, and the response to precooling

  12. Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution

    DEFF Research Database (Denmark)

    Pedersen, Thomas Quistgaard

    In this paper we derive an approximate analytical solution to the optimal con- sumption and portfolio choice problem of an infinitely-lived investor with power utility defined over the difference between consumption and an external habit. The investor is assumed to have access to two tradable......-linearized surplus consumption ratio. The "difference habit model" implies that the relative risk aversion is time-varying which is in line with recent ev- idence from the asset pricing literature. We show that accounting for habit a¤ects both the myopic and intertemporal hedge component of optimal asset demand......, and introduces an additional component that works as a hedge against changes in the investor's habit level. In an empirical application, we calibrate the model to U.S. data and show that habit formation has significant effects on both the optimal consumption and portfolio choice compared to a standard CRRA...

  13. Approximate ideal multi-objective solution Q(λ) learning for optimal carbon-energy combined-flow in multi-energy power systems

    International Nuclear Information System (INIS)

    Zhang, Xiaoshun; Yu, Tao; Yang, Bo; Zheng, Limin; Huang, Linni

    2015-01-01

    Highlights: • A novel optimal carbon-energy combined-flow (OCECF) model is firstly established. • A novel approximate ideal multi-objective solution Q(λ) learning is designed. • The proposed algorithm has a high convergence stability and reliability. • The proposed algorithm can be applied for OCECF in a large-scale power grid. - Abstract: This paper proposes a novel approximate ideal multi-objective solution Q(λ) learning for optimal carbon-energy combined-flow in multi-energy power systems. The carbon emissions, fuel cost, active power loss, voltage deviation and carbon emission loss are chosen as the optimization objectives, which are simultaneously optimized by five different Q-value matrices. The dynamic optimal weight of each objective is calculated online from the entire Q-value matrices such that the greedy action policy can be obtained. Case studies are carried out to evaluate the optimization performance for carbon-energy combined-flow in an IEEE 118-bus system and the regional power grid of southern China.

  14. Diagonal Pade approximations for initial value problems

    International Nuclear Information System (INIS)

    Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.

    1987-06-01

    Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab

  15. Fractional approximations for linear first order differential equation with polynomial coefficients-application to E1(x) and Z(s)

    International Nuclear Information System (INIS)

    Martin, P.; Zamudio-Cristi, J.

    1982-01-01

    A method is described to obtain fractional approximations for linear first order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the highest and lowest power of the variable after the sustitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Pade method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which give three exact digits for most of the real values of the variable. Approximations of higher accuracy and of the same degree than other authors are also obtained. (Author) [pt

  16. Approximation algorithms for guarding holey polygons ...

    African Journals Online (AJOL)

    Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...

  17. Americium separations from high salt solutions

    International Nuclear Information System (INIS)

    Barr, Mary E.; Jarvinen, Gordon D.; Schulte, Louis D.; Stark, Peter C.; Chamberlin, Rebecca M.; Abney, Kent D.; Ricketts, Thomas E.; Valdez, Yvette E.; Bartsch, Richard A.

    2000-01-01

    Americium (III) exhibits an unexpectedly high affinity for anion-exchange material from the high-salt evaporator bottoms solutions--an effect which has not been duplicated using simple salt solutions. Similar behavior is observed for its lanthanide homologue, Nd(III), in complex evaporator bottoms surrogate solutions. There appears to be no single controlling factor--acid concentration, total nitrate concentration or solution ionic strength--which accounts for the approximately 2-fold increase in retention of the trivalent ions from complex solutions relative to simple solutions. Calculation of species activities (i.e., water, proton and nitrate) in such concentrated mixed salt solutions is difficult and of questionable accuracy, but it is likely that the answer to forcing formation of anionic nitrate complexes of americium lies in the relative activities of water and nitrate. From a practical viewpoint, the modest americium removal needs (ca. 50--75%) from nitric acid evaporator bottoms allow sufficient latitude for the use of non-optimized conditions such as running existing columns filled with older, well-used Reillex HPQ. Newer materials, such as HPQ-100 and the experimental bifunctional resins, which exhibit higher distribution coefficients, would allow for either increased Am removal or the use of smaller columns. It is also of interest that one of the experimental neutral-donor solid-support extractants, DHDECMP, exhibits a similarly high level of americium (total alpha) removal from EV bottoms and is much less sensitive to total acid content than commercially-available material

  18. Approximate Solutions to the Dirac Equation with Effective Mass for the Manning-Rosen Potential in N Dimensions

    International Nuclear Information System (INIS)

    Bahar, M.K.; Yasuk, F.

    2012-01-01

    The solutions of the effective mass Dirac equation for the Manning-Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac-Manning-Rosen problem for α = 0 or α = 1. In this case, the Manning-Rosen potential reduces to the Hulthen potential. (author)

  19. A learning rule for very simple universal approximators consisting of a single layer of perceptrons.

    Science.gov (United States)

    Auer, Peter; Burgsteiner, Harald; Maass, Wolfgang

    2008-06-01

    One may argue that the simplest type of neural networks beyond a single perceptron is an array of several perceptrons in parallel. In spite of their simplicity, such circuits can compute any Boolean function if one views the majority of the binary perceptron outputs as the binary output of the parallel perceptron, and they are universal approximators for arbitrary continuous functions with values in [0,1] if one views the fraction of perceptrons that output 1 as the analog output of the parallel perceptron. Note that in contrast to the familiar model of a "multi-layer perceptron" the parallel perceptron that we consider here has just binary values as outputs of gates on the hidden layer. For a long time one has thought that there exists no competitive learning algorithm for these extremely simple neural networks, which also came to be known as committee machines. It is commonly assumed that one has to replace the hard threshold gates on the hidden layer by sigmoidal gates (or RBF-gates) and that one has to tune the weights on at least two successive layers in order to achieve satisfactory learning results for any class of neural networks that yield universal approximators. We show that this assumption is not true, by exhibiting a simple learning algorithm for parallel perceptrons - the parallel delta rule (p-delta rule). In contrast to backprop for multi-layer perceptrons, the p-delta rule only has to tune a single layer of weights, and it does not require the computation and communication of analog values with high precision. Reduced communication also distinguishes our new learning rule from other learning rules for parallel perceptrons such as MADALINE. Obviously these features make the p-delta rule attractive as a biologically more realistic alternative to backprop in biological neural circuits, but also for implementations in special purpose hardware. We show that the p-delta rule also implements gradient descent-with regard to a suitable error measure

  20. Well posedness and maximum entropy approximation for the dynamics of quantitative traits

    KAUST Repository

    Boďová , Katarí na; Haskovec, Jan; Markowich, Peter A.

    2017-01-01

    We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.

  1. Well posedness and maximum entropy approximation for the dynamics of quantitative traits

    KAUST Repository

    Boďová, Katarína

    2017-11-06

    We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.

  2. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  3. Approximate Implicitization Using Linear Algebra

    Directory of Open Access Journals (Sweden)

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  4. Simple Methods to Approximate CPC Shape to Preserve Collection Efficiency

    Directory of Open Access Journals (Sweden)

    David Jafrancesco

    2012-01-01

    Full Text Available The compound parabolic concentrator (CPC is the most efficient reflective geometry to collect light to an exit port. Anyway, to allow its actual use in solar plants or photovoltaic concentration systems, a tradeoff between system efficiency and cost reduction, the two key issues for sunlight exploitation, must be found. In this work, we analyze various methods to model an approximated CPC aimed to be simpler and more cost-effective than the ideal one, as well as to preserve the system efficiency. The manufacturing easiness arises from the use of truncated conic surfaces only, which can be realized by cheap machining techniques. We compare different configurations on the basis of their collection efficiency, evaluated by means of nonsequential ray-tracing software. Moreover, due to the fact that some configurations are beam dependent and for a closer approximation of a real case, the input beam is simulated as nonsymmetric, with a nonconstant irradiance on the CPC internal surface.

  5. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  6. The generalized approximation method and nonlinear heat transfer equations

    Directory of Open Access Journals (Sweden)

    Rahmat Khan

    2009-01-01

    Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.

  7. On Love's approximation for fluid-filled elastic tubes

    International Nuclear Information System (INIS)

    Caroli, E.; Mainardi, F.

    1980-01-01

    A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)

  8. Analytical solution of strongly nonlinear Duffing oscillators

    Directory of Open Access Journals (Sweden)

    A.M. El-Naggar

    2016-06-01

    Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.

  9. Logical gaps in the approximate solutions of the social learning game and an exact solution.

    Science.gov (United States)

    Dai, Wenjie; Wang, Xin; Di, Zengru; Wu, Jinshan

    2014-01-01

    After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.

  10. Exact solutions for a system of nonlinear plasma fluid equations

    International Nuclear Information System (INIS)

    Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

    1991-04-01

    A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

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

    Science.gov (United States)

    Bodin, Jacques

    2015-03-01

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

  12. So, What is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations

    Directory of Open Access Journals (Sweden)

    Adam Weintrit

    2013-06-01

    Full Text Available In the paper the author presents overview of the meridian distance approximations. He would like to find the answer for the question what is actually the distance from the equator to the pole - the polar distance. In spite of appearances this is not such a simple question. The problem of determining the polar distance is a great opportunity to demonstrate the multitude of possible solutions in common use. At the beginning of the paper the author discusses some approximations and a few exact expressions (infinite sums to calculate perimeter and quadrant of an ellipse, he presents convenient measurement units of the distance on the surface of the Earth, existing methods for the solution of the great circle and great elliptic sailing, and in the end he analyses and compares geodetic formulas for the meridian arc length.

  13. Group C∗-algebras without the completely bounded approximation property

    DEFF Research Database (Denmark)

    Haagerup, U.

    2016-01-01

    It is proved that: (1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2 with finite center does not have a multiplier bounded approximate unit. (2) The reduced C∗-algebra C∗ r of any lattice in a non-compact simple Lie group of real rank at least 2 with finite center does...... not have the completely bounded approximation property. Hence, the results obtained by de Canniere and the author for SOe (n, 1), n ≥ 2, and by Cowling for SU(n, 1) do not generalize to simple Lie groups of real rank at least 2. © 2016 Heldermann Verlag....

  14. Approximation of the Doppler broadening function by Frobenius method; Aproximacao da funcao de alargamento doppler atraves do metodo de Frobenius

    Energy Technology Data Exchange (ETDEWEB)

    Palma, Daniel A.P. [Centro Federal de Educacao Tecnologica de Quimica de Nilopolis/RJ (CEFET), RJ (Brazil)]. E-mail: dpalma@cefeteq.br; Martinez, Aquilino S.; Silva, Fernando C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br; fernando@lmn.con.ufrj.br

    2005-07-01

    An analytical approximation of the Doppler broadening function {psi}(x,{xi}) is proposed. This approximation is based on the solution of the differential equation for {psi}(x,{xi}) using the methods of Frobenius and the parameters variation. The analytical form derived for {psi}(x,{xi}) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)

  15. Variation Iteration Method for The Approximate Solution of Nonlinear ...

    African Journals Online (AJOL)

    In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...

  16. Explicit appropriate basis function method for numerical solution of stiff systems

    International Nuclear Information System (INIS)

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

    2015-01-01

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

  17. On the independent particle approximation of Gauge theories: a simple example

    International Nuclear Information System (INIS)

    Palladino, B.E.

    1992-08-01

    In this work, the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1+1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed. (author)

  18. A New Approach for the Approximations of Solutions to a Common Fixed Point Problem in Metric Fixed Point Theory

    Directory of Open Access Journals (Sweden)

    Ishak Altun

    2016-01-01

    Full Text Available We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings T,S:X→X, where X is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.

  19. The approximate analytical solution of the internal problem of conductive and laminar free convection

    Directory of Open Access Journals (Sweden)

    M. I. Popov

    2016-01-01

    Full Text Available The approximate analytical solution of a problem about nonstationary free convection in the conductive and laminar mode of the Newtonian liquid in square area at the instantaneous change of temperature of a sidewall and lack of heat fluxes is submitted on top and bottom the bases. The equations of free convection in an approximation of Oberbeka-Bussinesk are linearized due to neglect by convective items. For reduction of number of hydrothermal parameters the system is given to the dimensionless look by introduction of scales for effect and explanatory variables. Transition from classical variables to the variables "whirlwind-a flow function" allowed to reduce system to a nonstationary heat conduction equation and a nonstationary nonuniform biharmonic equation, and the first is not dependent on the second. The decision in the form of a flow function is received by application integral a sine - Fourier transforms with terminating limits to a biharmonic equation at first on a variable x, and then on a variable y. The flow function has an appearance of a double series of Fourier on sine with coefficients in an integral form. Coefficients of a row represent integrals from unknown functions. On the basis of a hypothesis of an express type of integrals coefficients are calculated from the linear equation system received from boundary conditions on partial derivatives of function. Dependence of structure of a current on Prandtl's number is investigated. The cards of streamlines and isolines of components of speed describing development of a current from the moment of emergence before transition to a stationary state are received. The schedules of a field of vectors of speeds in various time illustrating dynamics of a current are provided. Reliability of a hypothesis of an express type of integral coefficients is confirmed by adequacy to physical sense and coherence of the received results with the numerical solution of a problem.

  20. Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

    International Nuclear Information System (INIS)

    Stottmeister, Alexander; Thiemann, Thomas

    2016-01-01

    This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).

  1. The recursive solution of the Schroedinger equation

    International Nuclear Information System (INIS)

    Haydock, R.

    The transformation of an arbitrary quantum model and its subsequent analysis is proposed. The chain expresses mathematically the physical concept of local environment. The recursive transformation yields analytic chains for some systems, but it is also convenient and efficient for constructing numerical chain models enabling the solution of problems which are too big for numerical matrix methods. The chain model sugests new approach to quantum mechanical models. Because of the simple solution of chain models, the qualitative behaviour of different physical properties can be determined. Unlike many methods for solving quantum models, one has rigorous results about the convergence of approximation. Because they are defined recursively, the approsimations are suited to computation. (Ha)

  2. Protein solution structure determination using distances from two-dimensional nuclear Overhauser effect experiments: Effect of approximations on the accuracy of derived structures

    International Nuclear Information System (INIS)

    Thomas, P.D.; Basus, V.J.; James, T.L.

    1991-01-01

    Solution structures for many proteins have been determined to date utilizing interproton distance constraints estimated from two-dimensional nuclear Overhauser effect (2D NOE) spectra. Although the simple isolated spin pair approximation (ISPA) generally used can result in systematic errors in distances, the large number of constraints enables proteins structure to be defined with reasonably high resolution. Effects of these systematic errors on the resulting protein structure are examined. Iterative relaxation matrix calculations, which account for dipolar interactions between all protons in a molecule, can accurately determine internuclear distances with little or no a priori knowledge of the molecular structure. The value of this additional complexity is also addressed. To assess these distance determination methods, hypothetical experimental data, including random noise and peak overlap, are calculated for an arbitrary true protein structure. Three methods of obtaining distance constraints from 2D NOE peak intensities are examined: one entails a conservative use of ISPA, one assumes the ISPA to be fairly accurate, and on utilizes an iterative relaxation matrix method called MARDIGRAS (matrix analysis of relaxation for discerning the geometry of an aqueous structure), developed in this laboratory. An R factor for evaluating fit between experimental and calculated 2D NOE intensities is proposed

  3. Theory and application of an approximate model of saltwater upconing in aquifers

    Science.gov (United States)

    McElwee, C.; Kemblowski, M.

    1990-01-01

    Motion and mixing of salt water and fresh water are vitally important for water-resource development throughout the world. An approximate model of saltwater upconing in aquifers is developed, which results in three non-linear coupled equations for the freshwater zone, the saltwater zone, and the transition zone. The description of the transition zone uses the concept of a boundary layer. This model invokes some assumptions to give a reasonably tractable model, considerably better than the sharp interface approximation but considerably simpler than a fully three-dimensional model with variable density. We assume the validity of the Dupuit-Forchheimer approximation of horizontal flow in each layer. Vertical hydrodynamic dispersion into the base of the transition zone is assumed and concentration of the saltwater zone is assumed constant. Solute in the transition zone is assumed to be moved by advection only. Velocity and concentration are allowed to vary vertically in the transition zone by using shape functions. Several numerical techniques can be used to solve the model equations, and simple analytical solutions can be useful in validating the numerical solution procedures. We find that the model equations can be solved with adequate accuracy using the procedures presented. The approximate model is applied to the Smoky Hill River valley in central Kansas. This model can reproduce earlier sharp interface results as well as evaluate the importance of hydrodynamic dispersion for feeding salt water to the river. We use a wide range of dispersivity values and find that unstable upconing always occurs. Therefore, in this case, hydrodynamic dispersion is not the only mechanism feeding salt water to the river. Calculations imply that unstable upconing and hydrodynamic dispersion could be equally important in transporting salt water. For example, if groundwater flux to the Smoky Hill River were only about 40% of its expected value, stable upconing could exist where

  4. Magnus approximation in the adiabatic picture

    International Nuclear Information System (INIS)

    Klarsfeld, S.; Oteo, J.A.

    1991-01-01

    A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs

  5. Quasi-fractional approximation to the Bessel functions

    International Nuclear Information System (INIS)

    Guerrero, P.M.L.

    1989-01-01

    In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4

  6. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

    Science.gov (United States)

    Freund, Roland

    1989-01-01

    Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

  7. Phase equilibria of hydrogen sulfide and carbon dioxide simple hydrates in the presence of methanol, (methanol + NaCl) and (ethylene glycol + NaCl) aqueous solutions

    International Nuclear Information System (INIS)

    Mohammadi, Amir H.; Richon, Dominique

    2012-01-01

    Highlights: → Dissociation conditions of H 2 S or CO 2 hydrate + inhibitor aqueous solution are reported. → Methanol, methanol + NaCl and EG + NaCl aqueous solutions are considered as inhibitors. → Comparisons are made between our experimental data and the corresponding literature data. - Abstract: This work aims at reporting the dissociation pressures of hydrogen sulfide and carbon dioxide simple hydrates in the presence of methanol, (methanol + NaCl) and (ethylene glycol + NaCl) aqueous solutions at different temperatures and various concentrations of inhibitor in aqueous solution. The equilibrium results were generated using an isochoric pressure-search method. These values are compared with some selected experimental data from the literature on the dissociation conditions of hydrogen sulfide and carbon dioxide simple hydrates in the presence of pure water to show the inhibition effects of the above mentioned aqueous solutions. Comparisons are finally made between our experimental values and the corresponding literature data. Some disagreements among the literature data and our data are found.

  8. NVU perspective on simple liquids’ quasiuniversality

    DEFF Research Database (Denmark)

    Dyre, J. C.

    2013-01-01

    The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact...

  9. Approximation methods in loop quantum cosmology: from Gowdy cosmologies to inhomogeneous models in Friedmann–Robertson–Walker geometries

    International Nuclear Information System (INIS)

    Martín-Benito, Mercedes; Martín-de Blas, Daniel; Marugán, Guillermo A Mena

    2014-01-01

    We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann–Robertson–Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions. (paper)

  10. A CLOSED-FORM EXPRESSION APPROXIMATING THE MIE SOLUTION FOR THE REAL-IN-LINE TRANSMISSION OF CERAMICS WITH SPHERICAL INCLUSIONS OR PORES

    Directory of Open Access Journals (Sweden)

    Pabst W.

    2013-06-01

    Full Text Available A new closed-form expression is presented for estimating the real-in-line transmission of ceramics consisting of non-absorbing phases in dependence of the inclusion or pore size. The classic approximations to the exact Mie solution of the scattering problem for spheres are recalled (Rayleigh, Fraunhofer, Rayleigh-Gans-Debye/RGD, van de Hulst, and it is recalled that the large-size variant of the RGD approximation is the basis of the Apetz-van-Bruggen approach. All approximations and our closed-form expression are compared mutually and vis-a-vis the exact Mie solution. A parametric study is performed for monochromatic light in the visible range (600 nm for two model systems corresponding to composites of yttrium aluminum garnet (YAG, refractive index 1.832 with spherical alumina inclusions (refractive index 1.767, and to porous YAG ceramics with spherical pores (refractive index 1. It is shown that for the YAG-alumina composites to achieve maximum transmission with inclusion volume fractions of 1 % (and slab thickness 1 mm, inclusion sizes of up to 100 nm can be tolerated, while pore sizes of 100 nm will be completely detrimental for porosities as low as 0.1 %. While the van-de-Hulst approximation is excellent for small phase contrast and low concentration of inclusions, it fails for principal reasons for small inclusion or pore sizes. Our closed-form expression, while less precise in the aforementioned special case, is always the safer choice and performs better in most cases of practical interest, including high phase contrasts and high concentrations of inclusions or pores.

  11. A simple analytic approximation to the Rayleigh-Bénard stability threshold

    NARCIS (Netherlands)

    Prosperetti, Andrea

    2011-01-01

    The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the

  12. Solution of the point kinetics equations in the presence of Newtonian temperature feedback by Pade approximations via the analytical inversion method

    International Nuclear Information System (INIS)

    Aboanber, A E; Nahla, A A

    2002-01-01

    A method based on the Pade approximations is applied to the solution of the point kinetics equations with a time varying reactivity. The technique consists of treating explicitly the roots of the inhour formula. A significant improvement has been observed by treating explicitly the most dominant roots of the inhour equation, which usually would make the Pade approximation inaccurate. Also the analytical inversion method which permits a fast inversion of polynomials of the point kinetics matrix is applied to the Pade approximations. Results are presented for several cases of Pade approximations using various options of the method with different types of reactivity. The formalism is applicable equally well to non-linear problems, where the reactivity depends on the neutron density through temperature feedback. It was evident that the presented method is particularly good for cases in which the reactivity can be represented by a series of steps and performed quite well for more general cases

  13. SFU-driven transparent approximation acceleration on GPUs

    NARCIS (Netherlands)

    Li, A.; Song, S.L.; Wijtvliet, M.; Kumar, A.; Corporaal, H.

    2016-01-01

    Approximate computing, the technique that sacrifices certain amount of accuracy in exchange for substantial performance boost or power reduction, is one of the most promising solutions to enable power control and performance scaling towards exascale. Although most existing approximation designs

  14. A Simple, Low-cost, and Robust System to Measure the Volume of Hydrogen Evolved by Chemical Reactions with Aqueous Solutions.

    Science.gov (United States)

    Brack, Paul; Dann, Sandie; Wijayantha, K G Upul; Adcock, Paul; Foster, Simon

    2016-08-17

    There is a growing research interest in the development of portable systems which can deliver hydrogen on-demand to proton exchange membrane (PEM) hydrogen fuel cells. Researchers seeking to develop such systems require a method of measuring the generated hydrogen. Herein, we describe a simple, low-cost, and robust method to measure the hydrogen generated from the reaction of solids with aqueous solutions. The reactions are conducted in a conventional one-necked round-bottomed flask placed in a temperature controlled water bath. The hydrogen generated from the reaction in the flask is channeled through tubing into a water-filled inverted measuring cylinder. The water displaced from the measuring cylinder by the incoming gas is diverted into a beaker on a balance. The balance is connected to a computer, and the change in the mass reading of the balance over time is recorded using data collection and spreadsheet software programs. The data can then be approximately corrected for water vapor using the method described herein, and parameters such as the total hydrogen yield, the hydrogen generation rate, and the induction period can also be deduced. The size of the measuring cylinder and the resolution of the balance can be changed to adapt the setup to different hydrogen volumes and flow rates.

  15. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  16. An accurate analytical solution of a zero-dimensional greenhouse model for global warming

    International Nuclear Information System (INIS)

    Foong, S K

    2006-01-01

    In introducing the complex subject of global warming, books and papers usually use the zero-dimensional greenhouse model. When the ratio of the infrared radiation energy of the Earth's surface that is lost to outer space to the non-reflected average solar radiation energy is small, the model admits an accurate approximate analytical solution-the resulting energy balance equation of the model is a quartic equation that can be solved analytically-and thus provides an alternative solution and instructional strategy. A search through the literature fails to find an analytical solution, suggesting that the solution may be new. In this paper, we review the model, derive the approximation and obtain its solution. The dependence of the temperature of the surface of the Earth and the temperature of the atmosphere on seven parameters is made explicit. A simple and convenient formula for global warming (or cooling) in terms of the percentage change of the parameters is derived. The dependence of the surface temperature on the parameters is illustrated by several representative graphs

  17. A simple approach to the prediction of waterhammer transients in a pipe line with entrapped air

    International Nuclear Information System (INIS)

    Epstein, Michael

    2008-01-01

    The pressure histories within entrapped air bubbles in a pipe line during a waterhammer transient are treated theoretically. A convenient integral method is introduced, which takes full account of air/water interface movement and liquid compressibility. The significance of the method is that it provides a simple equation set for approximating, with good accuracy and with a small degree of conservatism, the solution to a problem that otherwise involves coupled partial differential equations on time dependent domains with non-linear boundary conditions. The accuracy of the method is defined by its comparison with available numerical-solution-predictions and measurements of the pressure within an entrapped-air-bubble at a dead end in a pipe. The method is shown to be a computationally simple and efficient way of assessing the impact of liquid compressibility on pressure rise when multiple water columns and air pockets are present in a pipe line

  18. How long does it take to boil an egg? A simple approach to the energy transfer equation

    Science.gov (United States)

    Roura, P.; Fort, J.; Saurina, J.

    2000-01-01

    The heating of simple geometric objects immersed in an isothermal bath is analysed qualitatively through Fourier's law. The approximate temperature evolution is compared with the exact solution obtained by solving the transport differential equation, the discrepancies being smaller than 20%. Our method succeeds in giving the solution as a function of the Fourier modulus so that the scale laws hold. It is shown that the time needed to homogenize temperature variations that extend over mean distances xm is approximately xm2/icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/>, where icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/> is the thermal diffusivity. This general relationship also applies to atomic diffusion. Within the approach presented there is no need to write down any differential equation. As an example, the analysis is applied to the process of boiling an egg.

  19. A New Method to Solve Numeric Solution of Nonlinear Dynamic System

    Directory of Open Access Journals (Sweden)

    Min Hu

    2016-01-01

    Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

  20. An overview on polynomial approximation of NP-hard problems

    Directory of Open Access Journals (Sweden)

    Paschos Vangelis Th.

    2009-01-01

    Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

  1. Approximate reasoning in physical systems

    International Nuclear Information System (INIS)

    Mutihac, R.

    1991-01-01

    The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

  2. Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

    International Nuclear Information System (INIS)

    Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.

    2009-01-01

    The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.

  3. Direct application of Padé approximant for solving nonlinear differential equations.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

    2014-01-01

    This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

  4. Approximation solutions for indifference pricing under general utility functions

    NARCIS (Netherlands)

    Chen, An; Pelsser, Antoon; Vellekoop, M.H.

    2008-01-01

    With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners

  5. Approximate Solutions for Indifference Pricing under General Utility Functions

    NARCIS (Netherlands)

    Chen, A.; Pelsser, A.; Vellekoop, M.

    2007-01-01

    With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners

  6. Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation

    Directory of Open Access Journals (Sweden)

    Ali Belhocine

    2018-01-01

    Full Text Available In the thermal entrance region, a thermal boundary layer develops and also reaches the circular tube center. The fully developed region is the zone in which the flow is both hydrodynamically and thermally developed. The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the thickness of the thermal boundary layer is zero and decreases gradually to the fully developed value. In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented. By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by Fortran code obtained via using Runge-Kutta fourth order (RK4 method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.

  7. Approximate Analysis of Two-Mass–Spring Systems and Buckling of a Column

    DEFF Research Database (Denmark)

    Ganji, S.S.; Barari, Amin; Ganji, D. D.

    2011-01-01

    Max–Min Approach (MMA) is applied to obtain an approximate solution of three practical cases in terms of a nonlinear oscillation system. After finding maximal and minimal solution thresholds of a nonlinear problem, an approximate solution of the nonlinear equation can be easily achieved using He ...

  8. A molecular-thermodynamic model for polyelectrolyte solutions

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, J.; Liu, H.; Hu, Y. [Thermodynamics Research Laboratory, East China University of Science and Technology, Shanghai 200237 (China); Prausnitz, J.M. [Department of Chemical Engineering, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States)

    1998-01-01

    Polyelectrolyte solutions are modeled as freely tangent-jointed, charged hard-sphere chains and corresponding counterions in a continuum medium with permitivity {var_epsilon}. By adopting the sticky-point model, the Helmholtz function for polyelectrolyte solutions is derived through the r-particle cavity-correlation function (CCF) for chains of sticky, charged hard spheres. The r-CCF is approximated by a product of effective nearest-neighbor two-particle CCFs; these are determined from the hypernetted-chain and mean-spherical closures (HNC/MSA) inside and outside the hard core, respectively, for the integral equation theory for electrolytes. The colligative properties are given as explicit functions of a scaling parameter {Gamma} that can be estimated by a simple iteration procedure. Osmotic pressures, osmotic coefficients, and activity coefficients are calculated for model solutions with various chain lengths. They are in good agreement with molecular simulation and experimental results. {copyright} {ital 1998 American Institute of Physics.}

  9. All-Norm Approximation Algorithms

    NARCIS (Netherlands)

    Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik

    2002-01-01

    A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation

  10. Finite approximations in fluid mechanics

    International Nuclear Information System (INIS)

    Hirschel, E.H.

    1986-01-01

    This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems

  11. Approximate reflection coefficients for a thin VTI layer

    KAUST Repository

    Hao, Qi

    2017-09-18

    We present an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer thickness is assumed to be much smaller than the wavelengths of P- and SV-waves inside. The exact reflection and transmission coefficients are derived by the propagator matrix method. In the case of normal incidence, the exact reflection and transmission coefficients are expressed in terms of the impedances of vertically propagating P- and S-waves. For subcritical incidence, the approximate reflection coefficients are expressed in terms of the contrast in the VTI parameters between the layer and the background. Numerical examples are designed to analyze the reflection coefficients at normal and oblique incidence, and investigate the influence of transverse isotropy on the reflection coefficients. Despite giving numerical errors, the approximate formulae are sufficiently simple to qualitatively analyze the variation of the reflection coefficients with the angle of incidence.

  12. Solutions of the Low equation in the no-crossing approximation

    International Nuclear Information System (INIS)

    Kumar, K.S.; Nogami, Y.

    1979-01-01

    In solving the Low equation for the Chew-Low model, if the crossing term is dropped a ghost state appears in the repulsive channels for a sufficiently large coupling constant. Ernst et al. suggested recently that this difficulty could be avoided by adopting a solution with a Castillejo-Dalitz-Dyson (CDD) pole in its denominator. Contrary to this suggestion, we show that the inclusion of the CDD pole, rather than avoiding the difficulty, only compounds it. We also reexamine Dyson's interpretation of the ''redundant'' CDD solutions, and point out that the Low equation we study possesses solutions to which Dyson's interpretation does not seem to apply

  13. Approximate analytical solutions to the condensation-coagulation equation of aerosols

    DEFF Research Database (Denmark)

    Smith, Naftali R.; Shaviv, Nir J.; Svensmark, Henrik

    2016-01-01

    to the coagulation limit plus a condensation correction. Our solutions are then compared with numerical results. We show that the solutions can be used to estimate the sensitivity of the cloud condensation nuclei number density to the nucleation rate of small condensation nuclei and to changes in the formation rate...

  14. Simple de Sitter solutions

    International Nuclear Information System (INIS)

    Silverstein, Eva

    2008-01-01

    We present a framework for de Sitter model building in type IIA string theory, illustrated with specific examples. We find metastable de Sitter (dS) minima of the potential for moduli obtained from a compactification on a product of two nil three-manifolds (which have negative scalar curvature) combined with orientifolds, branes, fractional Chern-Simons forms, and fluxes. As a discrete quantum number is taken large, the curvature, field strengths, inverse volume, and four-dimensional string coupling become parametrically small, and the de Sitter Hubble scale can be tuned parametrically smaller than the scales of the moduli, Kaluza Klein (KK), and winding mode masses. A subtle point in the construction is that although the curvature remains consistently weak, the circle fibers of the nilmanifolds become very small in this limit (though this is avoided in illustrative solutions at modest values of the parameters). In the simplest version of the construction, the heaviest moduli masses are parametrically of the same order as the lightest KK and winding masses. However, we provide a method for separating these marginally overlapping scales, and more generally the underlying supersymmetry of the model protects against large corrections to the low-energy moduli potential

  15. Approximate representation of optimal strategies from influence diagrams

    DEFF Research Database (Denmark)

    Jensen, Finn V.

    2008-01-01

    , and where the policy functions for the decisions have so large do- mains that they cannot be represented directly in a strategy tree. The approach is to have separate ID representations for each decision variable. In each representation the actual information is fully exploited, however the representation...... of policies for future decisions are approximations. We call the approximation information abstraction. It consists in introducing a dummy structure connecting the past with the decision. We study how to specify, implement and learn information abstraction.......There are three phases in the life of a decision problem, specification, solution, and rep- resentation of solution. The specification and solution phases are off-line, while the rep- resention of solution often shall serve an on-line situation with rather tough constraints on time and space. One...

  16. Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

    Science.gov (United States)

    Kilcrease, D. P.; Brookes, S.

    2013-12-01

    The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert-Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

  17. Exact and approximate Fourier rebinning algorithms for the solution of the data truncation problem in 3-D PET.

    Science.gov (United States)

    Bouallègue, Fayçal Ben; Crouzet, Jean-François; Comtat, Claude; Fourcade, Marjolaine; Mohammadi, Bijan; Mariano-Goulart, Denis

    2007-07-01

    This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.

  18. Solution of the schrodinger equation in one dimension by simple method for a simple step potential

    International Nuclear Information System (INIS)

    Ertik, H.

    2005-01-01

    The coefficients of the transmission and reflection for the simple-step barrier potential were calculated by a simple method. Their values were entirely different from those often encountered in the literature. Especially in the case that the total energy is equal to the barrier potential, the value of 0,20 for the reflection coefficient was obtained whereas this is zero in the literature. This may be considered as an interesting point

  19. Solute transport in aquifers: The comeback of the advection dispersion equation and the First Order Approximation

    Science.gov (United States)

    Fiori, A.; Zarlenga, A.; Jankovic, I.; Dagan, G.

    2017-12-01

    Natural gradient steady flow of mean velocity U takes place in heterogeneous aquifers of random logconductivity Y = lnK , characterized by the normal univariate PDF f(Y) and autocorrelation ρY, of variance σY2 and horizontal integral scale I. Solute transport is quantified by the Breakthrough Curve (BTC) M at planes at distance x from the injection plane. The study builds on the extensive 3D numerical simulations of flow and transport of Jankovic et al. (2017) for different conductivity structures. The present study further explores the predictive capabilities of the Advection Dispersion Equation (ADE), with macrodispersivity αL given by the First Order Approximation (FOA), by checking in a quantitative manner its applicability. After a discussion on the suitable boundary conditions for ADE, we find that the ADE-FOA solution is a sufficiently accurate predictor for applications, the many other sources of uncertainty prevailing in practice notwithstanding. We checked by least squares and by comparison of travel time of quantiles of M that indeed the analytical Inverse Gaussian M with αL =σY2 I , is able to fit well the bulk of the simulated BTCs. It tends to underestimate the late arrival time of the thin and persistent tail. The tail is better reproduced by the semi-analytical MIMSCA model, which also allows for a physical explanation of the success of the Inverse Gaussian solution. Examination of the pertinent longitudinal mass distribution shows that it is different from the commonly used Gaussian one in the analysis of field experiments, and it captures the main features of the plume measurements of the MADE experiment. The results strengthen the confidence in the applicability of the ADE and the FOA to predicting longitudinal spreading in solute transport through heterogeneous aquifers of stationary random structure.

  20. Stochastic quantization and mean field approximation

    International Nuclear Information System (INIS)

    Jengo, R.; Parga, N.

    1983-09-01

    In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)

  1. Approximate maximum parsimony and ancestral maximum likelihood.

    Science.gov (United States)

    Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat

    2010-01-01

    We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.

  2. Tension and Approximation in Poetic Translation

    Science.gov (United States)

    Al-Shabab, Omar A. S.; Baka, Farida H.

    2015-01-01

    Simple observation reveals that each language and each culture enjoys specific linguistic features and rhetorical traditions. In poetry translation difference and the resultant linguistic tension create a gap between Source Language and Target language, a gap that needs to be bridged by creating an approximation processed through the translator's…

  3. Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

    Science.gov (United States)

    Bardhan, Jaydeep P

    2008-10-14

    The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement

  4. A simple stationary semi-analytical wake model

    DEFF Research Database (Denmark)

    Larsen, Gunner Chr.

    We present an idealized simple, but fast, semi-analytical algorithm for computation of stationary wind farm wind fields with a possible potential within a multi-fidelity strategy for wind farm topology optimization. Basically, the model considers wakes as linear perturbations on the ambient non......-linear. With each of these approached, a parabolic system are described, which is initiated by first considering the most upwind located turbines and subsequently successively solved in the downstream direction. Algorithms for the resulting wind farm flow fields are proposed, and it is shown that in the limit......-uniform mean wind field, although the modelling of the individual stationary wake flow fields includes non-linear terms. The simulation of the individual wake contributions are based on an analytical solution of the thin shear layer approximation of the NS equations. The wake flow fields are assumed...

  5. Thermodynamic properties of sticky electrolytes in the HNC/MS approximation

    International Nuclear Information System (INIS)

    Herrera, J.N.; Blum, L.

    1991-01-01

    We study an approximation for a model which combines the sticky potential of Baxter and charged spheres. In the hypernetted chain (HNC)/mean spherical approximation (MSA), simple expressions for the thermodynamic functions are obtained. There equations should be useful in representing the properties of real electrolytes. Approximate expressions that are similar to those of the primitive model are obtained, for low densities (concentrations) of the electrolyte (Author)

  6. Discovery of functional and approximate functional dependencies in relational databases

    Directory of Open Access Journals (Sweden)

    Ronald S. King

    2003-01-01

    Full Text Available This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.

  7. Approximate, analytic solutions of the Bethe equation for charged particle range

    OpenAIRE

    Swift, Damian C.; McNaney, James M.

    2009-01-01

    By either performing a Taylor expansion or making a polynomial approximation, the Bethe equation for charged particle stopping power in matter can be integrated analytically to obtain the range of charged particles in the continuous deceleration approximation. Ranges match reference data to the expected accuracy of the Bethe model. In the non-relativistic limit, the energy deposition rate was also found analytically. The analytic relations can be used to complement and validate numerical solu...

  8. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  9. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  10. An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation

    KAUST Repository

    Hao, Q.

    2017-05-26

    We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.

  11. An Approximate Method for the Acoustic Attenuating VTI Eikonal Equation

    KAUST Repository

    Hao, Q.; Alkhalifah, Tariq Ali

    2017-01-01

    We present an approximate method to solve the acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis (VTI). A perturbation method is used to derive the perturbation formula for complex-valued traveltimes. The application of Shanks transform further enhances the accuracy of approximation. We derive both analytical and numerical solutions to the acoustic eikonal equation. The analytic solution is valid for homogeneous VTI media with moderate anellipticity and strong attenuation and attenuation-anisotropy. The numerical solution is applicable for inhomogeneous attenuating VTI media.

  12. Approximation of the decay of fission and activation product mixtures

    International Nuclear Information System (INIS)

    Henderson, R.W.

    1991-01-01

    The decay of the exposure rate from a mixture of fission and activation products is a complex function of time. The exact solution of the problem involves the solution of more than 150 tenth order Bateman equations. An approximation of this function is required for the practical solution of problems involving multiple integrations of this function. Historically this has been a power function, or a series of power functions, of time. The approach selected here has been to approximate the decay with a sum of exponential functions. This produces a continuous, single valued function, that can be made to approximate the given decay scheme to any desired degree of closeness. Further, the integral of the sum is easily calculated over any period. 3 refs

  13. A Simple Decontamination Approach Using Hydrogen ...

    Science.gov (United States)

    Journal article To evaluate the use of relatively low levels of hydrogen peroxide vapor (HPV) for the inactivation of Bacillus anthracis spores within an indoor environment. Methods and Results: Laboratory-scale decontamination tests were conducted using bacterial spores of both B. anthracis Ames and Bacillus atrophaeus inoculated onto several types of materials. Pilot-scale tests were also conducted using a larger chamber furnished as an indoor office. Commercial off-the-shelf (COTS) humidifiers filled with aqueous solutions of 3% or 8% hydrogen peroxide were used to generate the HPV inside the mock office. The spores were exposed to the HPV for periods ranging from 8 hours up to one week. Conclusions: Four to seven day exposures to low levels of HPV (average air concentrations of approximately 5-10 parts per million) were effective in inactivating B. anthracis spores on multiple materials. The HPV can be generated with COTS humidifiers and household H2O2 solutions. With the exception of one test/material, B. atrophaeus spores were equally or more resistant to HPV inactivation compared to those from B. anthracis Ames. Significance and Impact of Study: This simple and effective decontamination method is another option that could be widely applied in the event of a B. anthracis spore release.

  14. Hamilton-Jacobi equation and the breaking of the WKB approximation

    Energy Technology Data Exchange (ETDEWEB)

    Canfora, F. [Istituto Nazionale di Fisica Nucleare, GC di Salerno (Italy) and Dipartimento di Fisica E.R. Caianiello, Universita di Salerno, Via S. Allende, 84081 Baronissi (Salerno) (Italy)]. E-mail: canfora@sa.infn.it

    2005-03-17

    A simple method to deal with four-dimensional Hamilton-Jacobi equation for null hypersurfaces is introduced. This method allows to find simple geometrical conditions which give rise to the failure of the WKB approximation on curved spacetimes. The relation between such failure, extreme blackholes and the Cosmic Censor hypothesis is briefly discussed.

  15. Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm

    Directory of Open Access Journals (Sweden)

    Zaer Abo-Hammour

    2014-01-01

    Full Text Available A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch’s and Bratu’s problems. The underlying idea of the method is to convert the two differential problems into discrete versions by replacing each of the second derivatives by an appropriate difference quotient approximation. The new method has the following characteristics. First, it should not resort to more advanced mathematical tools; that is, the algorithm should be simple to understand and implement and should be thus easily accepted in the mathematical and physical application fields. Second, the algorithm is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical and physical problems. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. The algorithm is tested on different versions of Troesch’s and Bratu’s problems. Experimental results show that the proposed algorithm is effective, straightforward, and simple.

  16. Comment on ''Semiclassical treatment of vibrational--translational energy transfer in the near-adiabatic approximation''

    International Nuclear Information System (INIS)

    Cady, W.A.; Clark, A.P.; Dickinson, A.S.

    1975-01-01

    Recently a near-adiabatic (perturbed stationary states) approximation was used in an investigation the collinear vibrational excitation of a harmonic oscillator. This approximation reduced the problem to that of obtaining transition probabilities for a harmonic oscillator with time-dependent forcing function. Cady derived an apparently exact solution for this problem. It is shown that this solution is not exact but that the solution results from making a further adiabatic approximation and a derivation is given that clearly shows the adiabatic character of this further approximation

  17. An approximate solution of the two-group critical problem for reflected slabs

    International Nuclear Information System (INIS)

    Ishiguro, Y.; Garcia, R.D.M.

    1977-01-01

    A new approximation is developed to solve two group slab problems involving two media where one of the media is infinite. The method consists in combining the P sub(L) approximation with invariance principles. Several numerical results are reported for the critical slab problem [pt

  18. VMOMS: a computer code for finding moment solutions to the Grad-Shafranov equation

    International Nuclear Information System (INIS)

    Lao, L.L.; Wieland, R.M.; Houlberg, W.A.; Hirshman, S.P.

    1982-02-01

    A code VMOMS is described which finds approximate solutions to the Grad-Shafranov equation describing scalar pressure-balance equilibria for axisymmetric tokamak plasmas. A Fourier series expansion of the flux surface coordinates (R,Z) is made in terms of two new coordinates (rho, theta), and the resulting equation is conveniently reduced to a system of ordinary differential equations (ODE's) using a variational principle. The solution of these simple equations with pressure and current as driving functions, yields, in principle, a complete description of the equilibrium. Complete axisymmetry is assumed, as well as up-down symmetry about the toroidal midplane

  19. A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

    Science.gov (United States)

    Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

    2018-03-01

    Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

  20. Theoretical study of the countercurrent in an ultracentrifuge-approximate solution of the countercurrent equations

    Energy Technology Data Exchange (ETDEWEB)

    Jacques, R.

    1975-03-15

    Integrating the linearized Navier-Stokes equations linearized along the whole length of the centrifuge, we get a differential relation between the mean axial velocity and the centrifugal and viscosity forces on the ends. Then, these equations are integrated near the ends by a boundary layer approximation method. We assume that outside the boundary layer, the axial velocity reaches its mean value. So we obtain on the first hand the repartition of all physical quantities in the boundary layer, on the second hand a differential equation between the mean axial velocity and the boundary conditions imposed on the ends. This equation, valid both for the mechanical and thermal counter-current is solved numerically. Its solution shows the existence of a second boundary layer close to the wall of the tube. The present theory extends Martin's one in that it takes into account: (1) the action of pressure forces; (2) zero velocity on the wall with no transport; (3) the interaction between mechanical and thermal effects which tend to decrease the efficiency and the intensity of the counter-current. (author)

  1. Symmetric approximations of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Kobel'kov, G M

    2002-01-01

    A new method for the symmetric approximation of the non-stationary Navier-Stokes equations by a Cauchy-Kovalevskaya-type system is proposed. Properties of the modified problem are studied. In particular, the convergence as ε→0 of the solutions of the modified problem to the solutions of the original problem on an infinite interval is established

  2. Approximate source conditions for nonlinear ill-posed problems—chances and limitations

    International Nuclear Information System (INIS)

    Hein, Torsten; Hofmann, Bernd

    2009-01-01

    In the recent past the authors, with collaborators, have published convergence rate results for regularized solutions of linear ill-posed operator equations by avoiding the usual assumption that the solutions satisfy prescribed source conditions. Instead the degree of violation of such source conditions is expressed by distance functions d(R) depending on a radius R ≥ 0 which is an upper bound of the norm of source elements under consideration. If d(R) tends to zero as R → ∞ an appropriate balancing of occurring regularization error terms yields convergence rates results. This approach was called the method of approximate source conditions, originally developed in a Hilbert space setting. The goal of this paper is to formulate chances and limitations of an application of this method to nonlinear ill-posed problems in reflexive Banach spaces and to complement the field of low order convergence rates results in nonlinear regularization theory. In particular, we are going to establish convergence rates for a variant of Tikhonov regularization. To keep structural nonlinearity conditions simple, we update the concept of degree of nonlinearity in Hilbert spaces to a Bregman distance setting in Banach spaces

  3. Effects of radical scavengers on aqueous solutions exposed to heavy-ion irradiation using the liquid microjet technique

    Science.gov (United States)

    Nomura, Shinji; Tsuchida, Hidetsugu; Furuya, Ryousuke; Miyahara, Kento; Majima, Takuya; Itoh, Akio

    2015-12-01

    The effects of the radical scavenger ascorbic acid on water radiolysis are studied by fast heavy-ion irradiation of aqueous solutions of ascorbic acid, using the liquid microjet technique under vacuum. To understand the reaction mechanisms of hydroxyl radicals in aqueous solutions, we directly measure secondary ions emitted from solutions with different ascorbic acid concentrations. The yield of hydronium secondary ions is strongly influenced by the reaction between ascorbic acid and hydroxyl radicals. From analysis using a simple model considering chemical equilibria, we determine that the upper concentration limit of ascorbic acid with a radical scavenger effect is approximately 70 μM.

  4. Effects of radical scavengers on aqueous solutions exposed to heavy-ion irradiation using the liquid microjet technique

    Energy Technology Data Exchange (ETDEWEB)

    Nomura, Shinji [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Tsuchida, Hidetsugu, E-mail: tsuchida@nucleng.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Quantum Science and Engineering Center, Kyoto University, Uji 611-0011 (Japan); Furuya, Ryousuke; Miyahara, Kento [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Majima, Takuya; Itoh, Akio [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Quantum Science and Engineering Center, Kyoto University, Uji 611-0011 (Japan)

    2015-12-15

    The effects of the radical scavenger ascorbic acid on water radiolysis are studied by fast heavy-ion irradiation of aqueous solutions of ascorbic acid, using the liquid microjet technique under vacuum. To understand the reaction mechanisms of hydroxyl radicals in aqueous solutions, we directly measure secondary ions emitted from solutions with different ascorbic acid concentrations. The yield of hydronium secondary ions is strongly influenced by the reaction between ascorbic acid and hydroxyl radicals. From analysis using a simple model considering chemical equilibria, we determine that the upper concentration limit of ascorbic acid with a radical scavenger effect is approximately 70 μM.

  5. Effects of radical scavengers on aqueous solutions exposed to heavy-ion irradiation using the liquid microjet technique

    International Nuclear Information System (INIS)

    Nomura, Shinji; Tsuchida, Hidetsugu; Furuya, Ryousuke; Miyahara, Kento; Majima, Takuya; Itoh, Akio

    2015-01-01

    The effects of the radical scavenger ascorbic acid on water radiolysis are studied by fast heavy-ion irradiation of aqueous solutions of ascorbic acid, using the liquid microjet technique under vacuum. To understand the reaction mechanisms of hydroxyl radicals in aqueous solutions, we directly measure secondary ions emitted from solutions with different ascorbic acid concentrations. The yield of hydronium secondary ions is strongly influenced by the reaction between ascorbic acid and hydroxyl radicals. From analysis using a simple model considering chemical equilibria, we determine that the upper concentration limit of ascorbic acid with a radical scavenger effect is approximately 70 μM.

  6. Approximate reflection coefficients for a thin VTI layer

    KAUST Repository

    Hao, Qi; Stovas, Alexey

    2017-01-01

    We present an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer

  7. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

    Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

  8. Simple models with ALICE fluxes

    CERN Document Server

    Striet, J

    2000-01-01

    We introduce two simple models which feature an Alice electrodynamics phase. In a well defined sense the Alice flux solutions we obtain in these models obey first order equations similar to those of the Nielsen-Olesen fluxtube in the abelian higgs model in the Bogomol'nyi limit. Some numerical solutions are presented as well.

  9. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren

    2017-01-01

    , obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose

  10. Approximative calculation of transient short-circuit currents in power-systems

    Energy Technology Data Exchange (ETDEWEB)

    Heuck, K; Rosenberger, R; Dettmann, K D; Kegel, R

    1986-08-01

    The paper shows that it is approximatively possible to calculate the transient short-circuit currents for symmetrical and asymmetrical faults in power-systems. For that purpose a simple equivalent network is found. Its error of approximation is small. For the important maximum short-circuit current limits of error are pointed out compared to VDE 0102.

  11. A single continuum approximation of the solute transport in fractured porous media

    International Nuclear Information System (INIS)

    Jeong, J.T.; Lee, K.J.

    1992-01-01

    Solute transport in fractured porous media is described by the single continuum model, i.e., equivalent porous medium model. In this model, one-dimensional solute transport in the fracture and two-dimensional solute transport in the porous rock matrix is considered. The network of fractures embedded in the porous rock matrix is idealized as two orthogonally intersecting families of equally spaced, parallel fractures directed at 45 o to the regional groundwater flow direction. Governing equations are solved by the finite element method, and an upstream weighting technique is used in order to prevent the oscillation of the solution in the case of highly advection dominated transport. Breakthrough curves, similar to those of the one-dimensional solute transport problem in ordinary porous media, are obtained as a function of time according to volume or flux averaging of the concentration profile across the width of the flow region. The equivalent parameters, i.e., porosity and overall coefficient of longitudinal dispersivity, are obtained by a trial-and-error method. Analyses for the non-sorbing solute transport case show that within the range of considered parameters, and except for the region very close to the source, application of the single continuum model in the idealized fracture system is sufficient for modeling solute transport in fractured porous media. This numerical scheme is shown to be applicable to a sorbing solute and radionuclide transport. (author)

  12. Stability of Bifurcating Stationary Solutions of the Artificial Compressible System

    Science.gov (United States)

    Teramoto, Yuka

    2018-02-01

    The artificial compressible system gives a compressible approximation of the incompressible Navier-Stokes system. The latter system is obtained from the former one in the zero limit of the artificial Mach number ɛ which is a singular limit. The sets of stationary solutions of both systems coincide with each other. It is known that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion, then it is also stable as a solution of the artificial compressible one for sufficiently small ɛ . In general, the range of ɛ shrinks when the spectrum of the linearized operator for the incompressible system approaches to the imaginary axis. This can happen when a stationary bifurcation occurs. It is proved that when a stationary bifurcation from a simple eigenvalue occurs, the range of ɛ can be taken uniformly near the bifurcation point to conclude the stability of the bifurcating solution as a solution of the artificial compressible system.

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

    International Nuclear Information System (INIS)

    Adzri, E. P.

    2012-09-01

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

  14. Criticality safety validation: Simple geometry, single unit 233U systems

    International Nuclear Information System (INIS)

    Putman, V.L.

    1997-06-01

    Typically used LMITCO criticality safety computational methods are evaluated for suitability when applied to INEEL 233 U systems which reasonably can be modeled as simple-geometry, single-unit systems. Sixty-seven critical experiments of uranium highly enriched in 233 U, including 57 aqueous solution, thermal-energy systems and 10 metal, fast-energy systems, were modeled. These experiments include 41 cylindrical and 26 spherical cores, and 41 reflected and 26 unreflected systems. No experiments were found for intermediate-neutron-energy ranges, or with interstitial non-hydrogenous materials typical of waste systems, mixed 233 U and plutonium, or reflectors such as steel, lead, or concrete. No simple geometry experiments were found with cubic or annular cores, or approximating infinite sea systems. Calculations were performed with various tools and methodologies. Nine cross-section libraries, based on ENDF/B-IV, -V, or -VI.2, or on Hansen-Roach source data, were used with cross-section processing methods of MCNP or SCALE. The k eff calculations were performed with neutral-particle transport and Monte Carlo methods of criticality codes DANT, MCNP 4A, and KENO Va

  15. Improved Dutch Roll Approximation for Hypersonic Vehicle

    Directory of Open Access Journals (Sweden)

    Liang-Liang Yin

    2014-06-01

    Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.

  16. Comparison of the Debye–Hückel and the Mean Spherical Approximation Theories for Electrolyte Solutions

    DEFF Research Database (Denmark)

    Maribo-Mogensen, Bjørn; Kontogeorgis, Georgios M.; Thomsen, Kaj

    2012-01-01

    The thermodynamics of electrolyte solutions has been investigated by many scientists throughout the last century. While several theories have been presented, the most popular models for the electrostatic interactions are based on the Debye–Hückel and mean spherical approximation (MSA) theories....... In this paper we investigate the differences between the Debye–Hückel and the MSA theories, and comparisons of the numerical results for the Helmholtz energy and its derivatives with respect to temperature, volume and composition are presented. The investigation shows that the nonrestricted primitive MSA...... theory performs similarly to Debye–Hückel, despite the differences in the derivation. We furthermore show that the static permittivity is a key parameter for both models and that in many cases it completely dominates the results obtained from the two models. Consequently, we conclude that the simpler...

  17. Mathematical analysis, approximation theory and their applications

    CERN Document Server

    Gupta, Vijay

    2016-01-01

    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  18. An approximation to the interference term using Frobenius Method

    Energy Technology Data Exchange (ETDEWEB)

    Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mail: aquilino@lmp.ufrj.br

    2007-07-01

    An analytical approximation of the interference term {chi}(x,{xi}) is proposed. The approximation is based on the differential equation to {chi}(x,{xi}) using the Frobenius method and the parameter variation. The analytical expression of the {chi}(x,{xi}) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U{sup 238} isotope for different energies and temperature ranges. (author)

  19. An approximation to the interference term using Frobenius Method

    International Nuclear Information System (INIS)

    Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da

    2007-01-01

    An analytical approximation of the interference term χ(x,ξ) is proposed. The approximation is based on the differential equation to χ(x,ξ) using the Frobenius method and the parameter variation. The analytical expression of the χ(x,ξ) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U 238 isotope for different energies and temperature ranges. (author)

  20. A simple model for predicting solute concentration in agricultural tile lines shortly after application

    Directory of Open Access Journals (Sweden)

    T. S. Steenhuis

    1997-01-01

    Full Text Available Agricultural tile drainage lines have been implicated as a source of pesticide contamination of surface waters. Field experiments were conducted and a simple model was developed to examine preferential transport of applied chemicals to agricultural tile lines. The conceptual model consists of two linear reservoirs, one near the soil surface and one near the tile drain. The connection between the two reservoirs is via preferential flow paths with very little interaction with the soil matrix. The model assumes that only part of the field contributes solutes to the tile drain. The model was evaluated with data from the field experiments in which chloride, 2,4-D, and atrazine concentrations were measured on eight tile-drained plots that were irrigated twice. Atrazine was applied two months prior to the experiment, 2,4-D was sprayed just before the first irrigation, and chloride before the second irrigation. All three chemicals were found in the tile effluent shortly after the rainfall began. Generally, the concentration increased with increased flow rates and decreased exponentially after the rainfall ceased. Although the simple model could simulate the observed chloride concentration patterns in the tile outflow for six of the eight plots, strict validation was not possible because of the difficulty with independent measurement of the data needed for a preferential flow model applied to field conditions. The results show that, to simulate pesticide concentration in tile lines, methods that can measure field averaged preferential flow characteristics need to be developed.

  1. Newtonian and post-Newtonian approximations are asymptotic to general relativity

    International Nuclear Information System (INIS)

    Futamase, T.; Schutz, B.F.

    1983-01-01

    A precise definition of the Newtonian and post-Newtonian hierarchy of approximations to general relativity is given by studying a C/sup infinity/ sequence of solutions to Einstein's equations that is defined by initial data having the Newtonian scaling property: v/sup i/approx.epsilon, rhoapprox.epsilon 2 , papprox.epsilon 4 , where epsilon is the parameter along the sequence. We map one solution in the sequence to another by identifying them at constant spatial position x/sup i/ and Newtonian dynamical time tau = epsilont. This mapping defines a congruence parametrized by epsilon, and the various post-Newtonian approximations emerge as derivatives of the relativistic solutions along this congruence. We thereby show for the first time that the approximations are genuine asymptotic approximations to general relativity. The proof is given in detail up to first post-Newtonian order, but is easily extended. The results will be applied in the following paper to radiation reaction in binary star systems, to give a proof of the validity of the ''quadrupole formula'' free from any divergences

  2. Spherical anharmonic oscillator in self-similar approximation

    International Nuclear Information System (INIS)

    Yukalova, E.P.; Yukalov, V.I.

    1992-01-01

    The method of self-similar approximation is applied here for calculating the eigenvalues of the three-dimensional spherical anharmonic oscillator. The advantage of this method is in its simplicity and high accuracy. The comparison with other known analytical methods proves that this method is more simple and accurate. 25 refs

  3. A simple electron plasma wave

    International Nuclear Information System (INIS)

    Brodin, G.; Stenflo, L.

    2017-01-01

    Considering a class of solutions where the density perturbations are functions of time, but not of space, we derive a new exact large amplitude wave solution for a cold uniform electron plasma. This result illustrates that most simple analytical solutions can appear even if the density perturbations are large. - Highlights: • The influence of large amplitude electromagnetic waves on electrostatic oscillations is found. • A generalized Mathieu equation is derived. • Anharmonic wave profiles are computed numerically.

  4. A simple electron plasma wave

    Energy Technology Data Exchange (ETDEWEB)

    Brodin, G., E-mail: gert.brodin@physics.umu.se [Department of Physics, Umeå University, SE-901 87 Umeå (Sweden); Stenflo, L. [Department of Physics, Linköping University, SE-581 83 Linköping (Sweden)

    2017-03-18

    Considering a class of solutions where the density perturbations are functions of time, but not of space, we derive a new exact large amplitude wave solution for a cold uniform electron plasma. This result illustrates that most simple analytical solutions can appear even if the density perturbations are large. - Highlights: • The influence of large amplitude electromagnetic waves on electrostatic oscillations is found. • A generalized Mathieu equation is derived. • Anharmonic wave profiles are computed numerically.

  5. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

  6. Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

    Science.gov (United States)

    Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

    2018-04-01

    Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

  7. Polynomial approximation on polytopes

    CERN Document Server

    Totik, Vilmos

    2014-01-01

    Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

  8. Modeling rainfall infiltration on hillslopes using Flux-concentration relation and time compression approximation

    Science.gov (United States)

    Wang, Jie; Chen, Li; Yu, Zhongbo

    2018-02-01

    Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.

  9. Laplace transform homotopy perturbation method for the approximation of variational problems.

    Science.gov (United States)

    Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R

    2016-01-01

    This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.

  10. On the convergence of multigroup discrete-ordinates approximations

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  11. Spherical harmonics and energy polynomial solution of the Boltzmann equation for neutrons, 1

    International Nuclear Information System (INIS)

    Toledo, P.S. de

    1974-01-01

    The approximate solution of the source-free energy-dependent Boltzmann transport equation for neutrons in plane geometry and isotropic scattering case was given by Leonard and Ferziger using a truncated development in a series of energy-polynomials for the energy dependent neutron flux and solving exactly for the angular dependence. The presence in the general solution of eigenfunctions belonging to a continuous spectrum gives rise to difficult analytical problems in the application of their method even to simple problems. To avoid such difficulties, the angular dependence is treated by a spherical harmonics method and a general solution of the energy-dependent transport equation in plane geometry and isotropic scattering is obtained, in spite of the appearance of matrices as argument of the angular polynomials [pt

  12. Nernst effect beyond the relaxation-time approximation

    OpenAIRE

    Pikulin, D. I.; Hou, Chang-Yu; Beenakker, C. W. J.

    2011-01-01

    Motivated by recent interest in the Nernst effect in cuprate superconductors, we calculate this magneto-thermo-electric effect for an arbitrary (anisotropic) quasiparticle dispersion relation and elastic scattering rate. The exact solution of the linearized Boltzmann equation is compared with the commonly used relaxation-time approximation. We find qualitative deficiencies of this approximation, to the extent that it can get the sign wrong of the Nernst coefficient. Ziman's improvement of the...

  13. Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

    Science.gov (United States)

    Ladiges, Daniel R.; Sader, John E.

    2018-05-01

    Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

  14. On an Approximate Solution Method for the Problem of Surface and Groundwater Combined Movement with Exact Approximation on the Section Line

    Directory of Open Access Journals (Sweden)

    L.L. Glazyrina

    2016-12-01

    Full Text Available In this paper, the initial-boundary problem for two nonlinear parabolic combined equations has been considered. One of the equations is set on the bounded domain Ω from R2, another equation is set along the curve lying in Ω. Both of the equations are parabolic equations with double degeneration. The degeneration can be present at the space operator. Furthermore, the nonlinear function which is under the sign of partial derivative with respect to the variable t, can be bound to zero. This problem has an applied character: such structure is needed to describe the process of surface and ground water combined movement. In this case, the desired function determines the level of water above the given impenetrable bottom, the section simulates the riverbed. The Bussinesk equation has been used for mathematical description of the groundwater filtration process in the domain Ω; a diffusion analogue of the Saint-Venant's system has been used on the section for description of the process of water level change in the open channel. Earlier, the authors proved the theorems of generalized solution existence and uniqueness for the considered problem from the functions classes which are called strengthened Sobolev spaces in the literature. To obtain these results, we used the technique which was created by the German mathematicians (H.W. Alt, S. Luckhaus, F. Otto to establish the correctness of the problems with a double degeneration. In this paper, we have proposed and investigated an approximate solution method for the above-stated problem. This method has been constructed using semidiscretization with respect to the variable t and the finite element method for space variables. Triangulation of the domain has been accomplished by triangles. The mesh has been set on the section line. On each segment of the line section lying between the nearby mesh points, on both side of this segment we have constructed the triangles with a common side which matches with

  15. Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method

    International Nuclear Information System (INIS)

    Alomari, A. K.; Noorani, M. S. M.; Nazar, R.

    2008-01-01

    We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter ħ, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method

  16. An approximate and an analytical solution to the carousel-pendulum problem

    Energy Technology Data Exchange (ETDEWEB)

    Vial, Alexandre [Pole Physique, Mecanique, Materiaux et Nanotechnologies, Universite de technologie de Troyes, 12, rue Marie Curie BP-2060, F-10010 Troyes Cedex (France)], E-mail: alexandre.vial@utt.fr

    2009-09-15

    We show that an improved solution to the carousel-pendulum problem can be easily obtained through a first-order Taylor expansion, and its accuracy is determined after the obtention of an unusable analytical exact solution, advantageously replaced by a numerical one. It is shown that the accuracy is unexpectedly high, even when the ratio length of the pendulum to carousel radius approaches unity. (letters and comments)

  17. TN approximation to reflected slab and computation of the critical half thicknesses

    International Nuclear Information System (INIS)

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

    2006-01-01

    The criticality solution to one-speed neutron transport equation using the T N approximation is described for reflected slab. In the solution, Marshak type boundary condition is used. The critical half thicknesses are computed for different values of c and reflection coefficients. Computations are made by using the both T N and P N approximation for the comparison

  18. Solid-soluted content of cerium in solid solution of sphene

    International Nuclear Information System (INIS)

    Zhao Wei; Teng Yuancheng; Li Yuxiang; Ren Xuetan; Huang Junjun

    2010-01-01

    The sphene solid solution was synthesized by solid-state method,with calcium carbonate, silica, titanium dioxide, cerium oxalate and alumina as raw materials. The solid-soluted content of cerium in sphene was researched by means of X-ray diffraction (XRD), backscattering scanning electron microscopy (BSE), energy dispersive spectroscopy (EDS) and so on. The influence of A l3+ ion introduction to sphene on the solid-soluted content of cerium in sphene solid solution was studied. The results indicate that when introducing Al 3+ to sphene as electrovalence compensation, Ce 4+ could be well solidified to Ca 1-x Ce x Ti 1-2x A l2x SiO 5 , and the solid-soluted content is approximately 12.61%. With no electrovalence compensation, Ce 4+ could be solidified to Ca 1-2x Ce x TiSiO 5 , and the solid-soluted content is approximately 10.98%. The appropriate synthesis temperature of sphene solid solution is 1 260 degree C.(authors)

  19. An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    M. Bishehniasar

    2017-01-01

    Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

  20. Spline approximation, Part 1: Basic methodology

    Science.gov (United States)

    Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

    2018-04-01

    In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

  1. Optimized theory for simple and molecular fluids.

    Science.gov (United States)

    Marucho, M; Montgomery Pettitt, B

    2007-03-28

    An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

  2. Merging Belief Propagation and the Mean Field Approximation

    DEFF Research Database (Denmark)

    Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

    2010-01-01

    We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....

  3. Independent center, independent electron approximation for dynamics of molecules and clusters

    International Nuclear Information System (INIS)

    McGuire, J.H.; Straton, J.C.; Wang, J.; Wang, Y.D.; Weaver, O.L.; Corchs, S.E.; Rivarola, R.D.

    1996-01-01

    A formalism is developed for evaluating probabilities and cross sections for multiple-electron transitions in scattering of molecules and clusters by charged collision partners. First, the molecule is divided into subclusters each made up of identical centers (atoms). Within each subcluster coherent scattering from identical centers may lead to observable phase terms and a geometrical structure factor. Then, using a mean field approximation to describe the interactions between centers we obtain A I ∼ summation k product ke iδ k I A Ik . Second, the independent electron approximation for each center may be obtained by neglecting the correlation between electrons in each center. The probability amplitude for each center is then a product of single electron transition probability amplitudes, a Ik i , i.e. A Ik ≅ product iaik i . Finally, the independent subcluster approximation is introduced by neglecting the interactions between different subclusters in the molecule or cluster. The total probability amplitude then reduces to a simple product of amplitudes for each subcluster, A≅ product IAI . Limitations of this simple approximation are discussed. copyright 1996 American Institute of Physics

  4. Steepest descent approximations for accretive operator equations

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1993-03-01

    A necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators defined on a uniformly smooth Banach space. (author). 49 refs

  5. The relaxation time approximation

    International Nuclear Information System (INIS)

    Gairola, R.P.; Indu, B.D.

    1991-01-01

    A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs

  6. Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn Sham density functional theory

    International Nuclear Information System (INIS)

    Gonis, Antonios; Daene, Markus W.; Nicholson, Don M.; Stocks, George Malcolm

    2012-01-01

    We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.

  7. Validity of various approximations for the Bethe-Salpeter equation and their WKB quantization

    International Nuclear Information System (INIS)

    Silvestre-Brac, B.; Bilal, A.; Gignoux, C.; Schuck, P.

    1984-01-01

    The validity of the instantaneous approximation for the Bethe-Salpeter equation is questioned within the framework of the simple scalar-scalar model of Cutkosky. Detailed numerous results for various approximations are compared to the exact ones. WKB quantization is applied to these relativistic approximations. An unexpected question arises: is the currently used Bethe-Salpeter equation (i.e., the ladder approximation) well suited to describe two interacting relativistic particles

  8. Effective Summation and Interpolation of Series by Self-Similar Root Approximants

    Directory of Open Access Journals (Sweden)

    Simon Gluzman

    2015-06-01

    Full Text Available We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined.

  9. Approximate seismic analysis of piping or equipment mounted on elastoplastic structures

    International Nuclear Information System (INIS)

    Villaverde, R.

    1990-01-01

    A simple approximate procedure is presented to estimate the maximum response of equipment, piping, or any other light secondary system mounted on nonlinear structures subjected to earthquake ground motions. The procedure is based on the consideration of structure and equipment as an integrated combined system, and on a response spectrum method for the analysis of nonlinear multistory structures. It is formulated in terms of the initial dynamic properties of the independent structure and equipment components, and the nonlinear response spectrum of a specified earthquake ground motion. It may be applied to any linear multiple-degree-of-freedom secondary system connected at one or two arbitrary points of a multistory structure. It fully takes into account the interaction between primary and secondary systems and the nonclassical damping character of structure-equipment systems. It is restricted, however, to structures with elastoplastic load-deformation behaviour and to those cases in which the mass of the secondary system is small in comparison with the mass of the structure. Its accuracy is evaluated by means of a comparative study with the numerical integration solutions of a number of idealized systems. In this comparative study, the proposed procedure estimates the numerical integration solutions with an average error of about 2 per cent. (author)

  10. Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

    Science.gov (United States)

    Fymat, A. L.; Smith, C. B.

    1979-01-01

    It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

  11. Approximate Bayesian computation.

    Directory of Open Access Journals (Sweden)

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  12. Perturbative corrections for approximate inference in gaussian latent variable models

    DEFF Research Database (Denmark)

    Opper, Manfred; Paquet, Ulrich; Winther, Ole

    2013-01-01

    Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....

  13. An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

    Science.gov (United States)

    Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

    2010-07-01

    The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

  14. Euclidean shortest paths exact or approximate algorithms

    CERN Document Server

    Li, Fajie

    2014-01-01

    This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.

  15. A simple solution to type specialization

    DEFF Research Database (Denmark)

    Danvy, Olivier

    1998-01-01

    Partial evaluation specializes terms, but traditionally this specialization does not apply to the type of these terms. As a result, specializing, e.g., an interpreter written in a typed language, which requires a “universal” type to encode expressible values, yields residual programs with type tags...... all over. Neil Jones has stated that getting rid of these type tags was an open problem, despite possible solutions such as Torben Mogensen's “constructor specialization.” To solve this problem, John Hughes has proposed a new paradigm for partial evaluation, “Type Specialization”, based on type...... from the universal type to the specific type of the residual program. Standard partial evaluation then yields a residual program without type tags, simply and efficiently....

  16. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong

    2016-07-26

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

  17. Simple clamped connection for bamboo truss systems

    NARCIS (Netherlands)

    Blok, R.

    2016-01-01

    “How to make fast and simple tension connections for truss systems?” The Solution: The innovation is a connection that uses only widely available base components (boltsand threaded steel bars) and simple hand tools to install it. With a handsaw and aspanner, the bamboo stems can be combined into to

  18. Estimating the uncertainty of damage costs of pollution: A simple transparent method and typical results

    International Nuclear Information System (INIS)

    Spadaro, Joseph V.; Rabl, Ari

    2008-01-01

    Whereas the uncertainty of environmental impacts and damage costs is usually estimated by means of a Monte Carlo calculation, this paper shows that most (and in many cases all) of the uncertainty calculation involves products and/or sums of products and can be accomplished with an analytic solution which is simple and transparent. We present our own assessment of the component uncertainties and calculate the total uncertainty for the impacts and damage costs of the classical air pollutants; results for a Monte Carlo calculation for the dispersion part are also shown. The distribution of the damage costs is approximately lognormal and can be characterized in terms of geometric mean μ g and geometric standard deviation σ g , implying that the confidence interval is multiplicative. We find that for the classical air pollutants σ g is approximately 3 and the 68% confidence interval is [μ g / σ g , μ g σ g ]. Because the lognormal distribution is highly skewed for large σ g , the median is significantly smaller than the mean. We also consider the case where several lognormally distributed damage costs are added, for example to obtain the total damage cost due to all the air pollutants emitted by a power plant, and we find that the relative error of the sum can be significantly smaller than the relative errors of the summands. Even though the distribution for such sums is not exactly lognormal, we present a simple lognormal approximation that is quite adequate for most applications

  19. Maximum error-bounded Piecewise Linear Representation for online stream approximation

    KAUST Repository

    Xie, Qing; Pang, Chaoyi; Zhou, Xiaofang; Zhang, Xiangliang; Deng, Ke

    2014-01-01

    Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.

  20. Maximum error-bounded Piecewise Linear Representation for online stream approximation

    KAUST Repository

    Xie, Qing

    2014-04-04

    Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.

  1. Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations.

    Science.gov (United States)

    Chudnovsky, D V; Chudnovsky, G V

    1999-10-26

    The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent "accurately" harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in "accurate" reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Pade approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

  2. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

    2017-06-15

    We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

  3. Semiclassical approximation to time-dependent Hartree--Fock theory

    International Nuclear Information System (INIS)

    Dworzecka, M.; Poggioli, R.

    1976-01-01

    Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form

  4. The roles of shear and cross-correlations on the fluctuation levels in simple stochastic models. Revision

    International Nuclear Information System (INIS)

    Krommes, J.A.

    1999-01-01

    Highly simplified models of random flows interacting with background microturbulence are analyzed. In the limit of very rapid velocity fluctuations, it is shown rigorously that the fluctuation level of a passively advected scalar is not controlled by the rms shear. In a model with random velocities dependent only on time, the level of cross-correlations between the flows and the background turbulence regulates the saturation level. This effect is illustrated by considering a simple stochastic-oscillator model, both exactly and with analysis and numerical solutions of the direct-interaction approximation. Implications for the understanding of self-consistent turbulence are discussed briefly

  5. Presentation of some methods for the solution of the monoenergetic neutrons transport equation

    International Nuclear Information System (INIS)

    Valle G, E. del.

    1978-01-01

    The neutrons transport theory problems whose solution has been reached were collected in order to show that the transport equation is so complicated that different techniques were developed so as to give approximative numerical solutions to problems concerning the practical application. Such a technique, which had not been investigated in the literature dealing with these problems, is described here. The results which were obtained through this technique in undimensional problems of criticity are satisfactory and speaking in a conceptual way this method is extremely simple because it times. There is no limitation to deal with problems related neutrons sources with an arbitrary distribution and in principle the application of this technique can be extended to unhomogeneous environments. (author)

  6. SPARTAN: a simple performance assessment code for the Nevada Nuclear Waste Storage Investigations Project

    International Nuclear Information System (INIS)

    Lin, Y.T.

    1985-12-01

    SPARTAN is a simple computer model designed for the Nevada Nuclear Waste Storage Investigations Project to calculate radionuclide transport in geologic media. The physical processes considered are limited to Darcy's flow, radionuclide decay, and convective transport with constant retardation of radionuclides relative to water flow. Inputs for the model must be provided for the geometry, repository area, flow path, water flux, effective porosity, initial inventory, waste solubility, canister lifetime, and retardation factors. Results from the model consist of radionuclide release rates from the prospective Yucca Mountain repository for radioactive waste and cumulative curies released across the flow boundaries at the end of the flow path. The rates of release from the repository relative to NRC performance objectives and releases to the accessible environment relative to EPA requirements are also calculated. Two test problems compare the results of simulations from SPARTAN with analytical solutions. The comparisons show that the SPARTAN solution closely matches the analytical solutions across a range of conditions that approximate those that might occur at Yucca Mountain

  7. Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach

    KAUST Repository

    Collier, Nathan; Radwan, Hany; Dalcin, Lisandro; Calo, Victor M.

    2011-01-01

    We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity

  8. Cleaning UF membranes with simple and formulated solutions

    NARCIS (Netherlands)

    Levitsky, I.; Duek, A.; Naim, R.; Arkhangelsky, E.; Gitis, V.

    2012-01-01

    The ultrafiltration membranes fouled by proteins are typically cleaned by consecutive soaking in alkali, surfactant and oxidizing solutions. We combined all three chemicals into a formulated cleaning agent and examined its efficiency to restore the water flux without damaging the membrane or

  9. Approximate Solutions of Interactive Dynamic Influence Diagrams Using Model Clustering

    DEFF Research Database (Denmark)

    Zeng, Yifeng; Doshi, Prashant; Qiongyu, Cheng

    2007-01-01

    Interactive dynamic influence diagrams (I-DIDs) offer a transparent and semantically clear representation for the sequential decision-making problem over multiple time steps in the presence of other interacting agents. Solving I-DIDs exactly involves knowing the solutions of possible models...

  10. On an elastic dissipation model as continuous approximation for discrete media

    Directory of Open Access Journals (Sweden)

    I. V. Andrianov

    2006-01-01

    Full Text Available Construction of an accurate continuous model for discrete media is an important topic in various fields of science. We deal with a 1D differential-difference equation governing the behavior of an n-mass oscillator with linear relaxation. It is known that a string-type approximation is justified for low part of frequency spectra of a continuous model, but for free and forced vibrations a solution of discrete and continuous models can be quite different. A difference operator makes analysis difficult due to its nonlocal form. Approximate equations can be obtained by replacing the difference operators via a local derivative operator. Although application of a model with derivative of more than second order improves the continuous model, a higher order of approximated differential equation seriously complicates a solution of continuous problem. It is known that accuracy of the approximation can dramatically increase using Padé approximations. In this paper, one- and two-point Padé approximations suitable for justify choice of structural damping models are used.

  11. Approximation of bivariate copulas by patched bivariate Fréchet copulas

    KAUST Repository

    Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.

    2011-01-01

    Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

  12. Approximation of bivariate copulas by patched bivariate Fréchet copulas

    KAUST Repository

    Zheng, Yanting

    2011-03-01

    Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

  13. Simple simulation of diffusion bridges with application to likelihood inference for diffusions

    DEFF Research Database (Denmark)

    Bladt, Mogens; Sørensen, Michael

    2014-01-01

    the accuracy and efficiency of the approximate method and compare it to exact simulation methods. In the study, our method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to statistical inference. To illustrate the usefulness......With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and Bayesian inference for diffusion processes. First a simple......-dimensional diffusions and is applicable to all one-dimensional diffusion processes with finite speed-measure. One advantage of the new approach is that simple simulation methods like the Milstein scheme can be applied to bridge simulation. Another advantage over previous bridge simulation methods is that the proposed...

  14. Classifying supersymmetric solutions in 3D maximal supergravity

    Science.gov (United States)

    de Boer, Jan; Mayerson, Daniel R.; Shigemori, Masaki

    2014-12-01

    String theory contains various extended objects. Among those, objects of codimension two (such as the D7-brane) are particularly interesting. Codimension-two objects carry non-Abelian charges which are elements of a discrete U-duality group and they may not admit a simple spacetime description, in which case they are known as exotic branes. A complete classification of consistent codimension-two objects in string theory is missing, even if we demand that they preserve some supersymmetry. As a step toward such a classification, we study the supersymmetric solutions of 3D maximal supergravity, which can be regarded as an approximate description of the geometry near codimension-two objects. We present a complete classification of the types of supersymmetric solutions that exist in this theory. We found that this problem reduces to that of classifying nilpotent orbits associated with the U-duality group, for which various mathematical results are known. We show that the only allowed supersymmetric configurations are 1/2, 1/4, 1/8, and 1/16 BPS, and determine the nilpotent orbits that they correspond to. One example of 1/16 BPS configurations is a generalization of the MSW system, where momentum runs along the intersection of seven M5-branes. On the other hand, it turns out exceedingly difficult to translate this classification into a simple criterion for supersymmetry in terms of the non-Abelian (monodromy) charges of the objects. For example, it can happen that a supersymmetric solution exists locally but cannot be extended all the way to the location of the object. To illustrate the various issues that arise in constructing supersymmetric solutions, we present a number of explicit examples.

  15. Simple analytic formula for the period of the nonlinear pendulum via the Struve function: connection to acoustical impedance matching

    International Nuclear Information System (INIS)

    Douvropoulos, Theodosios G

    2012-01-01

    An approximate formula for the period of pendulum motion beyond the small amplitude regime is obtained based on physical arguments. Two different schemes of different accuracy are developed: in the first less accurate scheme, emphasis is given on the non-quadratic form of the potential in connection to isochronism, and a specific form of a generic formula that is met in many previous works is produced, while the second and main result contains the Struve function which is further approximated by a simple sinusoidal expression based on its maximum value. The accuracy of the final formula gives a relative error of less than 0.2% for angles up to 140°. In addition, a simple relation between the Struve function and the complete elliptic integral of the first kind is produced, since they both constitute solutions of the pendulum period. This relation makes it possible for someone to connect different areas in physics and solve a difficult task by comparison with another much more simple one. As an example, a connection between the pendulum period and the acoustical radiation impedance is proposed through impedance matching and some interesting relations are produced. This paper is intended for undergraduate students to be useful for analysing pendulum experiments in introductory physics labs and it is also believed to offer valuable insight into some properties of the simple pendulum in undergraduate courses on general physics. (paper)

  16. On the (In)Validity of Tests of Simple Mediation: Threats and Solutions

    Science.gov (United States)

    Pek, Jolynn; Hoyle, Rick H.

    2015-01-01

    Mediation analysis is a popular framework for identifying underlying mechanisms in social psychology. In the context of simple mediation, we review and discuss the implications of three facets of mediation analysis: (a) conceptualization of the relations between the variables, (b) statistical approaches, and (c) relevant elements of design. We also highlight the issue of equivalent models that are inherent in simple mediation. The extent to which results are meaningful stem directly from choices regarding these three facets of mediation analysis. We conclude by discussing how mediation analysis can be better applied to examine causal processes, highlight the limits of simple mediation, and make recommendations for better practice. PMID:26985234

  17. Multi-compartment linear noise approximation

    International Nuclear Information System (INIS)

    Challenger, Joseph D; McKane, Alan J; Pahle, Jürgen

    2012-01-01

    The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented. (paper)

  18. Diffusion of aqueous solutions of ionic, zwitterionic, and polar solutes

    Science.gov (United States)

    Teng, Xiaojing; Huang, Qi; Dharmawardhana, Chamila Chathuranga; Ichiye, Toshiko

    2018-06-01

    The properties of aqueous solutions of ionic, zwitterionic, and polar solutes are of interest to many fields. For instance, one of the many anomalous properties of aqueous solutions is the behavior of water diffusion in different monovalent salt solutions. In addition, solutes can affect the stabilities of macromolecules such as proteins in aqueous solution. Here, the diffusivities of aqueous solutions of sodium chloride, potassium chloride, tri-methylamine oxide (TMAO), urea, and TMAO-urea are examined in molecular dynamics simulations. The decrease in the diffusivity of water with the concentration of simple ions and urea can be described by a simple model in which the water molecules hydrogen bonded to the solutes are considered to diffuse at the same rate as the solutes, while the remainder of the water molecules are considered to be bulk and diffuse at almost the same rate as pure water. On the other hand, the decrease in the diffusivity of water with the concentration of TMAO is apparently affected by a decrease in the diffusion rate of the bulk water molecules in addition to the decrease due to the water molecules hydrogen bonded to TMAO. In other words, TMAO enhances the viscosity of water, while urea barely affects it. Overall, this separation of water molecules into those that are hydrogen bonded to solute and those that are bulk can provide a useful means of understanding the short- and long-range effects of solutes on water.

  19. Approximate Bayesian evaluations of measurement uncertainty

    Science.gov (United States)

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  20. Fatigue crack extension in nozzle junctions; comparison of analytical approximations with experimental data

    International Nuclear Information System (INIS)

    Broekhoven, M.J.G.; Ruijtenbeek, M.G. van de

    1975-01-01

    The fracture mechanics based stress intensity factor (K-factor) concept has obtained wide-spread acceptance as a tool for quantitative analysis of both fatigue crack growth and instable fracture. The present study discusses the applicability of various simple analytical approximations by comparing results with experimental data. A semi-analytical procedure has been developed whose main characteristics are: the true stress distribution perpendicular to the crack plane for the uncracked structure is used as input data; an extended version of the Shah and Kobayashi solution for elliptical cracks, loaded on their surfaces by tractions described by fourth order double symmetrical polynomials fit through the data of previous step is used to calculate full K-factor variations along the crack fronts; several corrections, a.o. to correct for free surfaces and for a corner radius are incorporated. The experiments concern careful monitoring crack growth rates (da/dN) under uniaxial fatigue loading of precracked nozzle-on-plate models, a.o. using a closed T.V. circuit. Resulting da/dN versus crack length (a) curves are converted into K versus a curves using da/dN versus ΔK curves for the same material (ASTM A 508 C12) obtained by standard procedures. Comparison of theoretical and experimental data yields the conclusion that: simple analytical approximations as sometimes recommended in literature may largely overestimate or underestimate K-factors for nozzle corner cracks; a computer program based on the semi-analytical procedure yields results within seconds of CPU-time once the input data have been generated. These results compare well with experimental and available finite element data for the range of crack depths of practical concern

  1. Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Gustavo [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Concepcion Univ. (Chile). Dept. de Fisica; Cvetic, Gorazd [Univ. Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. de Fisica; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Grupo de Matematica Aplicada; Univ. del Bio-Bio, Chillan (Chile). Grupo de Fisica de Altas Energias; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica

    2016-11-15

    We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.

  2. Structural and computational aspects of simple and influence games

    OpenAIRE

    Riquelme Csori, Fabián

    2014-01-01

    Simple games are a fundamental class of cooperative games. They have a huge relevance in several areas of computer science, social sciences and discrete applied mathematics. The algorithmic and computational complexity aspects of simple games have been gaining notoriety in the recent years. In this thesis we review different computational problems related to properties, parameters, and solution concepts of simple games. We consider different forms of representation of simple games, regular...

  3. Approximation scheme for strongly coupled plasmas: Dynamical theory

    International Nuclear Information System (INIS)

    Golden, K.I.; Kalman, G.

    1979-01-01

    The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability α (k, ω) at long wavelengths in strongly coupled one-component plasmas. Development of the scheme is carried out in two stages. The first stage follows the earlier Golden-Kalman-Silevitch (GKS) velocity-average approximation approach, but goes much further in its application of the nonlinear fluctuation-dissipation theorem to dynamical calculations. The result is the simple expression for α (k, ω), αatsub GKSat(k, ω) 4 moment sum rule. In the second stage, the above dynamical expression is made self-consistent at long wavelengths by postulating that a decomposition of the quadratic polarizabilities in terms of linear ones, which prevails in the k → 0 limit for weak coupling, can be relied upon as a paradigm for arbitrary coupling. The result is a relatively simple quadratic integral equation for α. Its evaluation in the weak-coupling limit and its comparison with known exact results in that limit reveal that almost all important correlational and long-time effects are reproduced by our theory with very good numerical accuracy over the entire frequency range; the only significant defect of the approximation seems to be the absence of the ''dominant'' γ ln γ -1 (γ is the plasma parameter) contribution to Im α

  4. Analytical Ballistic Trajectories with Approximately Linear Drag

    Directory of Open Access Journals (Sweden)

    Giliam J. P. de Carpentier

    2014-01-01

    Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.

  5. Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

    KAUST Repository

    Bramble, James H.

    2010-01-01

    We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.

  6. Approximate evaluation of viscous effects in the Rayleigh-Taylor instability

    International Nuclear Information System (INIS)

    Gratton, J.

    1989-01-01

    The effects of viscosity in the Rayleigh--Taylor instability are very important in many instances of interest but, although they have been investigated in some simple cases, the extensive algebraic complexities that are involved in the treatment of the problem tend to becloud the analysis and prevent generalizations of the results. In the paper a simple approximate method which improves a previous one by Plesset and Whipple is discussed. The viscous effects are accounted in an intuitive and transparent way, and can be easily estimated. The results are compared with exact calculations showing good agreement. For this purpose a method of analysis of the exact dispersion relation is developed, which circumvents most of the algebraic complications of the usual procedures. Both the approximate method and the novel treatment of the exact dispersion relation can be generalized to other problems of the same family

  7. Approximating Markov Chains: What and why

    International Nuclear Information System (INIS)

    Pincus, S.

    1996-01-01

    Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics

  8. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  9. When is the Anelastic Approximation a Valid Model for Compressible Convection?

    Science.gov (United States)

    Alboussiere, T.; Curbelo, J.; Labrosse, S.; Ricard, Y. R.; Dubuffet, F.

    2017-12-01

    Compressible convection is ubiquitous in large natural systems such Planetary atmospheres, stellar and planetary interiors. Its modelling is notoriously more difficult than the case when the Boussinesq approximation applies. One reason for that difficulty has been put forward by Ogura and Phillips (1961): the compressible equations generate sound waves with very short time scales which need to be resolved. This is why they introduced an anelastic model, based on an expansion of the solution around an isentropic hydrostatic profile. How accurate is that anelastic model? What are the conditions for its validity? To answer these questions, we have developed a numerical model for the full set of compressible equations and compared its solutions with those of the corresponding anelastic model. We considered a simple rectangular 2D Rayleigh-Bénard configuration and decided to restrict the analysis to infinite Prandtl numbers. This choice is valid for convection in the mantles of rocky planets, but more importantly lead to a zero Mach number. So we got rid of the question of the interference of acoustic waves with convection. In that simplified context, we used the entropy balances (that of the full set of equations and that of the anelastic model) to investigate the differences between exact and anelastic solutions. We found that the validity of the anelastic model is dictated by two conditions: first, the superadiabatic temperature difference must be small compared with the adiabatic temperature difference (as expected) ɛ = Δ TSA / delta Ta << 1, and secondly that the product of ɛ with the Nusselt number must be small.

  10. A new way of obtaining analytic approximations of Chandrasekhar's H function

    International Nuclear Information System (INIS)

    Vukanic, J.; Arsenovic, D.; Davidovic, D.

    2007-01-01

    Applying the mean value theorem for definite integrals in the non-linear integral equation for Chandrasekhar's H function describing conservative isotropic scattering, we have derived a new, simple analytic approximation for it, with a maximal relative error below 2.5%. With this new function as a starting-point, after a single iteration in the corresponding integral equation, we have obtained a new, highly accurate analytic approximation for the H function. As its maximal relative error is below 0.07%, it significantly surpasses the accuracy of other analytic approximations

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1968-07-01

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

  12. The complex variable boundary element method: Applications in determining approximative boundaries

    Science.gov (United States)

    Hromadka, T.V.

    1984-01-01

    The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

  13. Common approximations for density operators may lead to imaginary entropy

    International Nuclear Information System (INIS)

    Lendi, K.; Amaral Junior, M.R. do

    1983-01-01

    The meaning and validity of usual second order approximations for density operators are illustrated with the help of a simple exactly soluble two-level model in which all relevant quantities can easily be controlled. This leads to exact upper bound error estimates which help to select more precisely permissible correlation times as frequently introduced if stochastic potentials are present. A final consideration of information entropy reveals clearly the limitations of this kind of approximation procedures. (Author) [pt

  14. An improved saddlepoint approximation.

    Science.gov (United States)

    Gillespie, Colin S; Renshaw, Eric

    2007-08-01

    Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.

  15. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  16. Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

    CERN Document Server

    Rassias, Michael

    2014-01-01

    This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

  17. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  18. Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Ping; Zou, Ping [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China); Zhang, Zhi-Ming, E-mail: zmzhang@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China)

    2012-10-01

    We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution. -- Highlights: ► Our work shows that the adiabatic approximations may work also in the ultrastrong coupling limit. ► Both of the approximation methods are valid in a large range of coupling strength, including the ultrastrong coupling regime. ► The results of the approximate formula meet well the exact numerical solution.

  19. A simple solution for reducing artefacts due to conductive and dielectric effects in clinical magnetic resonance imaging at 3 T

    International Nuclear Information System (INIS)

    Sreenivas, M.; Lowry, M.; Gibbs, P.; Pickles, M.; Turnbull, L.W.

    2007-01-01

    The quality of imaging obtained at high magnetic field strengths can be degraded by various artefacts due to conductive and dielectric effects, which leads to loss of signal. Various methods have been described and used to improve the quality of the image affected by such artefacts. In this article, we describe the construction and use of a simple solution that can be used to diminish artefacts due to conductive and dielectric effects in clinical imaging at 3 T field strength and thereby improve the diagnostic quality of the images obtained

  20. A simple solution for reducing artefacts due to conductive and dielectric effects in clinical magnetic resonance imaging at 3 T

    Energy Technology Data Exchange (ETDEWEB)

    Sreenivas, M. [Department of Radiology (Yorkshire Deanery-East), Hull Royal Infirmary, Anlaby Road, Hull HU3 2JZ (United Kingdom)]. E-mail: aprilsreenivas@hotmail.com; Lowry, M. [Centre for Magnetic Resonance Investigations, University of Hull, Hull Royal Infirmary, Anlaby Road, 1PR, Hull HU3 2JZ (United Kingdom); Gibbs, P. [Centre for Magnetic Resonance Investigations, University of Hull, Hull Royal Infirmary, Anlaby Road, 1PR, Hull HU3 2JZ (United Kingdom); Pickles, M. [Centre for Magnetic Resonance Investigations, University of Hull, Hull Royal Infirmary, Anlaby Road, 1PR, Hull HU3 2JZ (United Kingdom); Turnbull, L.W. [Centre for Magnetic Resonance Investigations, University of Hull, Hull Royal Infirmary, Anlaby Road, 1PR, Hull HU3 2JZ (United Kingdom)

    2007-04-15

    The quality of imaging obtained at high magnetic field strengths can be degraded by various artefacts due to conductive and dielectric effects, which leads to loss of signal. Various methods have been described and used to improve the quality of the image affected by such artefacts. In this article, we describe the construction and use of a simple solution that can be used to diminish artefacts due to conductive and dielectric effects in clinical imaging at 3 T field strength and thereby improve the diagnostic quality of the images obtained.

  1. Evaluation of Fresnel's corrections to the eikonal approximation by the separabilization method

    International Nuclear Information System (INIS)

    Musakhanov, M.M.; Zubarev, A.L.

    1975-01-01

    Method of separabilization of potential over the Schroedinger approximate solutions, leading to Schwinger's variational principle for scattering amplitude, is suggested. The results are applied to calculation of the Fresnel corrections to the Glauber approximation

  2. Criticality safety validation: Simple geometry, single unit {sup 233}U systems

    Energy Technology Data Exchange (ETDEWEB)

    Putman, V.L.

    1997-06-01

    Typically used LMITCO criticality safety computational methods are evaluated for suitability when applied to INEEL {sup 233}U systems which reasonably can be modeled as simple-geometry, single-unit systems. Sixty-seven critical experiments of uranium highly enriched in {sup 233}U, including 57 aqueous solution, thermal-energy systems and 10 metal, fast-energy systems, were modeled. These experiments include 41 cylindrical and 26 spherical cores, and 41 reflected and 26 unreflected systems. No experiments were found for intermediate-neutron-energy ranges, or with interstitial non-hydrogenous materials typical of waste systems, mixed {sup 233}U and plutonium, or reflectors such as steel, lead, or concrete. No simple geometry experiments were found with cubic or annular cores, or approximating infinite sea systems. Calculations were performed with various tools and methodologies. Nine cross-section libraries, based on ENDF/B-IV, -V, or -VI.2, or on Hansen-Roach source data, were used with cross-section processing methods of MCNP or SCALE. The k{sub eff} calculations were performed with neutral-particle transport and Monte Carlo methods of criticality codes DANT, MCNP 4A, and KENO Va.

  3. 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

  4. Dynamics of unwinding of a simple entaglement

    NARCIS (Netherlands)

    Wiegel, F.W.; Michels, J.P.J.

    1987-01-01

    The dynamics of unwinding of a simple entanglement is studied in two ways, firstly using an optimal path approximation in the Rouse model and secondly by simulating the movement of a more realistic model using Brownian molecular dynamics

  5. Green's Kernels and meso-scale approximations in perforated domains

    CERN Document Server

    Maz'ya, Vladimir; Nieves, Michael

    2013-01-01

    There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domai...

  6. A note on the geometric phase in adiabatic approximation

    International Nuclear Information System (INIS)

    Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.

    2005-01-01

    The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough

  7. Hadronic distributions and correlations at 'small x' in quantum chromodynamics; Distributions et correlations hadroniques en chromodynamique quantique dans l'approximation des 'petit X'

    Energy Technology Data Exchange (ETDEWEB)

    Perez Ramos, R

    2006-09-15

    We exactly calculate the double and simple inclusive transverse momentum (kt) distributions and the 2-particle momentum correlations inside high energy hadronic jets at the Modified Leading Logarithmic Approximation (MLLA) of Quantum Chromodynamics. We first obtain the exact solution of the evolution equations at 'small x', which we calculate at the so called 'limiting spectrum'. We then generalize this approximation by performing the steepest descent evaluation. Our predictions are in good agreement with data from Tevatron and improve those which have been obtained in the past. The comparison with forthcoming data (Tevatron, LHC) will further test the hypothesis of Local Hadron Parton Duality, and the eventual need to incorporate next-MLLA corrections. (authors)

  8. Error Analysis on Plane-to-Plane Linear Approximate Coordinate ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, the error analysis has been done for the linear approximate transformation between two tangent planes in celestial sphere in a simple case. The results demonstrate that the error from the linear transformation does not meet the requirement of high-precision astrometry under some conditions, so the ...

  9. Approximate approaches to the one-dimensional finite potential well

    International Nuclear Information System (INIS)

    Singh, Shilpi; Pathak, Praveen; Singh, Vijay A

    2011-01-01

    The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m i ) is taken to be distinct from mass outside (m o ). A relevant parameter is the mass discontinuity ratio β = m i /m o . To correctly account for the mass discontinuity, we apply the BenDaniel-Duke boundary condition. We obtain approximate solutions for two cases: when the well is shallow and when the well is deep. We compare the approximate results with the exact results and find that higher-order approximations are quite robust. For the shallow case, the approximate solution can be expressed in terms of a dimensionless parameter σ l = 2m o V 0 L 2 /ℎ 2 (or σ = β 2 σ l for the deep case). We show that the lowest-order results are related by a duality transform. We also discuss how the energy upscales with L (E∼1/L γ ) and obtain the exponent γ. Exponent γ → 2 when the well is sufficiently deep and β → 1. The ratio of the masses dictates the physics. Our presentation is pedagogical and should be useful to students on a first course on elementary quantum mechanics or low-dimensional semiconductors.

  10. Quantum tunneling beyond semiclassical approximation

    International Nuclear Information System (INIS)

    Banerjee, Rabin; Majhi, Bibhas Ranjan

    2008-01-01

    Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

  11. Approximation of ruin probabilities via Erlangized scale mixtures

    DEFF Research Database (Denmark)

    Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue

    2018-01-01

    In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....

  12. Effective medium super-cell approximation for interacting disordered systems: an alternative real-space derivation of generalized dynamical cluster approximation

    International Nuclear Information System (INIS)

    Moradian, Rostam

    2006-01-01

    We develop a generalized real-space effective medium super-cell approximation (EMSCA) method to treat the electronic states of interacting disordered systems. This method is general and allows randomness both in the on-site energies and in the hopping integrals. For a non-interacting disordered system, in the special case of randomness in the on-site energies, this method is equivalent to the non-local coherent potential approximation (NLCPA) derived previously. Also, for an interacting system the EMSCA method leads to the real-space derivation of the generalized dynamical cluster approximation (DCA) for a general lattice structure. We found that the original DCA and the NLCPA are two simple cases of this technique, so the EMSCA is equivalent to the generalized DCA where there is included interaction and randomness in the on-site energies and in the hopping integrals. All of the equations of this formalism are derived by using the effective medium theory in real space

  13. 5th International Conference on Algorithms for Approximation

    CERN Document Server

    Levesley, Jeremy

    2007-01-01

    Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microso...

  14. Finite-rank potential that reproduces the Pade approximant

    International Nuclear Information System (INIS)

    Tani, S.

    1979-01-01

    If a scattering potential is of a finite rank, say N, the exact solution of the problem can be obtained from the Born series, if the potential strength is within the radius of convergence; the exact solution can be obtained from the analytical continuation of the formal Born series outside the radius of convergence. Beyond the first 2N terms of the Born series, an individual term of the Born series depends on the first 2N terms, and the [N/N] Pade approximant and the exact solution agree with each other. The above-mentioned features of a finite-rank problem are relevant to scattering theory in general, because most scattering problems may be handled as an extension of the rank-N problem, in which the rank N tends to infinity. The foregoing aspects of scattering theory will be studied in depth in the present paper, and in so doing we proceed in the opposite direction. Namely, given a potential, we calculate the first 2N terms of the Born series for the K matrix and the first N terms of the Born series for the wave function. Using these data, a special rank-N potential is constructed in such a way that it reproduces the [N/N] Pade approximant of the K matrix of the original scattering problem. One great advantage of obtaining such a rank-N potential is that the wave function of the system may be approximated in the same spirit as done for the K matrix; hence, we can introduce a new approximation method for dealing with an off-shell T matrix. A part of the mathematical work is incomplete, but the physical aspects are thoroughly discussed

  15. Isotope effects in the solution of gases in liquids. Progress report, November 1, 1979-October 31, 1980

    International Nuclear Information System (INIS)

    Benson, B.B.; Krause, D. Jr.

    1980-09-01

    Research under this contract provides strong evidence for the existence of structure in liquid water. Application of a simple zero-point-energy argument to our data for the isotopic fractionation of nonpolar gases during aqueous solution shows that a dissolved gas molecule may be considered to occupy a cavity with a size characteristic of water and independent of the size of the solute molecule. For a cubical cavity model for water, the length of a side of the cube would be approximately 6.3 A at 0 0 C, while a spherical cavity model would have a dia of 6.8 A. The isotopic measurements in addition may lead to a more consistent set of diameters for the solute molecules. Precise new measurements show that the isotopic fractionation of nitrogen during solution is only slightly smaller than that for oxygen, despite the fact that the difference between the reciprocal masses of the 28 to 29 pair is only one-half the difference for the 32 to 34 pair. The cavity model provides a simple quantitative explanation for this result. Measurements on the polar molecules 12 C 16 O, 13 C 16 O, and 12 C 18 O do not fit the simple model, because of the asymmetrical distributions of their masses. This leads to a correlation between rotational and translational degrees of freedom, which affects the energies of the ground states of these heteronuclear molecules as they oscillate within the cavity

  16. Effect of the spherical Earth on a simple pendulum

    OpenAIRE

    Burko, Lior M.

    2003-01-01

    We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

  17. Approximating optimal behavioural strategies down to rules-of-thumb: energy reserve changes in pairs of social foragers.

    Directory of Open Access Journals (Sweden)

    Sean A Rands

    Full Text Available Functional explanations of behaviour often propose optimal strategies for organisms to follow. These 'best' strategies could be difficult to perform given biological constraints such as neural architecture and physiological constraints. Instead, simple heuristics or 'rules-of-thumb' that approximate these optimal strategies may instead be performed. From a modelling perspective, rules-of-thumb are also useful tools for considering how group behaviour is shaped by the behaviours of individuals. Using simple rules-of-thumb reduces the complexity of these models, but care needs to be taken to use rules that are biologically relevant. Here, we investigate the similarity between the outputs of a two-player dynamic foraging game (which generated optimal but complex solutions and a computational simulation of the behaviours of the two members of a foraging pair, who instead followed a rule-of-thumb approximation of the game's output. The original game generated complex results, and we demonstrate here that the simulations following the much-simplified rules-of-thumb also generate complex results, suggesting that the rule-of-thumb was sufficient to make some of the model outcomes unpredictable. There was some agreement between both modelling techniques, but some differences arose - particularly when pair members were not identical in how they gained and lost energy. We argue that exploring how rules-of-thumb perform in comparison to their optimal counterparts is an important exercise for biologically validating the output of agent-based models of group behaviour.

  18. Approximating optimal behavioural strategies down to rules-of-thumb: energy reserve changes in pairs of social foragers.

    Science.gov (United States)

    Rands, Sean A

    2011-01-01

    Functional explanations of behaviour often propose optimal strategies for organisms to follow. These 'best' strategies could be difficult to perform given biological constraints such as neural architecture and physiological constraints. Instead, simple heuristics or 'rules-of-thumb' that approximate these optimal strategies may instead be performed. From a modelling perspective, rules-of-thumb are also useful tools for considering how group behaviour is shaped by the behaviours of individuals. Using simple rules-of-thumb reduces the complexity of these models, but care needs to be taken to use rules that are biologically relevant. Here, we investigate the similarity between the outputs of a two-player dynamic foraging game (which generated optimal but complex solutions) and a computational simulation of the behaviours of the two members of a foraging pair, who instead followed a rule-of-thumb approximation of the game's output. The original game generated complex results, and we demonstrate here that the simulations following the much-simplified rules-of-thumb also generate complex results, suggesting that the rule-of-thumb was sufficient to make some of the model outcomes unpredictable. There was some agreement between both modelling techniques, but some differences arose - particularly when pair members were not identical in how they gained and lost energy. We argue that exploring how rules-of-thumb perform in comparison to their optimal counterparts is an important exercise for biologically validating the output of agent-based models of group behaviour.

  19. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  20. Proposing buffer zones and simple technical solutions for safeguarding river water quality and public health

    Science.gov (United States)

    Podimata, M. V.; Bekri, E. S.; Yannopoulos, P. C.

    2012-04-01

    Alfeios River Basin (ARB) constitutes one of the major hydrologic basins (≈3650km2) of Peloponnisos peninsula in Southern Greece. It is drained by Alfeios River and its tributaries, such as Lousios, Ladhon, Erymanthos, Kladheos, Selinous etc. The present manuscript takes a closer look at the importance of tributary basins and focuses on Erymanthos sub-basin that covers about 360 km2. Erymanthos River springs from Erymanthos Mountain that reaches altitudes of 2200 m and discharges 10 m3/sec, approximately, during the winter period, presenting a sound decrease from half to about an order of magnitude during summertime. Two factors stand out as reasons to select Erymanthos sub-basin as a case study. First, the sub-basin presents a significant variety of ecosystems and comprises a very important river system, since Erymanthos Tributary satisfies, among other uses, drinking water supply for a great majority of citizens in the region. Second, authors' experience of the study area in Research Program Pythagoras II, funded by the European Social Fund (ESF) and the Operational Program for Educational and Vocational Training II (EPEAEK II) of Greece, offers a basis for better understanding of the real problems in the area. Erymanthos watershed, in fact, faces a lot of pressures, in several levels, provoked by human activities and Erymanthos Tributary is vulnerable to pollution. Recognizing the importance of clean water for healthy people, a developing economy, and a sustainable environment, the challenge of the present paper is elaborating human-induced pressures in the study area, analyzing their effects, estimating pollution factors and proposing integrated solutions/tools and a number of methodologies/initiatives used to overcome the problem of contaminating water supply in a catchment that lacks of wastewater treatment and disposal systems. The preservation of a good ecological status in Erymanthos River is not only a necessity for achieving the goals of EU Water

  1. Semiclassical solution to the BFKL equation with massive gluons

    International Nuclear Information System (INIS)

    Levin, Eugene; Lipatov, Lev; Siddikov, Marat

    2015-01-01

    In this paper we proceed to study the high energy behavior of scattering amplitudes in a simple field model, with the Higgs mechanism for the gauge boson mass. The spectrum of the j-plane singularities of the t-channel partial waves and the corresponding eigenfunctions of the BFKL equation in leading log(1/x) approximation were previously calculated numerically. Here we develop a semiclassical approach to investigate the influence of the exponential decrease of the impact parameter dependence existing in this model, on the high energy asymptotic behavior of the scattering amplitude. This approach is much simpler than our earlier numerical calculations, and it reproduces those results. The analytical (semi-analytical) solutions which have been found in the approximation can be used to incorporate correctly the large impact parameter behavior in the framework of CGC/saturation approach. This behavior is interesting as it provides the high energy amplitude for the electroweak theory, which can be measured experimentally. (orig.)

  2. Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

    Science.gov (United States)

    Khajehtourian, Romik

    Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

  3. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  4. Approximate analytical methods for solving ordinary differential equations

    CERN Document Server

    Radhika, TSL; Rani, T Raja

    2015-01-01

    Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti

  5. Approximate representations of propagators in an external field

    International Nuclear Information System (INIS)

    Fried, H.M.

    1979-01-01

    A method of forming approximate representations for propagators with external field dependence is suggested and discussed in the context of potential scattering. An integro-differential equation in D+1 variables, where D represents the dimensionality of Euclidian space-time, is replaced by a Volterra equation in one variable. Approximate solutions to the latter provide a generalization of the Bloch-Nordsieck representation, containing the effects of all powers of hard-potential interactions, each modified by a characteristic soft-potential dependence [fr

  6. Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation

    Energy Technology Data Exchange (ETDEWEB)

    Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)

    1975-01-04

    Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.

  7. Description logics with approximate definitions precise modeling of vague concepts

    NARCIS (Netherlands)

    Schlobach, Stefan; Klein, Michel; Peelen, Linda

    2007-01-01

    We extend traditional Description Logics (DL) with a simple mechanism to handle approximate concept definitions in a qualitative way. Often, for example in medical applications, concepts are not definable in a crisp way but can fairly exhaustively be constrained through a particular sub- and a

  8. The dilute random field Ising model by finite cluster approximation

    International Nuclear Information System (INIS)

    Benyoussef, A.; Saber, M.

    1987-09-01

    Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs

  9. On the (In)Validity of Tests of Simple Mediation: Threats and Solutions

    OpenAIRE

    Pek, Jolynn; Hoyle, Rick H.

    2016-01-01

    Mediation analysis is a popular framework for identifying underlying mechanisms in social psychology. In the context of simple mediation, we review and discuss the implications of three facets of mediation analysis: (a) conceptualization of the relations between the variables, (b) statistical approaches, and (c) relevant elements of design. We also highlight the issue of equivalent models that are inherent in simple mediation. The extent to which results are meaningful stem directly from choi...

  10. Simple Analysis of Historical Lime Mortars

    Science.gov (United States)

    Pires, Joa~o

    2015-01-01

    A laboratory experiment is described in which a simple characterization of a historical lime mortar is made by the determination of its approximate composition by a gravimetric method. Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) are also used for the qualitative characterization of the lime mortar components. These…

  11. A simple interpolation for high and low momentum transfers in QCD

    International Nuclear Information System (INIS)

    Mignaco, J.A.; Roditi, I.

    1982-01-01

    It is shown that a simple rational approximation for the function β(g) of the renormalization group provides a useful expansion parameter for the perturbative regime in QCD and, simultaneously, allows for confinement the functional integral approximation to this problem. (Author) [pt

  12. Effects of scattering anisotropy approximation in multigroup radiation shielding calculations

    International Nuclear Information System (INIS)

    Altiparmakov, D.

    1983-01-01

    Expansion of the scattering cross sections into Legendre series is the usual way of solving neutron transport problems. Because of the large space gradients of the neutron flux, the effects of that approximation become especially remarkable in the radiation shielding calculations. In this paper, a method taking into account the scattering anisotropy is presented. From the point od view of the accuracy and computing rate, the optimal approximation of the scattering anisotropy is established for the basic protective materials on the basis of simple problem calculations. (author)

  13. Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium

    International Nuclear Information System (INIS)

    Patra, A.; Saha Ray, S.

    2014-01-01

    Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution

  14. Study on the generalized WKB approximation for the inverse scattering problem at fixed energy for complex potentials

    International Nuclear Information System (INIS)

    Pozdnyakov, Yu.A.; Terenetskij, K.O.

    1981-01-01

    The approximate method for solution of the inverse scattering problem (ISP) at fixed energy for complex spherically symmetric potentials decreasing faster 1/r is considered. The method is based on using a generalized WKB approximation. For the designed potential V(r) a sufficiently ''close'' reference potential V(r) has been chosen. For both potentials S-matrix elements (ME) have been calculated and inversion procedure has been carried out. S-ME have been calculated for integral-valued and intermediate angular moment values. S-ME are presented in a graphical form for being restored reference, and restored potentials for proton scattering with Esub(p)=49.48 MeV energy on 12 C nuclei. The restoration is the better the ''closer'' the sought-for potential to the reference one. This allows to specify the potential by means of iterations: the restored potential can be used as a reference one, etc. The operation of a restored potential smoothing before the following iteration is introduced. Drawbacks and advantages of the ISP solution method under consideration are pointed out. The method application is strongly limited by the requirement that the energy should be higher than a certain ''critical'' one. The method is applicable in a wider region of particle energies (in the low-energies direction) than the ordinary WKB method. The method is more simple in realization conformably to complex potentials. The investigations carried out of the proposed ISP solution method at fixed energy for complex spherically-symmetric potentials allow to conclude that the method can be successFully applied to specify the central part of interaction of nucleons, α-particles and heavy ions of average and high energies with atomic nuclei [ru

  15. Optical properties of non-spherical desert dust particles in the terrestrial infrared – An asymptotic approximation approach

    International Nuclear Information System (INIS)

    Klüser, Lars; Di Biagio, Claudia; Kleiber, Paul D.; Formenti, Paola; Grassian, Vicki H.

    2016-01-01

    Optical properties (extinction efficiency, single scattering albedo, asymmetry parameter and scattering phase function) of five different desert dust minerals have been calculated with an asymptotic approximation approach (AAA) for non-spherical particles. The AAA method combines Rayleigh-limit approximations with an asymptotic geometric optics solution in a simple and straightforward formulation. The simulated extinction spectra have been compared with classical Lorenz–Mie calculations as well as with laboratory measurements of dust extinction. This comparison has been done for single minerals and with bulk dust samples collected from desert environments. It is shown that the non-spherical asymptotic approximation improves the spectral extinction pattern, including position of the extinction peaks, compared to the Lorenz–Mie calculations for spherical particles. Squared correlation coefficients from the asymptotic approach range from 0.84 to 0.96 for the mineral components whereas the corresponding numbers for Lorenz–Mie simulations range from 0.54 to 0.85. Moreover the blue shift typically found in Lorenz–Mie results is not present in the AAA simulations. The comparison of spectra simulated with the AAA for different shape assumptions suggests that the differences mainly stem from the assumption of the particle shape and not from the formulation of the method itself. It has been shown that the choice of particle shape strongly impacts the quality of the simulations. Additionally, the comparison of simulated extinction spectra with bulk dust measurements indicates that within airborne dust the composition may be inhomogeneous over the range of dust particle sizes, making the calculation of reliable radiative properties of desert dust even more complex. - Highlights: • A fast and simple method for estimating optical properties of dust. • Can be used with non-spherical particles of arbitrary size distributions. • Comparison with Mie simulations and

  16. Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk

    Directory of Open Access Journals (Sweden)

    Devendra Kumar

    2013-07-01

    Full Text Available Pseudoanalytic functions (PAF are constructed as complex combination of real-valued analytic solutions to the Stokes-Betrami System. These solutions include the generalized biaxisymmetric potentials. McCoy [10] considered the approximation of pseudoanalytic functions on the disk. Kumar et al. [9] studied the generalized order and generalized type of PAF in terms of the Fourier coefficients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. The aim of this paper is to improve the results of McCoy [10] and Kumar et al. [9]. Our results apply satisfactorily for slow growth.

  17. An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

    KAUST Repository

    Karlsson, Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

    2015-01-01

    This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.

  18. A Simple Preparation Method for Diphosphoimidazole

    DEFF Research Database (Denmark)

    Rosenberg, T.

    1964-01-01

    A simple method for the preparation of diphosphoimidazole is presented that involves direct phosphorylation of imidazole by phosphorus oxychloride in alkaline aqueous solution. Details are given on the use of diphosphoimidazole in preparing sodium phosphoramidate and certain phosphorylated amino...

  19. Simple Perturbation Example for Quantum Chemistry.

    Science.gov (United States)

    Goodfriend, P. L.

    1985-01-01

    Presents a simple example that illustrates various aspects of the Rayleigh-Schrodinger perturbation theory. The example is a particularly good one because it is straightforward and can be compared with both the exact solution and with experimental data. (JN)

  20. Sampling and Low-Rank Tensor Approximation of the Response Surface

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann Georg; El-Moselhy, Tarek A.

    2013-01-01

    Most (quasi)-Monte Carlo procedures can be seen as computing some integral over an often high-dimensional domain. If the integrand is expensive to evaluate-we are thinking of a stochastic PDE (SPDE) where the coefficients are random fields and the integrand is some functional of the PDE-solution-there is the desire to keep all the samples for possible later computations of similar integrals. This obviously means a lot of data. To keep the storage demands low, and to allow evaluation of the integrand at points which were not sampled, we construct a low-rank tensor approximation of the integrand over the whole integration domain. This can also be viewed as a representation in some problem-dependent basis which allows a sparse representation. What one obtains is sometimes called a "surrogate" or "proxy" model, or a "response surface". This representation is built step by step or sample by sample, and can already be used for each new sample. In case we are sampling a solution of an SPDE, this allows us to reduce the number of necessary samples, namely in case the solution is already well-represented by the low-rank tensor approximation. This can be easily checked by evaluating the residuum of the PDE with the approximate solution. The procedure will be demonstrated in the computation of a compressible transonic Reynolds-averaged Navier-Strokes flow around an airfoil with random/uncertain data. © Springer-Verlag Berlin Heidelberg 2013.

  1. An analytical approximation for resonance integral

    International Nuclear Information System (INIS)

    Magalhaes, C.G. de; Martinez, A.S.

    1985-01-01

    It is developed a method which allows to obtain an analytical solution for the resonance integral. The problem formulation is completely theoretical and based in concepts of physics of general character. The analytical expression for integral does not involve any empiric correlation or parameter. Results of approximation are compared with pattern values for each individual resonance and for sum of all resonances. (M.C.K.) [pt

  2. Approximate Dynamic Programming Solving the Curses of Dimensionality

    CERN Document Server

    Powell, Warren B

    2011-01-01

    Praise for the First Edition "Finally, a book devoted to dynamic programming and written using the language of operations research (OR)! This beautiful book fills a gap in the libraries of OR specialists and practitioners."-Computing Reviews This new edition showcases a focus on modeling and computation for complex classes of approximate dynamic programming problems Understanding approximate dynamic programming (ADP) is vital in order to develop practical and high-quality solutions to complex industrial problems, particularly when those problems involve making decisions in the presence of unce

  3. The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

    Science.gov (United States)

    Ito, K.

    1983-01-01

    Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

  4. Approximation of the Thomas-Fermi-Dirac potential for neutral atoms

    International Nuclear Information System (INIS)

    Jablonski, A.

    1992-01-01

    The frequently used analytical expression of Bonham and Strand approximating the Thomas-Fermi-Dirac (TFD) potential is closely analyzed. This expression does not satisfy the boundary conditions of the TFD differential equation, in particular, does not comprise the finite radius of the TFD potential. A modification of the analytical expression is proposed to adjust it to the boundary conditions. A new fit is made on the basis of the variational formulation of the TFD problem. An attempt is also made in the present work to develop a new numerical procedure providing very accurate solutions of this problem. Such solutions form a reference to check the quality of analytical approximations. Exemplary calculations of the elastic scattering cross sections are made for different expressions approximating the TFD potential to visualize the influence of the inaccuracies of the fit. It seems that the elastic scattering calculations should be based on extensive tables with the accurate values of the TFD screening function rather than on fitted analytical expressions. (orig.)

  5. A gradient approximation for calculating Debye temperatures from pairwise interatomic potentials

    International Nuclear Information System (INIS)

    Jackson, D.P.

    1975-09-01

    A simple gradient approximation is given for calculating the effective Debye temperature of a cubic crystal from central pairwise interatomic potentials. For examples of the Morse potential applied to cubic metals the results are in generally good agreement with experiment. (author)

  6. Scaling laws and accurate small-amplitude stationary solution for the motion of a planar vortex filament in the Cartesian form of the local induction approximation.

    Science.gov (United States)

    Van Gorder, Robert A

    2013-04-01

    We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.

  7. Approximate treatment of two soliton solutions of the sine-Gordon equation

    International Nuclear Information System (INIS)

    Mihaly, L.

    1979-05-01

    The so called breather solution of the sine-Gordon equation is phenomenologically described by an appropri.ately choosen potential acting between two particles. For some applications the method proves to be equivalent to other classical and quantum calculations. (author)

  8. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-05-01

    Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.

  9. Theory of inelastic electron tunneling from a localized spin in the impulsive approximation.

    Science.gov (United States)

    Persson, Mats

    2009-07-31

    A simple expression for the conductance steps in inelastic electron tunneling from spin excitations in a single magnetic atom adsorbed on a nonmagnetic metal surface is derived. The inelastic coupling between the tunneling electron and the spin is via the exchange coupling and is treated in an impulsive approximation using the Tersoff-Hamann approximation for the tunneling between the tip and the sample.

  10. A general approach for cache-oblivious range reporting and approximate range counting

    DEFF Research Database (Denmark)

    Afshani, Peyman; Hamilton, Chris; Zeh, Norbert

    2010-01-01

    We present cache-oblivious solutions to two important variants of range searching: range reporting and approximate range counting. Our main contribution is a general approach for constructing cache-oblivious data structures that provide relative (1+ε)-approximations for a general class of range c...

  11. Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

    International Nuclear Information System (INIS)

    Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.

    2008-01-01

    He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient

  12. Variational, projection methods and Pade approximants in scattering theory

    International Nuclear Information System (INIS)

    Turchetti, G.

    1980-12-01

    Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt

  13. Approximate spatio-temporal top-k publish/subscribe

    KAUST Repository

    Chen, Lisi

    2018-04-26

    Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

  14. Approximate spatio-temporal top-k publish/subscribe

    KAUST Repository

    Chen, Lisi; Shang, Shuo

    2018-01-01

    Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

  15. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    Energy Technology Data Exchange (ETDEWEB)

    Garcia Velarde, M

    1977-07-01

    Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.

  16. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    International Nuclear Information System (INIS)

    Garcia Velarde, M.

    1977-01-01

    Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es

  17. Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

    International Nuclear Information System (INIS)

    Garcia Velarde, M.

    1977-01-01

    Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

  18. A solution for the narrow rectangular punch

    NARCIS (Netherlands)

    Panek, C.F.; Kalker, J.J.

    1977-01-01

    This paper considers the problem of a rectangular flat ended punch acting on an elastic half-space. An approximate solution is generated through application of the elastic line integral equations. The results produced by this method are then compared with another approximate solution already

  19. WKB approximation in atomic physics

    International Nuclear Information System (INIS)

    Karnakov, Boris Mikhailovich

    2013-01-01

    Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.

  20. An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

    KAUST Repository

    Karlsson, Peer Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

    2015-01-01

    This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system