Integrodifferential equation approach. Pt. 1

International Nuclear Information System (INIS)

Oehm, W.; Sofianos, S.A.; Fiedeldey, H.; South Africa Univ., Pretoria. Dept. of Physics); Fabre de la Ripelle, M.; South Africa Univ., Pretoria. Dept. of Physics)

1990-02-01

A single integrodifferential equation in two variables, valid for A nucleons interacting by pure Wigner forces, which has previously only been solved in the extreme and uncoupled adiabatic approximations is now solved exactly for three- and four-nucleon systems. The results are in good agreement with the values obtained for the binding energies by means of an empirical interpolation formula. This validates all our previous conclusions, in particular that the omission of higher (than two) order correlations in our four-body equation only produces a rather small underbinding. The integrodifferential equation approach (IDEA) is here also extended to spin-dependent forces of the Malfliet-Tjon type, resulting in two coupled integrodifferential equations in two variables. The exact solution and the interpolated adiabatic approximation are again in good agreement. The inclusion of the hypercentral part of the two-body interaction in the definition of the Faddeev-type components again leads to substantial improvement for fully local potentials, acting in all partial waves. (orig.)

Action principles for the Vlasov equation

International Nuclear Information System (INIS)

Ye, H.; Morrison, P.J.

1992-01-01

Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables

Nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

Nonlinear differential equations

International Nuclear Information System (INIS)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

Nonlinear Electrostatic Wave Equations for Magnetized Plasmas

DEFF Research Database (Denmark)

Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans

1984-01-01

The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....

The stability of locus equation slopes across stop consonant voicing/aspiration

Science.gov (United States)

Sussman, Harvey M.; Modarresi, Golnaz

2004-05-01

The consistency of locus equation slopes as phonetic descriptors of stop place in CV sequences across voiced and voiceless aspirated stops was explored in the speech of five male speakers of American English and two male speakers of Persian. Using traditional locus equation measurement sites for F2 onsets, voiceless labial and coronal stops had significantly lower locus equation slopes relative to their voiced counterparts, whereas velars failed to show voicing differences. When locus equations were derived using F2 onsets for voiced stops that were measured closer to the stop release burst, comparable to the protocol for measuring voiceless aspirated stops, no significant effects of voicing/aspiration on locus equation slopes were observed. This methodological factor, rather than an underlying phonetic-based explanation, provides a reasonable account for the observed flatter locus equation slopes of voiceless labial and coronal stops relative to voiced cognates reported in previous studies [Molis et al., J. Acoust. Soc. Am. 95, 2925 (1994); O. Engstrand and B. Lindblom, PHONUM 4, 101-104]. [Work supported by NIH.

On a closed form solution of the point kinetics equations with reactivity feedback of temperature

International Nuclear Information System (INIS)

Silva, Jeronimo J.A.; Vilhena, Marco T.M.B.; Petersen, Claudio Z.; Bodmann, Bardo E.J.; Alvim, Antonio C.M.

2011-01-01

An analytical solution of the point kinetics equations to calculate reactivity as a function of time by the Decomposition method has recently appeared in the literature. In this paper, we go one step forward, by considering the neutron point kinetics equations together with temperature feedback effects. To accomplish that, we extended the point kinetics by a temperature perturbation, obtaining a second order nonlinear ordinary differential equation. This equation is then solved by the Decomposition Method, that is, by expanding the neutron density in a series and the nonlinear terms into Adomian Polynomials. Substituting these expansions into the nonlinear ordinary equation, we construct a recursive set of linear problems that can be solved by the methodology previously mentioned for the point kinetics equation. We also report on numerical simulations and comparisons against literature results. (author)

The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

Correction Equations to Adjust Self-Reported Height and Weight for Obesity Estimates among College Students

Science.gov (United States)

Mozumdar, Arupendra; Liguori, Gary

2011-01-01

The purposes of this study were to generate correction equations for self-reported height and weight quartiles and to test the accuracy of the body mass index (BMI) classification based on corrected self-reported height and weight among 739 male and 434 female college students. The BMIqc (from height and weight quartile-specific, corrected…

Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

International Nuclear Information System (INIS)

Carter, B.; McLenaghan, R.G.

1982-01-01

It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

Self-reported previous knee injury and low knee function increase knee injury risk in adolescent female football

DEFF Research Database (Denmark)

Clausen, Mikkel Bek; Tang, L; Zebis, M K

2016-01-01

with low KOOS subscale scores (Sport/Recreational (RR: 2.2) and Quality of Life (RR: 3.0) (P time-loss knee...... questionnaires were collected at baseline. Time-loss knee injuries and football exposures were reported weekly by answers to standardized text-message questions, followed by injury telephone interviews. A priori, self-reported previous knee injury and low KOOS subscale scores (... as independent variables in the risk factor analyses. The study showed that self-reported previous knee injury significantly increased the risk of time-loss knee injury [relative risk (RR): 3.65, 95% confidence (CI) 1.73-7.68; P time-loss knee injury was also significantly increased in players...

Performance of Chronic Kidney Disease Epidemiology Collaboration Creatinine-Cystatin C Equation for Estimating Kidney Function in Cirrhosis

Science.gov (United States)

Mindikoglu, Ayse L.; Dowling, Thomas C.; Weir, Matthew R.; Seliger, Stephen L.; Christenson, Robert H.; Magder, Laurence S.

2013-01-01

Conventional creatinine-based glomerular filtration rate (GFR) equations are insufficiently accurate for estimating GFR in cirrhosis. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) recently proposed an equation to estimate GFR in subjects without cirrhosis using both serum creatinine and cystatin C levels. Performance of the new CKD-EPI creatinine-cystatin C equation (2012) was superior to previous creatinine- or cystatin C-based GFR equations. To evaluate the performance of the CKD-EPI creatinine-cystatin C equation in subjects with cirrhosis, we compared it to GFR measured by non-radiolabeled iothalamate plasma clearance (mGFR) in 72 subjects with cirrhosis. We compared the “bias”, “precision” and “accuracy” of the new CKD-EPI creatinine-cystatin C equation to that of 24-hour urinary creatinine clearance (CrCl), Cockcroft-Gault (CG) and previously reported creatinine- and/or cystatin C-based GFR-estimating equations. Accuracy of CKD-EPI creatinine-cystatin C equation as quantified by root mean squared error of difference scores [differences between mGFR and estimated GFR (eGFR) or between mGFR and CrCl, or between mGFR and CG equation for each subject] (RMSE=23.56) was significantly better than that of CrCl (37.69, P=0.001), CG (RMSE=36.12, P=0.002) and GFR-estimating equations based on cystatin C only. Its accuracy as quantified by percentage of eGFRs that differed by greater than 30% with respect to mGFR was significantly better compared to CrCl (P=0.024), CG (P=0.0001), 4-variable MDRD (P=0.027) and CKD-EPI creatinine 2009 (P=0.012) equations. However, for 23.61% of the subjects, GFR estimated by CKD-EPI creatinine-cystatin C equation differed from the mGFR by more than 30%. CONCLUSIONS The diagnostic performance of CKD-EPI creatinine-cystatin C equation (2012) in patients with cirrhosis was superior to conventional equations in clinical practice for estimating GFR. However, its diagnostic performance was substantially worse than

The horizontally homogeneous model equations of incompressible atmospheric flow in general orthogonal coordinates

DEFF Research Database (Denmark)

Jørgensen, Bo Hoffmann

2003-01-01

The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow overcomplex terrain. This idea was set forth...... by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Functional Fourier transforms and the loop equation

International Nuclear Information System (INIS)

Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.

1986-01-01

The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables

Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation

International Nuclear Information System (INIS)

Zecca, A.

2010-01-01

The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.

Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

Science.gov (United States)

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

Development and test of ion emitter modules for the projects ASPOC/CLUSTER (8th project year) and EQUATOR-S (4th project year). Final report

International Nuclear Information System (INIS)

Fehringer, H.M.; Ruedenauer, F.G.; Steiger, W.

1997-02-01

Not only was the failure of flight V001 of the newly developed ARIANE-V rocket a disaster for the European space industry and a drawback in the highly competitive launcher business, with the loss of its payload, ESA's 4 scientific CLUSTER satellites, also the work and expectations of hundreds of scientists and engineers were buried in the swamps of French Guyana. The Austrian experiment ASPOC, for which ion emitters have been developed under the contract reported here, was one of the 12 instruments onboard. In a meeting following the launch failure ESA's Science Policy Committee (SPC) decided to immediately rebuild one CLUSTER satellite and use the instrument spare models as the payload. This new mission was called PHOENIX. Furthermore, the SPC initiated studies to look for options of a CLUSTER reflight. The final decision about the future of the CLUSTER project is now due in February 1997. Since ASPOC has been lost, this report only very shortly deals with the work done up to the launch date. More important are two aspects: First, the ion emitters, the product which has been developed within this long term project, are of such high quality that they survived both the explosion of the rocket and the subsequent free fall from 3.6 km height. Ten ion emitters have been recovered from the debris and all of them were still working well. Second, new applications both in the scientific and in the commercial area have been found for the indium ion sources. Under an ESA contract their potential use as ion thrusters has recently successfully been studied. A further contract now has been placed for the development of a prototype ion thruster. Furthermore, the indium ion source has been selected as the primary ion emitter for the time of flight mass spectrometer COSIMA, a key instrument of the ROSETTA mission. Concerning EQUATOR-S, a new set of ion emitter modules has to be built, as those originally foreseen for EQUATOR-S are now being used for PHOENIX. The respective

Partial differential equations of parabolic type

CERN Document Server

Friedman, Avner

2008-01-01

This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman - Director of the Mathematical Biosciences Institute at The Ohio State University - offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations. Subsequent chapters explore asymptotic behavior of solutions, semi-linear equations and free boundary problems, and the extension of results concerning fundamenta

Construction of alternative Hamiltonian structures for field equations

Energy Technology Data Exchange (ETDEWEB)

Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2001-08-10

We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

Equations of State: From the Ideas of van der Waals to Association Theories

DEFF Research Database (Denmark)

Kontogeorgis, Georgios; Economou, Ioannis G.

2010-01-01

equations of state are sensitive to the mixing and combining rules used. Moreover, it is shown that previously reported deficiencies for size-asymmetric systems are more related to the van der Waals one fluid mixing rules used rather than the functionality of the cubic equation of state itself. Improved...... models for polar systems have been developed using the so-called EoS/GE mixing rules and we illustrate with the same methodology how these mixing rules should best be used for size-asymmetric systems. Despite the significant capabilities of cubic equations of state, their limitations lie especially...... in the description of complex phase behavior, e.g. liquid–liquid equilibria for highly polar and/or hydrogen bonding containing molecules. In these cases, advanced equations of state based on statistical mechanics that incorporate ideas from perturbation (e.g. SAFT and CPA), chemical (e.g. APACT) and lattice (e...

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

International Nuclear Information System (INIS)

Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

2003-01-01

We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

Nucleon Mass from a Covariant Three-Quark Faddeev Equation

International Nuclear Information System (INIS)

Eichmann, G.; Alkofer, R.; Krassnigg, A.; Nicmorus, D.

2010-01-01

We report the first study of the nucleon where the full Poincare-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ∼5% from the quark-diquark result obtained in previous studies.

Improving the Bandwidth Selection in Kernel Equating

Science.gov (United States)

Andersson, Björn; von Davier, Alina A.

2014-01-01

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…

Dynamics with infinitely many derivatives: variable coefficient equations

International Nuclear Information System (INIS)

Barnaby, Neil; Kamran, Niky

2008-01-01

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also from cosmologists. Crucial to any application is a firm understanding of the mathematical structure of infinite order partial differential equations. In our previous work we developed a formalism to study the initial value problem for linear infinite order equations with constant coefficients. Our approach relied on the use of a contour integral representation for the functions under consideration. In many applications, including the study of cosmological perturbations in nonlocal inflation, one must solve linearized partial differential equations about some time-dependent background. This typically leads to variable coefficient equations, in which case the contour integral methods employed previously become inappropriate. In this paper we develop the theory of a particular class of linear infinite order partial differential equations with variable coefficients. Our formalism is particularly well suited to the types of equations that arise in nonlocal cosmological perturbation theory. As an example to illustrate our formalism we compute the leading corrections to the scalar field perturbations in p-adic inflation and show explicitly that these are small on large scales.

Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

Notes on solving Maxwell equations, part 2, Green's function for stratified media

OpenAIRE

Rook, R.

2011-01-01

In the previous report (part 1), the problem and its governing equations are described and is discarded in this report. The finite element method in part 1, or any other method for that matter, determines the fields in and close to the scatterer (near-field) that is used to construct the fields in the far-field. The goal of part 2 is to find far-field expressions formulated as total fields or the Radar Cross Section (RCS) of the scattered fields. The far-field is calculated from the scatterer...

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2014-01-01

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation

Integrable semi-discretizations of the reduced Ostrovsky equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

Based on our previous work on the reduced Ostrovsky equation (J. Phys. A: Math. Theor. 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one being its original form, the other the differentiated form (the short wave limit of the Degasperis–Procesi equation) two semi-discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified. (paper)

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Directory of Open Access Journals (Sweden)

Lieberman Gary M

2007-01-01

Full Text Available We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation.

Functional equations and Green's functions for augmented scalar fields

International Nuclear Information System (INIS)

Klauder, J.R.

1977-01-01

Certain noncanonical self-coupled scalar quantum field theories, previously formulated by means of functional integration, are herein recast into the form of functional differential equations for the Green's functional. From these expressions the set of coupled equations relating the Green's functions is obtained. The new equations are compared with those of the conventional formulation, and are proposed as alternatives, especially for nonrenormalizable models when the conventional equations fail

From the continuous PV to discrete Painleve equations

International Nuclear Information System (INIS)

Tokihiro, T.; Grammaticos, B.; Ramani, A.

2002-01-01

We study the discrete transformations that are associated with the auto-Baecklund of the (continuous) P V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P V . Among them we find the asymmetric d-P II equation which is a well-known form of discrete P III . The relation between the ternary P I (previously obtained through the discrete dressing approach) and P V is also established. A new discrete Painleve equation is also derived. (author)

Higher order field equations. II

International Nuclear Information System (INIS)

Tolhoek, H.A.

1977-01-01

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

Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

International Nuclear Information System (INIS)

Aslan İsmail

2014-01-01

The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)

Hydrodynamic Equations for Flocking Models without Velocity Alignment

Science.gov (United States)

Peruani, Fernando

2017-10-01

The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently that several flocking behaviors can emerge in the absence of velocity alignment and as a result of short-range, position-based, attractive forces that act inside a vision cone. Here, we derive the corresponding hydrodynamic equations of a microscopic position-based flocking model, reviewing and extending previous reported results. In particular, we show that three distinct macroscopic collective behaviors can be observed: i) the coarsening of aggregates with no orientational order, ii) the emergence of static, elongated nematic bands, and iii) the formation of moving, locally polar structures, which we call worms. The derived hydrodynamic equations indicate that active particles interacting via position-based interactions belong to a distinct class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems.

Exact solutions of the neutron slowing down equation

International Nuclear Information System (INIS)

Dawn, T.Y.; Yang, C.N.

1976-01-01

The problem of finding the exact analytic closed-form solution for the neutron slowing down equation in an infinite homogeneous medium is studied in some detail. The existence and unique properties of the solution of this equation for both the time-dependent and the time-independent cases are studied. A direct method is used to determine the solution of the stationary problem. The final result is given in terms of a sum of indefinite multiple integrals by which solutions of some special cases and the Placzek-type oscillation are examined. The same method can be applied to the time-dependent problem with the aid of the Laplace transformation technique, but the inverse transform is, in general, laborious. However, the solutions of two special cases are obtained explicitly. Results are compared with previously reported works in a variety of cases. The time moments for the positive integral n are evaluated, and the conditions for the existence of the negative moments are discussed

Exact RG flow equations and quantum gravity

Science.gov (United States)

de Alwis, S. P.

2018-03-01

We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

Fast sweeping method for the factored eikonal equation

Science.gov (United States)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

Eikenella corrodens endocarditis and liver abscess in a previously healthy male, a case report

DEFF Research Database (Denmark)

Nordholm, Anne Christine; Vøgg, Ruth Ottilia Birgitta; Permin, Henrik

2018-01-01

BACKGROUND: Eikenella corrodens is one of the HACEK bacteria constituting part of the normal flora of the oropharynx, however, still an uncommon pathogen. We report a case of a large Eikenella corrodens liver abscess with simultaneously endocarditis in a previously healthy male. CASE PRESENTATION...... on pneumonia treatment, a PET-CT scan was performed, which showed a large multiloculated abscess in the liver. The abscess was drained using ultrasound guidance. Culture demonstrated Eikenella corrodens. Transesophageal echocardiography revealed aortic endocarditis. The patient was treated with antibiotics...... corrodens concurrent liver abscess and endocarditis. The case report highlights that Eikenella corrodens should be considered as a cause of liver abscess. Empirical treatment of pyogenic liver abscess will most often cover Eikenella corrodens, but the recommended treatment is a third generation...

New exact solutions for two nonlinear equations

International Nuclear Information System (INIS)

Wang Quandi; Tang Minying

2008-01-01

In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended

Entire solutions of nonlinear differential-difference equations.

Science.gov (United States)

Li, Cuiping; Lü, Feng; Xu, Junfeng

2016-01-01

In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.

Covariant Conformal Decomposition of Einstein Equations

Science.gov (United States)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Effective electronic-only Kohn–Sham equations for the muonic molecules

Science.gov (United States)

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the Nuclear-Electronic Orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing muon vibration, which are optimized during the solution of the EKS equations making muon KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a duality between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential maybe derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding muonium atom to ferrocene. In line with previous computational studies, from the six possible species the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

Effective electronic-only Kohn-Sham equations for the muonic molecules.

Science.gov (United States)

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

2018-03-28

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

New solitary wave solutions of the time-fractional Cahn-Allen equation via the improved (G'/G)-expansion method

Science.gov (United States)

Batool, Fiza; Akram, Ghazala

2018-05-01

An improved (G'/G)-expansion method is proposed for extracting more general solitary wave solutions of the nonlinear fractional Cahn-Allen equation. The temporal fractional derivative is taken in the sense of Jumarie's fractional derivative. The results of this article are generalized and extended version of previously reported solutions.

Equations for the stochastic cumulative multiplying chain

Energy Technology Data Exchange (ETDEWEB)

Lewins, J D [Cambridge Univ. (UK). Dept. of Engineering

1980-01-01

The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage.

Equations for the stochastic cumulative multiplying chain

International Nuclear Information System (INIS)

Lewins, J.D.

1980-01-01

The forward and backward equations for the conditional probability of the neutron multiplying chain are derived in a new generalization accounting for the chain length and admitting time dependent properties. These Kolmogorov equations form the basis of a variational and hence complete description of the 'lumped' multiplying system. The equations reduce to the marginal distribution, summed over all chain lengths, and to the simpler equations previously derived for that problem. The method of derivation, direct and in the probability space with the minimum of mathematical manipulations, is perhaps the chief attraction: the equations are also displayed in conventional generating function form. As such, they appear to apply to number of problems in areas of social anthropology, polymer chemistry, genetics and cell biology as well as neutron reactor theory and radiation damage. (author)

Numerical method for the nonlinear Fokker-Planck equation

International Nuclear Information System (INIS)

Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.

1997-01-01

A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society

Erysipelothrix endocarditis with previous cutaneous lesion: report of a case and review of the literature

Directory of Open Access Journals (Sweden)

Marion P. Rocha

1989-08-01

Full Text Available This report describes the first documented case of Erysipelothrix rhusiopathiae endocarditis in Latin America. The patient was a 51-years-old male, moderate alcoholic, with a previous history of aortic failure. He was used to fishing and cooking as a hobby and had his left hand wounded by a fish-bone. The disease began with erysipeloid form and developed to septicemia and endocarditis. He was treated with antibiotics and surgery for aortic valve replacement. There are only 46 cases of E. rhusiopathiae endocarditis reported to date. The authors wonder if several other cases might go unreported for lack of microbiological laboratorial diagnosis.

Ideal solar cell equation in the presence of photon recycling

International Nuclear Information System (INIS)

Lan, Dongchen; Green, Martin A.

2014-01-01

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included

Ideal solar cell equation in the presence of photon recycling

Energy Technology Data Exchange (ETDEWEB)

Lan, Dongchen, E-mail: d.lan@unsw.edu.au; Green, Martin A., E-mail: m.green@unsw.edu.au [Australian Centre for Advanced Photovoltaics, School of Photovoltaic and Renewable Energy Engineering, University of New South Wales, Sydney 2052 (Australia)

2014-11-07

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

Evaluating Equating Accuracy and Assumptions for Groups that Differ in Performance

Science.gov (United States)

Powers, Sonya; Kolen, Michael J.

2014-01-01

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

Change in bias in self-reported body mass index in Australia between 1995 and 2008 and the evaluation of correction equations.

Science.gov (United States)

Hayes, Alison J; Clarke, Philip M; Lung, Tom Wc

2011-09-25

Many studies have documented the bias in body mass index (BMI) determined from self-reported data on height and weight, but few have examined the change in bias over time. Using data from large, nationally-representative population health surveys, we examined change in bias in height and weight reporting among Australian adults between 1995 and 2008. Our study dataset included 9,635 men and women in 1995 and 9,141 in 2007-2008. We investigated the determinants of the bias and derived correction equations using 2007-2008 data, which can be applied when only self-reported anthropometric data are available. In 1995, self-reported BMI (derived from height and weight) was 1.2 units (men) and 1.4 units (women) lower than measured BMI. In 2007-2008, there was still underreporting, but the amount had declined to 0.6 units (men) and 0.7 units (women) below measured BMI. The major determinants of reporting error in 2007-2008 were age, sex, measured BMI, and education of the respondent. Correction equations for height and weight derived from 2007-2008 data and applied to self-reported data were able to adjust for the bias and were accurate across all age and sex strata. The diminishing reporting bias in BMI in Australia means that correction equations derived from 2007-2008 data may not be transferable to earlier self-reported data. Second, predictions of future overweight and obesity in Australia based on trends in self-reported information are likely to be inaccurate, as the change in reporting bias will affect the apparent increase in self-reported obesity prevalence.

Final report [on solving the multigroup diffusion equations

International Nuclear Information System (INIS)

Birkhoff, G.

1975-01-01

Progress achieved in the development of variational methods for solving the multigroup neutron diffusion equations is described. An appraisal is made of the extent to which improved variational methods could advantageously replace difference methods currently used

Unsteady analytical solutions to the Poisson–Nernst–Planck equations

International Nuclear Information System (INIS)

Schönke, Johannes

2012-01-01

It is shown that the Poisson–Nernst–Planck equations for a single ion species can be formulated as one equation in terms of the electric field. This previously not analyzed equation shows similarities to the vector Burgers equation and is identical with it in the one dimensional case. Several unsteady exact solutions for one and multidimensional cases are presented. Besides new mathematical insights which these first known unsteady solutions give, they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code. (paper)

Lack of Cetuximab induced skin toxicity in a previously irradiated field: case report and review of the literature

Science.gov (United States)

2010-01-01

Introduction Mutation, amplification or dysregulation of the EGFR family leads to uncontrolled division and predisposes to cancer. Inhibiting the EGFR represents a form of targeted cancer therapy. Case report We report the case of 79 year old gentlemen with a history of skin cancer involving the left ear who had radiation and surgical excision. He had presented with recurrent lymph node in the left upper neck. We treated him with radiation therapy concurrently with Cetuximab. He developed a skin rash over the face and neck area two weeks after starting Cetuximab, which however spared the previously irradiated area. Conclusion The etiology underlying the sparing of the previously irradiated skin maybe due to either decrease in the population of EGFR expressing cells or decrease in the EGFR expression. We raised the question that "Is it justifiable to use EGFR inhibitors for patients having recurrence in the previously irradiated field?" We may need further research to answer this question which may guide the physicians in choosing appropriate drug in this scenario. PMID:20478052

New correct solutions of the Dirac equation. 5

International Nuclear Information System (INIS)

Bagrov, V.G.; Byzov, N.N.; Gitman, D.M.; Klimenko, Yu.I.; Meshkov, A.G.; Shapovalov, V.N.; Shakhmatov, V.M.

1975-01-01

Some exact solutions for the Dirac equation, Klein-Gordon equation and classical relativistic equations of motion of an electron in external electromagnetic fields of a special type are considered. When fields E vector and H vector are related by the expression H vector=[n vector E vector]+n vector H 3 , where n vector is a constant unit vector, it turns out that among fields permitting the separation of variables in the Klein-Gordon equation more than half satisfy this relationship. For such fields the solution of the Dirac equation may be simplified considerably. Four specific kinds of fields are examined. The character of electron motion in such fields is peculiar but in the mathematical aspect, part of the problem is reduced to those considered previously

Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods

International Nuclear Information System (INIS)

Reynolds, J. M.; Lopez-Bruna, D.

2009-01-01

In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs

Lyapunov functionals and stability of stochastic functional differential equations

CERN Document Server

Shaikhet, Leonid

2013-01-01

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

International Nuclear Information System (INIS)

Delhaye, J.M.

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

An efficient numerical technique for solving navier-stokes equations for rotating flows

International Nuclear Information System (INIS)

Haroon, T.; Shah, T.M.

2000-01-01

This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)

Prediction of cardiorespiratory fitness from self-reported data in elderly

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Geraldo A Maranhao Neto

2017-12-01

Full Text Available Cardiorespiratory fitness (CRF is associated with several health outcomes. Some non-exercise equations are available for CRF estimation. However, little is known about the validation of these equations among elderly. The aim of this study was to exam the validity of non-exercise equations with self-reported information in elderly. Participants (n= 93 aged 60 to 91 years measured CRF using maximal cardiopulmonary exercise test. Five non-exercise equations were selected. Data included in the equations (age, sex, weight, height, body mass index, physical activity and smoking were self-reported. Coefficient of determination (R2 of linear regressions with laboratory-measured VO2 peak ranged from 0.04 to 0.64. The Bland-Altman plots showed higher agreement between achieved and predicted CRF obtained by Jackson and colleagues, and Wier and colleagues equations. On the other hand, the other equations showed lower agreement and overestimation. Our findings provide evidences that two non-exercise equations, previously developed, could be used on the prediction of CRF among elderly.

Electroweak evolution equations

International Nuclear Information System (INIS)

Ciafaloni, Paolo; Comelli, Denis

2005-01-01

Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings

Ordinary differential equation for local accumulation time.

Science.gov (United States)

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program

International Nuclear Information System (INIS)

Sharp, W.M.; Yu, S.S.; Lee, E.P.

1987-01-01

A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations

Linear Einstein equations and Kerr-Schild maps

International Nuclear Information System (INIS)

Gergely, Laszlo A

2002-01-01

We prove that given a solution of the Einstein equations g ab for the matter field T ab , an autoparallel null vector field l a and a solution (l a l c , T ac ) of the linearized Einstein equation on the given background, the Kerr-Schild metric g ac + λl a l c (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor T ac + λT ac + λ 2 l (a T c)b l b . The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Guerses and Guersey

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

Science.gov (United States)

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

Analytical solution to the hybrid diffusion-transport equation

International Nuclear Information System (INIS)

Nanneh, M.M.; Williams, M.M.R.

1986-01-01

A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)

The electromagnetic field equations for moving media

International Nuclear Information System (INIS)

Ivezić, T

2017-01-01

In this paper a formulation of the field equation for moving media is developed by the generalization of an axiomatic geometric formulation of the electromagnetism in vacuum (Ivezić T 2005 Found. Phys. Lett. 18 401). First, the field equations with bivectors F ( x ) and ℳ ( x ) are presented and then these equations are written with the 4D vectors E ( x ), B ( x ), P ( x ) and M ( x ). The latter contain both the 4D velocity vector u of a moving medium and the 4D velocity vector v of the observers who measure E and B fields. They do not appear in previous literature. All these equations are also written in the standard basis and compared with Maxwell’s equations with 3D vectors. In this approach the Ampère-Maxwell law and Gauss’s law are inseparably connected in one law and the same happens with Faraday’s law and the law that expresses the absence of magnetic charge. It is shown that Maxwell’s equations with 3D vectors and the field equations with 4D geometric quantities are not equivalent in 4D spacetime (paper)

FITTING AND TESTING ALLOMETRIC EQUATIONS FOR MEXICO’S SINALOAN TROPICAL DRY TREES AND FOREST INVENTORY PLOTS

Directory of Open Access Journals (Sweden)

Jose de Jesus Navar Chaidez

2016-05-01

Full Text Available Aboveground tree biomass (bole, branches and foliage, M, plays a key role in the conventional and sustainable management of forest communities. The standard approach to assess tree or plot M is harvesting trees, developing and fitting allometric equations to trees or forest inventory plot data. In the absence of local tree allometry, it is usually recommended to fit off site allometric equations to evaluate tree or plot M. This research aims: (a to develop an updated on site allometric equation (b to fit available off site allometric equations to destructively harvested trees and (c to fit available allometric equations to plot M of Mexico’s Sinaloan tropical dry forests to understand sources of inherent tree and plot M variability. Results showed that: (a the improved on site allometric equation increases precision in contrast to the conventional biomass equation previously reported as well as to off site tree M equations, (b off site allometry projects tree and plot M deviates by close to one order of magnitude. Two tested and recommended approaches to increase tree and plot M precision when fitting off site equations are: (i to use all available tree allometric functions to come up with a mean equation or (ii to calibrate off site equations by fitting new, local parameters that can be calculated using statistical programs.These options would eventually increase tree and plot M precision in regional evaluations.

Incompressible spectral-element method: Derivation of equations

Science.gov (United States)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Field equations for gravity quadratic in the curvature

International Nuclear Information System (INIS)

Rose, B.

1992-01-01

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs

Irreducibility and co-primeness as an integrability criterion for discrete equations

International Nuclear Information System (INIS)

Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji

2014-01-01

We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor. 47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. (paper)

Proposal of the penalty factor equations considering weld strength over-match

International Nuclear Information System (INIS)

Kim, Jong Sung; Jeong, Jae Wook; Lee, Kang Yong

2017-01-01

This paper proposes penalty factor equations that take into consideration the weld strength over-match given in the classified form similar to the revised equations presented in the Code Case N-779 via cyclic elastic-plastic finite element analysis. It was found that the Ke analysis data reflecting elastic follow-up can be consolidated by normalizing the primary-plus-secondary stress intensity ranges excluding the nonlinear thermal stress intensity component, S_n to over-match degree of yield strength, M_F. For the effect of over-match on K_n × K_v_"1, dispersion of the Kn × K_v analysis data can be sharply reduced by dividing total stress intensity range, excluding local thermal stresses, S_p_-_l_t by M_F. Finally, the proposed equations were applied to the weld between the safe end and the piping of a pressurizer surge nozzle in pressurized water reactors in order to calculate a cumulative usage factor. The cumulative usage factor was then compared with those derived by the previous K_e factor equations. The result shows that application of the proposed equations can significantly reduce conservatism of fatigue assessment using the previous K_e factor equations

Proposal of the Penalty Factor Equations Considering Weld Strength Over-Match

Directory of Open Access Journals (Sweden)

Jong-Sung Kim

2017-06-01

Full Text Available This paper proposes penalty factor equations that take into consideration the weld strength over-match given in the classified form similar to the revised equations presented in the Code Case N-779 via cyclic elastic-plastic finite element analysis. It was found that the Ke analysis data reflecting elastic follow-up can be consolidated by normalizing the primary-plus-secondary stress intensity ranges excluding the nonlinear thermal stress intensity component, Sn to over-match degree of yield strength, MF. For the effect of over-match on Kn × Κν, dispersion of the Kn × Κν analysis data can be sharply reduced by dividing total stress intensity range, excluding local thermal stresses, Sp-lt by MF. Finally, the proposed equations were applied to the weld between the safe end and the piping of a pressurizer surge nozzle in pressurized water reactors in order to calculate a cumulative usage factor. The cumulative usage factor was then compared with those derived by the previous Ke factor equations. The result shows that application of the proposed equations can significantly reduce conservatism of fatigue assessment using the previous Ke factor equations.

AdS3/CFT2, finite-gap equations and massless modes

International Nuclear Information System (INIS)

Lloyd, Thomas; Stefański, Bogdan Jr.

2014-01-01

It is known that string theory on AdS 3 ×M 7 backgrounds, where M 7 =S 3 ×S 3 ×S 1 or S 3 ×T 4 , is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finite-gap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finite-gap equations on these AdS 3 ×M 7 backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we re-examine the derivation of the AdS 3 ×M 7 finite-gap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finite-gap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS 3 ×M 7

A calderón multiplicative preconditioner for the combined field integral equation

KAUST Repository

Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric

2009-01-01

A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation

Klein paradox in the Breit equation

International Nuclear Information System (INIS)

Krolikowski, W.; Turski, A.; Rzewuski, J.

1979-01-01

We demonstrate that in the Breit equation with a central potential V(r) having the property V(r 0 )=E there appears a Klein paradox at r=r 0 . This phenomenon, besides the previously found Klein paradox at r→infinite appearing if V(r)→infinite at r→infinite, seems to indicate that in the Breit equation valid in the single-particle theory the sea of particle-antiparticle pairs is not well separated from the considered two-body configuration. We conjecture that both phenomena should be absent from the Salpeter equation which is consistent with the hole theory. We prove this conjecture in the limit of m( 1 )→infinite and m( 2 )→infinite, where we neglect the terms approx. 1/m( 1 ) and 1/m( 2 ). (orig./WL) [de

Nonlinear electrostatic wave equations for magnetized plasmas - II

DEFF Research Database (Denmark)

Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.

1985-01-01

For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....

Adenylosuccinate lyase (ADSL) and infantile autism: Absence of previously reported point mutation

Energy Technology Data Exchange (ETDEWEB)

Fon, E.A.; Sarrazin, J.; Rouleau, G.A. [Montreal General Hospital (Canada)] [and others

1995-12-18

Autism is a heterogeneous neuropsychiatric syndrome of unknown etiology. There is evidence that a deficiency in the enzyme adenylosuccinate lyase (ADSL), essential for de novo purine biosynthesis, could be involved in the pathogenesis of certain cases. A point mutation in the ADSL gene, resulting in a predicted serine-to-proline substitution and conferring structural instability to the mutant enzyme, has been reported previously in 3 affected siblings. In order to determine the prevalence of the mutation, we PCR-amplified the exon spanning the site of this mutation from the genomic DNA of patients fulfilling DSM-III-R criteria for autistic disorder. None of the 119 patients tested were found to have this mutation. Furthermore, on preliminary screening using single-strand conformation polymorphism (SSCP), no novel mutations were detected in the coding sequence of four ADSL exons, spanning approximately 50% of the cDNA. In light of these findings, it appears that mutations in the ADSL gene represent a distinctly uncommon cause of autism. 12 refs., 2 figs.

On the solution of the Liouville equation over a rectangle

Directory of Open Access Journals (Sweden)

A. M. Arthurs

1996-01-01

Full Text Available Methods for integral equations are used to derive pointwise bounds for the solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the resulting solutions are more accurate than those obtained previously by other methods.

Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity

Science.gov (United States)

Hamilton, Ian

1992-01-01

For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.

Feynman integrals and difference equations

International Nuclear Information System (INIS)

Moch, S.; Schneider, C.

2007-09-01

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

Preliminary bioelectrical impedance analysis (BIA) equation for body composition assessment in young females from Colombia

International Nuclear Information System (INIS)

Caicedo, J C; González-Correa, C H; González-Correa, C A

2013-01-01

A previous study showed that reported BIA equations for body composition are not suitable for Colombian population. The purpose of this study was to develop and validate a preliminary BIA equation for body composition assessment in young females from Colombia, using hydrodensitometry as reference method. A sample of 30 young females was evaluated. Inclusion and exclusion criteria were defined to minimize the variability of BIA. Height, weight, BIA, residual lung volume (RV) and underwater weight (UWW) were measured. A preliminary BIA equation was developed (r 2 = 0.72, SEE = 2.48 kg) by stepwise multiple regression with fat-free mass (FFM) as dependent variable and weight, height and impedance measurements as independent variables. The quality of regression was evaluated and a cross-validation against 50% of sample confirmed that results obtained with the preliminary BIA equation is interchangeable with results obtained with hydrodensitometry (r 2 = 0.84, SEE = 2.62 kg). The preliminary BIA equation can be used for body composition assessment in young females from Colombia until a definitive equation is developed. The next step will be increasing the sample, including a second reference method, as deuterium oxide dilution (D 2 O), and using multi-frequency BIA (MF-BIA). It would also be desirable to develop equations for males and other ethnic groups in Colombia.

Traveling solitary wave solutions to evolution equations with nonlinear terms of any order

International Nuclear Information System (INIS)

Feng Zhaosheng

2003-01-01

Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature

Stevens-Johnson Syndrome Induced by Carbamazepine Treatment in a Patient Who Previously Had Carbamazepine Induced Pruritus - A Case Report -

OpenAIRE

Bae, Hyun Min; Park, Yoo Jung; Kim, Young Hoon; Moon, Dong Eon

2013-01-01

Stevens-Johnson syndrome (SJS) is a rare but life-threatening skin reaction disease and carbamazepine is one of its most common causes. We report a case of SJS secondary to carbamazepine in a patient with previous pruritus due to carbamazepine which was given for treatment of trigeminal neuralgia. We would like to caution all providers that carbamazepine readministration should be avoided in the patient with a previous history of SJS or adverse skin reaction. In addition, we strongly recommen...

Evaluation of time correlation functions from a generalized Enskog equation

Energy Technology Data Exchange (ETDEWEB)

Yip, S.; Alley, W.E.; Alder, B.J.

1982-01-01

Numerical results for the density and current correlation functions in dense hard-shape fluids are obtained from a kinetic equation which is the extension of the linearized Enskog equation to finite wavelengths in order to demonstrate the convergence of the method of solution. Comparison is made to a previously proposed approximate solution.

Evaluation of time correlation functions from a generalized Enskog equation

International Nuclear Information System (INIS)

Yip, S.; Alley, W.E.; Alder, B.J.

1982-01-01

Numerical results for the density and current correlation functions in dense hard-shape fluids are obtained from a kinetic equation which is the extension of the linearized Enskog equation to finite wavelengths in order to demonstrate the convergence of the method of solution. Comparison is made to a previously proposed approximate solution

Derivation of the Finslerian gauge field equations

International Nuclear Information System (INIS)

Asanov, G.S.

1984-01-01

As is well known the simplest way of formulating the equations for the Yang-Mills gauge fields consists in taking the Lagrangian to be quadratic in the gauge tensor, whereas the application of such an approach to the gravitational field yields equations which are of essentially more complicated structure than the Einstein equations. On the other hand, in the gravitational field theory the Lagrangian can be constructed to be of forms which may be both quadratic and linear in the curvature tensor, whereas the latter possibility is absent in the current gauge field theories. In previous work it has been shown that the Finslerian structure of the space-time gives rise to certain gauge fields provided that the internal symmetries may be regarded as symmetries of a three-dimensional Riemannian space. Continuing this work we show that appropriate equations for these gauge fields can be formulated in both ways, namely on the basis of the quadratic Lagrangian or, if a relevant generalization of the Palatini method is applied, on the basis of a Lagrangian linear in the gauge field strength tensor. The latter possibility proves to result in equations which are similar to the Einstein equations, a distinction being that the Finslerian Cartan curvature tensor rather then the Riemann curvature tensor enters the equations. (author)

Solution of differential equations by application of transformation groups

Science.gov (United States)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Feynman integrals and difference equations

Energy Technology Data Exchange (ETDEWEB)

Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

2007-09-15

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

Differential equations and integrable models: the SU(3) case

International Nuclear Information System (INIS)

Dorey, Patrick; Tateo, Roberto

2000-01-01

We exhibit a relationship between the massless a 2 (2) integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schroedinger equation. This forms part of a more general correspondence involving A 2 -related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators phi 12 , phi 21 and phi 15 . This is checked against previous results obtained using the thermodynamic Bethe ansatz

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Some Additional Remarks on the Cumulant Expansion for Linear Stochastic Differential Equations

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1984-01-01

We summarize our previous results on cumulant expansions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

Some additional remarks on the cumulant expansion for linear stochastic differential equations

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1984-01-01

We summarize our previous results on cumular expasions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

Reference Values for Spirometry Derived Using Lambda, Mu, Sigma (LMS) Method in Korean Adults: in Comparison with Previous References.

Science.gov (United States)

Jo, Bum Seak; Myong, Jun Pyo; Rhee, Chin Kook; Yoon, Hyoung Kyu; Koo, Jung Wan; Kim, Hyoung Ryoul

2018-01-15

The present study aimed to update the prediction equations for spirometry and their lower limits of normal (LLN) by using the lambda, mu, sigma (LMS) method and to compare the outcomes with the values of previous spirometric reference equations. Spirometric data of 10,249 healthy non-smokers (8,776 females) were extracted from the fourth and fifth versions of the Korea National Health and Nutrition Examination Survey (KNHANES IV, 2007-2009; V, 2010-2012). Reference equations were derived using the LMS method which allows modeling skewness (lambda [L]), mean (mu [M]), and coefficient of variation (sigma [S]). The outcome equations were compared with previous reference values. Prediction equations were presented in the following form: predicted value = e{a + b × ln(height) + c × ln(age) + M - spline}. The new predicted values for spirometry and their LLN derived using the LMS method were shown to more accurately reflect transitions in pulmonary function in young adults than previous prediction equations derived using conventional regression analysis in 2013. There were partial discrepancies between the new reference values and the reference values from the Global Lung Function Initiative in 2012. The results should be interpreted with caution for young adults and elderly males, particularly in terms of the LLN for forced expiratory volume in one second/forced vital capacity in elderly males. Serial spirometry follow-up, together with correlations with other clinical findings, should be emphasized in evaluating the pulmonary function of individuals. Future studies are needed to improve the accuracy of reference data and to develop continuous reference values for spirometry across all ages. © 2018 The Korean Academy of Medical Sciences.

Singularities of Type-Q ABS Equations

Directory of Open Access Journals (Sweden)

James Atkinson

2011-07-01

Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.

Review on mathematical basis for thermal conduction equation

Energy Technology Data Exchange (ETDEWEB)

Park, D. G.; Kim, H. M

2007-10-15

In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation.

Review on mathematical basis for thermal conduction equation

International Nuclear Information System (INIS)

Park, D. G.; Kim, H. M.

2007-10-01

In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation

Gravitational closure of matter field equations

Science.gov (United States)

Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

2018-04-01

The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

An equation satisfied by the tangent to a shear-free, geodesic, null congruence

International Nuclear Information System (INIS)

Hogan, P.A.; Dublin Inst. for Advanced Studies

1987-01-01

A tensorial equation satisfied by the tangent to a shear-free geodesic, null congruence is presented. If the congruence is neither twist-free nor expansion-free then the equation defines a second, unique, null direction previously obtained, using the spinor formalism, by Somers. Some further properties of the equation are discussed. (orig.)

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

Energy Technology Data Exchange (ETDEWEB)

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

1990-03-01

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

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

Energy Technology Data Exchange (ETDEWEB)

Boiti, M; Leon, J J.P.; Pempinelli, F [Montpellier-2 Univ., 34 (France). Lab. de Physique Mathematique

1989-10-30

We define a new spectral transform r(k,l) of the potential u in the time dependent Schroedinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schroedinger equation are used to express the spectral transform f(k,l) previously introduced by Manakov and Fokas and Ablowitz in terms of r(k,l). The main advantage of the new spectral transform r(k,l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r(k,l) are also obtained. (orig.).

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

International Nuclear Information System (INIS)

Boiti, M.; Leon, J.J.P.; Pempinelli, F.

1989-01-01

We define a new spectral transform r(k,l) of the potential u in the time dependent Schroedinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schroedinger equation are used to express the spectral transform f(k,l) previously introduced by Manakov and Fokas and Ablowitz in terms of r(k,l). The main advantage of the new spectral transform r(k,l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r(k,l) are also obtained. (orig.)

Proposal of the penalty factor equations considering weld strength over-match

Energy Technology Data Exchange (ETDEWEB)

Kim, Jong Sung [Dept. of Nuclear Engineering, Sejong University, Seoul (Korea, Republic of); Jeong, Jae Wook [Korea Hydro and Nuclear Power Co., Ltd., Gyeongju (Korea, Republic of); Lee, Kang Yong [State Key Laboratory of Structural Analysis for Industrial Equipment, Dept. of Engineering Mechanics, Dalian University of Technology, Dalian (China)

2017-06-15

This paper proposes penalty factor equations that take into consideration the weld strength over-match given in the classified form similar to the revised equations presented in the Code Case N-779 via cyclic elastic-plastic finite element analysis. It was found that the Ke analysis data reflecting elastic follow-up can be consolidated by normalizing the primary-plus-secondary stress intensity ranges excluding the nonlinear thermal stress intensity component, S{sub n} to over-match degree of yield strength, M{sub F}. For the effect of over-match on K{sub n} × K{sub v{sup 1}}, dispersion of the Kn × K{sub v} analysis data can be sharply reduced by dividing total stress intensity range, excluding local thermal stresses, S{sub p-lt} by M{sub F}. Finally, the proposed equations were applied to the weld between the safe end and the piping of a pressurizer surge nozzle in pressurized water reactors in order to calculate a cumulative usage factor. The cumulative usage factor was then compared with those derived by the previous K{sub e} factor equations. The result shows that application of the proposed equations can significantly reduce conservatism of fatigue assessment using the previous K{sub e} factor equations.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.

Some physical solutions of Yang's equations for SU (2) gauge fields ...

Indian Academy of Sciences (India)

Some previously obtained physical solutions [1–3] of Yang's equations for (2) gauge fields [4], Charap's equations for pion dynamics [5,6] and their combination as proposed by Chakraborty and Chanda [1] have been presented. They represent different physical characteristics, e.g. spreading wave with solitary profile ...

Pan tropical biomass equations for Mexico's dry forests

Directory of Open Access Journals (Sweden)

José Návar

2014-12-01

Full Text Available This study reports a set of robust regional M-tree allometric equations for Mexico's tropical dry forests and their application to a forest inventory dataset for the States of Durango and Sinaloa, Mexico. Calculated M data from 15 reported equations were fitted, applied and validated for regional and global models. Proposed theoretical models, empirically derived equations, as well as global and local reported equations were fitted and applied to calculated M-tree data using wood specific gravity, diameter at breast height, and top height as exogenous variables. Empirically-derived, computer-based equations assessed the M-tree evaluations slightly better than the theoretical, the global and the local models. However, the theoretical models projected compatible M-tree values and deserve further attention once wood specific gravity data are collected in the field. Using the best fit equation, mean M plot density values of 30, 41 and 35 Mg ha-1 were estimated from 57 plots (1,600 m² each, 217 plots (1,000 m² each and 166 plots (1,000 m² each in the tropical dry forests of the States of Durango, Tiniaquis and Vado Hondo (Sinaloa, respectively. The large sample size, the richness of the tested allometric models, the economic and ecological importance of this data-source, and the spatial coverage of these equations made this dataset uniquely useful for biomass, charcoal, and other bio-energy estimations, as well as for understanding the inherent heterogeneity of the stand-structure in dynamic tropical forest environments.

Asymptotic problems for stochastic partial differential equations

Science.gov (United States)

Salins, Michael

Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

Pautz, S. D.; Franke, B. C.; Prinja, A. K.

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

Guiding Center Equations in Toroidal Equilibria

International Nuclear Information System (INIS)

White, Roscoe; Zakharov, Leonid

2002-01-01

Guiding center equations for particle motion in a general toroidal magnetic equilibrium configuration are derived using magnetic coordinates. Previous derivations made use of Boozer coordinates, in which the poloidal and toroidal angle variables are chosen so that the Jacobian is inversely proportional to the square of the magnetic field. It is shown that the equations for guiding center motion in any equilibrium possessing nested flux surfaces have exactly the same simple form as those derived in this special case. This allows the use of more spatially uniform coordinates instead of the Boozer coordinates, greatly increasing the accuracy of calculations in large beta and strongly shaped equilibria

Analysis of regularized Navier-Stokes equations, 2

Science.gov (United States)

Ou, Yuh-Roung; Sritharan, S. S.

1989-01-01

A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

An Evaluation of Five Linear Equating Methods for the NEAT Design

Science.gov (United States)

Mroch, Andrew A.; Suh, Youngsuk; Kane, Michael T.; Ripkey, Douglas R.

2009-01-01

This study uses the results of two previous papers (Kane, Mroch, Suh, & Ripkey, this issue; Suh, Mroch, Kane, & Ripkey, this issue) and the literature on linear equating to evaluate five linear equating methods along several dimensions, including the plausibility of their assumptions and their levels of bias and root mean squared difference…

Swarm analysis by using transport equations

International Nuclear Information System (INIS)

Dote, Toshihiko.

1985-01-01

As the basis of weak ionization plasma phenomena, the motion, i.e. swarm, of charged particles in the gas is analyzed by use of the transport equations, from which basic nature of the swarm is discussed. The present report is an overview of the studies made in the past several years. Described are principally the most basic aspects concerning behaviors of the electrons and positive ions, that is, the basic equations and their significance, characteristics of the behaviors of the electron and positive ion swarms as revealed by solving the equations, and various characteristics of the swarm parameters. Contents are: Maxwell-Boltzmann's transport equations, behavior of the electron swarm, energy loss of the electrons, and behavior of the positive ion swarm. (Mori, K.)

Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

International Nuclear Information System (INIS)

Krolikowski, W.

1983-01-01

A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

ALLOMETRIC EQUATIONS FOR ESTIMATING ABOVEGROUND BIOMASS IN PAPUA TROPICAL FOREST

Directory of Open Access Journals (Sweden)

Sandhi Imam Maulana

2014-10-01

Full Text Available Allometric equations can be used to estimate biomass and carbon stock of  the forest. However, so far the allometric equations for commercial species in Papua tropical forests have not been appropriately developed. In this research, allometric equations are presented based on the genera of  commercial species. Few equations have been developed for the commercial species of  Intsia, Pometia, Palaquium and Vatica genera and an equation of  a mix of  these genera. The number of  trees sampled in this research was 49, with diameters (1.30 m above-ground or above buttresses ranging from 5 to 40 cm. Destructive sampling was used to collect the samples where Diameter at Breast Height (DBH and Wood Density (WD were used as predictors for dry weight of  Total Above-Ground Biomass (TAGB. Model comparison and selection were based on the values of  F-statistics, R-sq, R-sq (adj, and average deviation. Based on these statistical indicators, the most suitable model for Intsia, Pometia, Palaquium and Vatica genera respectively are Log(TAGB = -0.76 + 2.51Log(DBH, Log(TAGB = -0.84 + 2.57Log(DBH, Log(TAGB = -1.52 + 2.96Log(DBH, and Log(TAGB = -0.09 + 2.08Log(DBH. Additional explanatory variables such as Commercial Bole Height (CBH do not really increase the indicators’ goodness of  fit for the equation. An alternative model to incorporate wood density should  be considered for estimating the above-ground biomass for mixed genera. Comparing the presented mixed-genera equation; Log(TAGB = 0.205 + 2.08Log(DBH + 1.75Log(WD, R-sq: 97.0%, R-sq (adj: 96.9%, F statistics 750.67, average deviation: 3.5%; to previously published datashows that this local species specific equation differs substantially from previously published equations and this site-specific equation is  considered to give a better estimation of  biomass.

A calderón multiplicative preconditioner for the combined field integral equation

KAUST Repository

Bagci, Hakan

2009-10-01

A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation. © 2009 IEEE.

A stable penalty method for the compressible Navier-Stokes equations: II: One-dimensional domain decomposition schemes

DEFF Research Database (Denmark)

Hesthaven, Jan

1997-01-01

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.

2014-12-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method\\'s efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam

2014-01-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

New derivation of quantum equations from classical stochastic arguments

OpenAIRE

Bergeron, H.

2003-01-01

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This procedure was based on a Koopman-von Neumann approach where classical equations are reformulated into a quantumlike form. In this article, we develop a different derivation of quantum equations, based on purely classical stochastic arguments, taking some elem...

Relativistic phenomenological equations and transformation laws of relative coefficients

Directory of Open Access Journals (Sweden)

Patrizia Rogolino

2017-06-01

Full Text Available The aim of this paper is to derive the phenomenological equations in the context of special relativistic non-equilibrium thermodynamics with internal variables. In particular, after introducing some results developed in our previous paper, by means of classical non-equilibrium thermodynamic procedure and under suitable assumptions on the entropy density production, the phenomenological equations and transformation laws of phenomenological coefficients are derived. Finally, some symmetries of aforementioned coefficients are obtained.

Implementing statistical equating for MRCP(UK) Parts 1 and 2.

Science.gov (United States)

McManus, I C; Chis, Liliana; Fox, Ray; Waller, Derek; Tang, Peter

2014-09-26

The MRCP(UK) exam, in 2008 and 2010, changed the standard-setting of its Part 1 and Part 2 examinations from a hybrid Angoff/Hofstee method to statistical equating using Item Response Theory, the reference group being UK graduates. The present paper considers the implementation of the change, the question of whether the pass rate increased amongst non-UK candidates, any possible role of Differential Item Functioning (DIF), and changes in examination predictive validity after the change. Analysis of data of MRCP(UK) Part 1 exam from 2003 to 2013 and Part 2 exam from 2005 to 2013. Inspection suggested that Part 1 pass rates were stable after the introduction of statistical equating, but showed greater annual variation probably due to stronger candidates taking the examination earlier. Pass rates seemed to have increased in non-UK graduates after equating was introduced, but was not associated with any changes in DIF after statistical equating. Statistical modelling of the pass rates for non-UK graduates found that pass rates, in both Part 1 and Part 2, were increasing year on year, with the changes probably beginning before the introduction of equating. The predictive validity of Part 1 for Part 2 was higher with statistical equating than with the previous hybrid Angoff/Hofstee method, confirming the utility of IRT-based statistical equating. Statistical equating was successfully introduced into the MRCP(UK) Part 1 and Part 2 written examinations, resulting in higher predictive validity than the previous Angoff/Hofstee standard setting. Concerns about an artefactual increase in pass rates for non-UK candidates after equating were shown not to be well-founded. Most likely the changes resulted from a genuine increase in candidate ability, albeit for reasons which remain unclear, coupled with a cognitive illusion giving the impression of a step-change immediately after equating began. Statistical equating provides a robust standard-setting method, with a better

Phase Equilibria of Mixtures Containing Glycol and n-Alkane: Experimental Study of Infinite Dilution Activity Coefficients and Modeling Using the Cubic-Plus-Association Equation of State

DEFF Research Database (Denmark)

Afzal, Waheed; Breil, Martin Peter; Théveneau, Pascal

2009-01-01

previously reported in the literature, along with the data measured in this work have been modeled using the cubic-plus-association (CPA) equation of state (EoS). Satisfactory results have been obtained using temperature-independent interaction parameters. Useful remarks are presented about the application...

Local energy decay for linear wave equations with variable coefficients

Science.gov (United States)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Effective electrodiffusion equation for non-uniform nanochannels.

Science.gov (United States)

Marini Bettolo Marconi, Umberto; Melchionna, Simone; Pagonabarraga, Ignacio

2013-06-28

We derive a one-dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non-trivial fashion. We consider two kinds of non-uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one- and three-dimensional solutions of the electrokinetic equations.

Ratio equations for loblolly pine trees

Science.gov (United States)

Dehai Zhao; Michael Kane; Daniel Markewitz; Robert. Teskey

2015-01-01

The conversion factors (CFs) or expansion factors (EFs) are often used to convert volume to green or dry weight, or from one component biomass to estimate total biomass or other component biomass. These factors might be inferred from the previously developed biomass and volume equations with or without destructive sampling data. However, how the factors are related to...

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

Science.gov (United States)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

Application of the bifurcation method to the modified Boussinesq equation

Directory of Open Access Journals (Sweden)

Shaoyong Li

2014-08-01

Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.

A neuro approach to solve fuzzy Riccati differential equations

Energy Technology Data Exchange (ETDEWEB)

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)

2015-10-22

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation

International Nuclear Information System (INIS)

Deng Xijun; Han Libo; Li Xi

2009-01-01

In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)

Exact solutions of a nonpolynomially nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R.; Tan, H.S.

2007-01-01

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

An Algorithm to Automatically Generate the Combinatorial Orbit Counting Equations

Science.gov (United States)

Melckenbeeck, Ine; Audenaert, Pieter; Michoel, Tom; Colle, Didier; Pickavet, Mario

2016-01-01

Graphlets are small subgraphs, usually containing up to five vertices, that can be found in a larger graph. Identification of the graphlets that a vertex in an explored graph touches can provide useful information about the local structure of the graph around that vertex. Actually finding all graphlets in a large graph can be time-consuming, however. As the graphlets grow in size, more different graphlets emerge and the time needed to find each graphlet also scales up. If it is not needed to find each instance of each graphlet, but knowing the number of graphlets touching each node of the graph suffices, the problem is less hard. Previous research shows a way to simplify counting the graphlets: instead of looking for the graphlets needed, smaller graphlets are searched, as well as the number of common neighbors of vertices. Solving a system of equations then gives the number of times a vertex is part of each graphlet of the desired size. However, until now, equations only exist to count graphlets with 4 or 5 nodes. In this paper, two new techniques are presented. The first allows to generate the equations needed in an automatic way. This eliminates the tedious work needed to do so manually each time an extra node is added to the graphlets. The technique is independent on the number of nodes in the graphlets and can thus be used to count larger graphlets than previously possible. The second technique gives all graphlets a unique ordering which is easily extended to name graphlets of any size. Both techniques were used to generate equations to count graphlets with 4, 5 and 6 vertices, which extends all previous results. Code can be found at https://github.com/IneMelckenbeeck/equation-generator and https://github.com/IneMelckenbeeck/graphlet-naming. PMID:26797021

Coupling and reduction of the HAWC equations

DEFF Research Database (Denmark)

Nim, E.

2001-01-01

This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system.......This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model...

Separation of massive field equation of arbitrary spin in Robertson-Walker space-time

International Nuclear Information System (INIS)

Zecca, A.

2006-01-01

The massive spin-(3/2) field equation is explicitly integrated in the Robertson-Walker space-time by the Newman Penrose formalism. The solution is obtained by extending a separation procedure previously used to solve the spin-1 equation. The separated time dependence results in two coupled equations depending on the cosmological background evolution. The separated angular equations are explicitly integrated and the eigenvalues determined. The separated radial equations are integrated in the flat space-time case. The separation method of solution is then generalized, by induction, to prove the main result, that is the separability of the massive field equations of arbitrary spin in the Robertson-Walker space-time

Turbulent kinetic energy equation and free mixing

Science.gov (United States)

Morel, T.; Torda, T. P.; Bradshaw, P.

1973-01-01

Calculation of free shear flows was carried out to investigate the usefulness of several concepts which were previously successfully applied to wall flows. The method belongs to the class of differential approaches. The turbulence is taken into account by the introduction of one additional partial differential equation, the transport equation for the turbulent shear stress. The structure of turbulence is modeled after Bradshaw et al. This model was used successfully in boundary layers and its applicability to other flows is demonstrated. The work reported differs substantially from that of an earlier attempt to use this approach for calculation of free flows. The most important difference is that the region around the center line is treated by invoking the interaction hypothesis (concerning the structure of turbulence in the regions separated by the velocity extrema). The compressibility effects on shear layer spreading at low and moderate Mach numbers were investigated. In the absence of detailed experiments in free flows, the evidence from boundary layers that at low Mach numbers the structure of turbulence is unaffected by the compressibility was relied on. The present model was tested over a range of self-preserving and developing flows including pressure gradients using identical empirical input. The dependence of the structure of turbulence on the spreading rate of the shear layer was established.

Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses

Science.gov (United States)

Joseph, Rose M.; Hagness, Susan C.; Taflove, Allen

1991-01-01

The initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwell's equations are reported. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 x 10 to the 16th Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits 2D and 3D electromagnetic pulse propagation directly from the full-vector Maxwell's equations.

Previously unreported abnormalities in Wolfram Syndrome Type 2.

Science.gov (United States)

Akturk, Halis Kaan; Yasa, Seda

2017-01-01

Wolfram syndrome (WFS) is a rare autosomal recessive disease with non-autoimmune childhood onset insulin dependent diabetes and optic atrophy. WFS type 2 (WFS2) differs from WFS type 1 (WFS1) with upper intestinal ulcers, bleeding tendency and the lack ofdiabetes insipidus. Li-fespan is short due to related comorbidities. Only a few familieshave been reported with this syndrome with the CISD2 mutation. Here we report two siblings with a clinical diagnosis of WFS2, previously misdiagnosed with type 1 diabetes mellitus and diabetic retinopathy-related blindness. We report possible additional clinical and laboratory findings that have not been pre-viously reported, such as asymptomatic hypoparathyroidism, osteomalacia, growth hormone (GH) deficiency and hepatomegaly. Even though not a requirement for the diagnosis of WFS2 currently, our case series confirm hypogonadotropic hypogonadism to be also a feature of this syndrome, as reported before. © Polish Society for Pediatric Endocrinology and Diabetology.

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Equating error in observed-score equating

NARCIS (Netherlands)

van der Linden, Willem J.

2006-01-01

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

Science.gov (United States)

Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

1999-01-01

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Simulation of transport equations with Monte Carlo

International Nuclear Information System (INIS)

Matthes, W.

1975-09-01

The main purpose of the report is to explain the relation between the transport equation and the Monte Carlo game used for its solution. The introduction of artificial particles carrying a weight provides one with high flexibility in constructing many different games for the solution of the same equation. This flexibility opens a way to construct a Monte Carlo game for the solution of the adjoint transport equation. Emphasis is laid mostly on giving a clear understanding of what to do and not on the details of how to do a specific game

Dynamic data analysis modeling data with differential equations

CERN Document Server

Ramsay, James

2017-01-01

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

Global solution branches for a nonlocal Allen-Cahn equation

Science.gov (United States)

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

2018-05-01

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

The equation of state of liquid Flibe

International Nuclear Information System (INIS)

Chen, Xiang M.; Schrock, V.E.; Peterson, P.F.

1991-01-01

Flibe (Li 2 BeF 4 ) is a candidate material for the liquid blanket in the HYLIFE-2 fusion reactor. The thermodynamic properties of the material are important for the study of thermohydraulic behavior of the concept design, including the compressible analysis of the blanket isochoric heating problem and resulting jet breakup. The equation of state provides the relationship between all the thermodynamic properties. Previously, a soft sphere model of liquid equation of state was used for describing a number of liquid metals. In this paper we have fitted the available experimental data for liquid Flibe with a modified soft sphere model. 5 refs

A three operator split-step method covering a larger set of non-linear partial differential equations

Science.gov (United States)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Geometric Implications of Maxwell's Equations

Science.gov (United States)

Smith, Felix T.

2015-03-01

Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.

Novel Exponentially Fitted Two-Derivative Runge-Kutta Methods with Equation-Dependent Coefficients for First-Order Differential Equations

Directory of Open Access Journals (Sweden)

Yanping Yang

2016-01-01

Full Text Available The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.

2017-08-29

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow

International Nuclear Information System (INIS)

Baransky, Y.A.

1987-01-01

The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-β. The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.

2017-01-01

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

AdS{sub 3}/CFT{sub 2}, finite-gap equations and massless modes

Energy Technology Data Exchange (ETDEWEB)

Lloyd, Thomas; Stefański, Bogdan Jr. [Centre for Mathematical Science, City University London,Northampton Square, London EC1V 0HB (United Kingdom)

2014-04-29

It is known that string theory on AdS{sub 3}×M{sub 7} backgrounds, where M{sub 7}=S{sup 3}×S{sup 3}×S{sup 1} or S{sup 3}×T{sup 4}, is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finite-gap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finite-gap equations on these AdS{sub 3}×M{sub 7} backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we re-examine the derivation of the AdS{sub 3}×M{sub 7} finite-gap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finite-gap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS{sub 3}×M{sub 7}.

Coupled-channel equations and off-shell transformations in many-body scattering

International Nuclear Information System (INIS)

Cattapan, G.; Vanzani, V.

1977-01-01

The general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. The connection between different formulations has been clarified and the role played by some off-shell transformations for many-body transition operators has been discussed. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. Several sets of linear relations between transition operators have also been presented and used in a three-body context to derive uncoupled integral equations with connected kernel

A New Solution for Einstein Field Equation in General Relativity

Science.gov (United States)

Mousavi, Sadegh

2006-05-01

There are different solutions for Einstein field equation in general relativity that they have been proposed by different people the most important solutions are Schwarzchild, Reissner Nordstrom, Kerr and Kerr Newmam. However, each one of these solutions limited to special case. I've found a new solution for Einstein field equation which is more complete than all previous ones and this solution contains the previous solutions as its special forms. In this talk I will present my new metric for Einstein field equation and the Christofel symbols and Richi and Rieman tensor components for the new metric that I have calculated them by GR TENSOR software. As a result I will determine the actual movement of black holes which is different From Kerr black hole's movement. Finally this new solution predicts, existence of a new and constant field in the nature (that nobody can found it up to now), so in this talk I will introduce this new field and even I will calculate the amount of this field. SADEGH MOUSAVI, Amirkabir University of Technology.

Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2

International Nuclear Information System (INIS)

Velarde, G.

1976-01-01

Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)

Equations-of-motion approach to a quantum theory of large-amplitude collective motion

International Nuclear Information System (INIS)

Klein, A.

1984-01-01

The equations-of-motion approach to large-amplitude collective motion is implemented both for systems of coupled bosons, also studied in a previous paper, and for systems of coupled fermions. For the fermion case, the underlying formulation is that provided by the generalized Hartree-Fock approximation (or generalized density matrix method). To obtain results valid in the semi-classical limit, as in most previous work, we compute the Wigner transform of quantum matrices in the representation in which collective coordinates are diagonal and keep only the leading contributions. Higher-order contributions can be retained, however, and, in any case, there is no ambiguity of requantization. The semi-classical limit is seen to comprise the dynamics of time-dependent Hartree-Fock theory (TDHF) and a classical canonicity condition. By utilizing a well-known parametrization of the manifold of Slater determinants in terms of classical canonical variables, we are able to derive and understand the equations of the adiabatic limit in full parallelism with the boson case. As in the previous paper, we can thus show: (i) to zero and first order in the adiabatic limit the physics is contained in Villar's equations; (ii) to second order there is consistency and no new conditions. The structure of the solution space (discussed thoroughly in the previous paper) is summarized. A discussion of associated variational principles is given. A form of the theory equivalent to self-consistent cranking is described. A method of solution is illustrated by working out several elementary examples. The relationship to previsous work, especially that of Zelevinsky and Marumori and coworkers is discussed briefly. Three appendices deal respectively with the equations-of-motion method, with useful properties of Slater determinants, and with some technical details associated with the fermion equations of motion. (orig.)

New analytic solutions of stochastic coupled KdV equations

International Nuclear Information System (INIS)

Dai Chaoqing; Chen Junlang

2009-01-01

In this paper, firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures.

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Efficient Traveltime Solutions of the TI Acoustic Eikonal Equation

KAUST Repository

Waheed, Umair bin

2014-10-22

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.

Efficient Traveltime Solutions of the TI Acoustic Eikonal Equation

KAUST Repository

Waheed, Umair bin; Alkhalifah, Tariq Ali

2014-01-01

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.

Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

Directory of Open Access Journals (Sweden)

Nakao Hayashi

2004-04-01

Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13

Thermodynamic Equations of State for Aqueous Solutions Applied to Deep Icy Satellite and Exoplanet Oceans

Science.gov (United States)

Vance, S.; Brown, J. M.; Bollengier, O.; Journaux, B.; Sotin, C.; Choukroun, M.; Barnes, R.

2014-12-01

Supporting life in icy world or exoplanet oceans may require global seafloor chemical reactions between water and rock. Such interactions have been regarded as limited in larger icy worlds such as Ganymede and Titan, where ocean depths approach 800 km and GPa pressures (>10katm). If the oceans are composed of pure water, such conditions are consistent with the presence of dense ice phases V and VI that cover the rocky seafloor. Exoplanets with oceans can obtain pressures sufficient to generate ices VII and VIII. We have previously demonstrated temperature gradients in such oceans on the order of 20 K or more, resulting from fluid compressibility in a deep adiabatic ocean based on our experimental work. Accounting for increases in density for highly saline oceans leads to the possibility of oceans perched under and between high pressure ices. Ammonia has the opposite effect, instead decreasing ocean density, as reported by others and confirmed by our laboratory measurements in the ammonia water system. Here we report on the completed equation of state for aqueous ammonia derived from our prior measurements and optimized global b-spline fitting methods We use recent diamond anvil cell measurements for water and ammonia to extend the equation of state to 400°C and beyond 2 GPa, temperatures and pressures applicable to icy worlds and exoplanets. Densities show much less temperature dependence but comparabe high-pressure derivatives to previously published ammonia-water properties derived for application to Titan (Croft et al. 1988). Thermal expansion is in better agreement with the more self-consistent equation of state of Tillner-Roth and Friend (1998). We also describe development of a planetary NaCl equation of state using recent measurements of phase boundaries and sound speeds. We examine implications of realistic ocean-ice thermodynamics for Titan and exoplanet interiors using the methodology recently applied to Ganymede for oceans dominated by MgSO4. High

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Science.gov (United States)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

International Nuclear Information System (INIS)

Indekeu, Joseph O; Smets, Ruben

2017-01-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

A nondissipative simulation method for the drift kinetic equation

International Nuclear Information System (INIS)

Watanabe, Tomo-Hiko; Sugama, Hideo; Sato, Tetsuya

2001-07-01

With the aim to study the ion temperature gradient (ITG) driven turbulence, a nondissipative kinetic simulation scheme is developed and comprehensively benchmarked. The new simulation method preserving the time-reversibility of basic kinetic equations can successfully reproduce the analytical solutions of asymmetric three-mode ITG equations which are extended to provide a more general reference for benchmarking than the previous work [T.-H. Watanabe, H. Sugama, and T. Sato: Phys. Plasmas 7 (2000) 984]. It is also applied to a dissipative three-mode system, and shows a good agreement with the analytical solution. The nondissipative simulation result of the ITG turbulence accurately satisfies the entropy balance equation. Usefulness of the nondissipative method for the drift kinetic simulations is confirmed in comparisons with other dissipative schemes. (author)

A comprehensive treatment of electromagnetic interactions and the three-body spectator equations

Energy Technology Data Exchange (ETDEWEB)

Jiri Adam; Jay Van Orden

2004-10-01

We present a general derivation the three-body spectator (Gross) equations and the corresponding electromagnetic currents. As in previous paper on two-body systems, the wave equations and currents are derived from those for Bethe-Salpeter equation with the help of algebraic method using a concise matrix notation. The three-body interactions and currents introduced by the transition to the spectator approach are isolated and the matrix elements of the e.m. current are presented in detail for system of three indistinguishable particles, namely for elastic scattering and for two and three body break-up. The general expressions are reduced to the one-boson-exchange approximation to make contact with previous work. The method is general in that it does not rely on introduction of the electromagnetic interaction with the help of the minimal replacement. It would therefore work also for other external fields.

Calculation of proper values {lambda}{sub mn}(c) of the spheroidal equation; Calcul des valeurs propres {lambda}{sub mn}(c) de l'equation spheroidale

Energy Technology Data Exchange (ETDEWEB)

Dufour, J M [CEA Limeil Valenton, 94 - Villeneuve-Saint-Georges (France)

1969-05-01

The aim of this report is to find, with a fair accuracy, a proper value {lambda}{sub mn}(c) for the spheroidal differential equation: d/dz[(1-z{sup 2})du/dz]+[ {lambda} - c{sup 2}z{sup 2} - m{sup 2}/(1-z{sup 2})]u = 0 obtained by the separation of the three variables of the wave equation: {delta}{sup 2}u + k{sup 2}u = 0 with rotational elongated or flattened ellipsoidal coordinates. The program drawn up calculates {lambda}{sub mn}(c) for any values of (mnc) chosen in the zones 0 {<=} | m | {<=} 10, a whole number; |m| {<=} n {<=} 20, n a whole number; 0 {<=} |c | {<=} 30; previous work has covered a smaller field of values. The function to be solved by the approximation method of the Newton-Raphson type, and the initial value, are chosen so as to converge towards the required solution. (author) [French] L'objet de ce rapport est de rechercher avec une tres bonne approximation, une valeur propre {lambda}{sub mn}(c) de l'equation differentielle spheroidale: d/dz[(1-z{sup 2})du/dz]+[ {lambda} - c{sup 2}z{sup 2} - m{sup 2}/1-z{sup 2}]u = 0 obtenue par separation des 3 variables de l'equation des ondes: {delta}{sup 2}u + k{sup 2}u = 0 en coordonnees des ellipsoides de revolution allonges ou aplatis. Le programme etabli calcule {lambda}{sub mn}(c) quel que soit le jeu (mnc) choisi dans le domaine 0 {<=} | m | {<=} 10 entier; |m| {<=} n {<=} 20, n entier; 0 {<=} |c | {<=} 30; alors que les etudes precedentes portaient sur un domaine plus restreint. La fonction a resoudre par la methode d'approximation du type NEWTON-RAPHSON et la valeur initiale, sont choisies de facon a converger vers la solution desiree. (auteur)

Redundancy-free single-particle equation-of-motion method for nuclei. Pt. 1

International Nuclear Information System (INIS)

Rolnick, P.; Goswami, A.; Oregon Univ., Eugene

1986-01-01

The problem of coupling an odd nucleon to the collective states of an even core is considered in the intermediate-coupling limit. It is now well known that such intermediate-coupling calculations in spherical open-shell nuclei necessitate the inclusion of ground-state correlation or backward coupling which gives rise to an overcomplete basic set of states for the diagonalization of the hamiltonian. In a recent letter, we have derived a technique to free the single-particle equation-of-motion method of redundancy. Here we shall apply this redundancy-free equation-of-motion method to intermediate-coupling calculations in two regions of near-spherical odd-mass nuclei where forward coupling alone has not been successful. It is shown that qualitative effects of backward coupling previously reported are not spurious effects of double counting, although they are significantly modified by the removal of redundancy. We also discuss what further modifications of the theory will be needed in order to treat the dynamical interplay of collective and single-particle modes in nuclei self-consistently on the same footing. (orig.)

Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

Directory of Open Access Journals (Sweden)

Resat Yilmazer

2016-02-01

Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics

International Nuclear Information System (INIS)

Oezis, Turgut; Aslan, Imail

2009-01-01

With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered. (general)

Exact renormalization group equation for the Lifshitz critical point

Science.gov (United States)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

Science.gov (United States)

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge-Ampère Equations

Science.gov (United States)

Le, Nam Q.

2018-05-01

We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior Hölder estimate in two dimensions for an inhomogeneous linearized Monge-Ampère equation with right hand side being the divergence of a bounded vector field. As a further application of our Hölder estimate, we prove the Hölder regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.

Conserved quantities for generalized KdV equations

International Nuclear Information System (INIS)

Calogero, F.; Rome Univ.; Degasperis, A.; Rome Univ.

1980-01-01

It is noted that the nonlinear evolution equation usub(t) = α(t)usub(xxx) - 6ν(t) usub(x)u, u is identical to u(x,t), possesses three (and, in some cases, four) conserved quantities, that are explicitly displayed. These results are of course relevant only to the cases in which this evolution equation is not known to possess an infinite number of conserved quantities. Purpose and scope of this paper is to report three or four simple conservation laws possessed by the evolution equation usub(t) = α(t)usub(xxx) - 6ν(t)usub(x)u, u is identical to u(x,t). (author)

Calibration methods for the Hargreaves-Samani equation

Directory of Open Access Journals (Sweden)

Lucas Borges Ferreira

Full Text Available ABSTRACT The estimation of the reference evapotranspiration is an important factor for hydrological studies, design and management of irrigation systems, among others. The Penman Monteith equation presents high precision and accuracy in the estimation of this variable. However, its use becomes limited due to the large number of required meteorological data. In this context, the Hargreaves-Samani equation could be used as alternative, although, for a better performance a local calibration is required. Thus, the aim was to compare the calibration process of the Hargreaves-Samani equation by linear regression, by adjustment of the coefficients (A and B and exponent (C of the equation and by combinations of the two previous alternatives. Daily data from 6 weather stations, located in the state of Minas Gerais, from the period 1997 to 2016 were used. The calibration of the Hargreaves-Samani equation was performed in five ways: calibration by linear regression, adjustment of parameter “A”, adjustment of parameters “A” and “C”, adjustment of parameters “A”, “B” and “C” and adjustment of parameters “A”, “B” and “C” followed by calibration by linear regression. The performances of the models were evaluated based on the statistical indicators mean absolute error, mean bias error, Willmott’s index of agreement, correlation coefficient and performance index. All the studied methodologies promoted better estimations of reference evapotranspiration. The simultaneous adjustment of the empirical parameters “A”, “B” and “C” was the best alternative for calibration of the Hargreaves-Samani equation.

Is the kinetic equation for turbulent gas-particle flows ill posed?

Science.gov (United States)

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Improving North American forest biomass estimates from literature synthesis and meta-analysis of existing biomass equations

Science.gov (United States)

David C. Chojnacky; Jennifer C. Jenkins; Amanda K. Holland

2009-01-01

Thousands of published equations purport to estimate biomass of individual trees. These equations are often based on very small samples, however, and can provide widely different estimates for trees of the same species. We addressed this issue in a previous study by devising 10 new equations that estimated total aboveground biomass for all species in North America (...

Measuring the neutron star equation of state with gravitational wave observations

International Nuclear Information System (INIS)

Read, Jocelyn S.; Markakis, Charalampos; Creighton, Jolien D. E.; Friedman, John L.; Shibata, Masaru; Uryu, Koji

2009-01-01

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron-star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron-star compactness (the ratio of the mass of the neutron-star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point-particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of δR∼1 km at 100 Mpc.

An analytical solution of the one-dimensional neutron diffusion kinetic equation in cartesian geometry

International Nuclear Information System (INIS)

Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.

2009-01-01

In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)

Final Report: Symposium on Adaptive Methods for Partial Differential Equations

Energy Technology Data Exchange (ETDEWEB)

Pernice, M.; Johnson, C.R.; Smith, P.J.; Fogelson, A.

1998-12-10

OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.

A previously unreported variant of the synostotic sagittal suture: Case report and review of salient literature

Directory of Open Access Journals (Sweden)

Madison Budinich

2016-12-01

Full Text Available Introduction: Sagittal synostosis is a rare congenital disease caused by the premature fusion of the sagittal suture. Craniosynostosis occurs for a variety of reasons, different for every case, and often the etiology is unclear but the anomaly can frequently be seen as part of Crouzon's or Apert's syndromes. Herein, we discuss a rare case of craniosynostosis where the patient presented with a, to our knowledge, a previously undescribed variant of sagittal synostosis. Case report: A 3-month-old female infant presented to a craniofacial clinic for a consultation regarding an abnormal head shape. Images of the skull were performed, demonstrating that the patient had craniosynostosis. The patient displayed no other significant symptoms besides abnormalities in head shape. The sagittal suture was found to extend into the occipital bone where it was synostotic. Conclusion: To our knowledge, a synostotic sagittal suture has not been reported that extended posteriorly it involve the occipital bone. Those who interpret imaging or operate on this part of the skull should consider such a variation. Keywords: Anatomy, Craniosynostosis, Skull, Malformation, Pediatrics

Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form

Directory of Open Access Journals (Sweden)

Reza Abazari

2013-01-01

Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.

Resolution of hydrodynamical equations for transverse expansions

International Nuclear Information System (INIS)

Hama, Y.; Pottag, F.W.

1985-01-01

The three-dimensional hydrodynamical expansion is treated with a method similar to that of Milekhin, but more explicit. Although in the final stage we have to appeal to numerical calculation, the partial differential equations governing the transverse expansions are treated without transforming them into ordinary equations with an introduction of averaged quantities. The present paper is concerned with the formalism and the numerical results will be reported in another paper. (Author) [pt

Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies

International Nuclear Information System (INIS)

Racine, Etienne; Flanagan, Eanna E.

2005-01-01

We give a surface-integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current multipole moments. The derivation requires only that the post-1-Newtonian vacuum field equations are satisfied in weak field regions between the bodies; the bodies' internal gravity can be arbitrarily strong. In particular, black holes are not excluded. The derivation extends previous results due to Damour, Soffel, and Xu (DSX) for weakly self-gravitating bodies in which the post-1-Newtonian field equations are satisfied everywhere. The derivation consists of a number of steps: (i) The definition of each body's current and mass multipole moments and center-of-mass world line in terms of the behavior of the metric in a weak field region surrounding the body. (ii) The definition for each body of a set of gravitoelectric and gravitomagnetic tidal moments that act on that body, again in terms of the behavior of the metric in a weak field region surrounding the body. For the special case of weakly self-gravitating bodies, our definitions of these multipole and tidal moments agree with definitions given previously by DSX. (iii) The derivation of a formula, for any given body, of the second time derivative of its mass dipole moment in terms of its other multipole and tidal moments and their time derivatives. This formula was obtained previously by DSX for weakly self-gravitating bodies. (iv) A derivation of the relation between the tidal moments acting on each body and the multipole moments and center-of-mass world lines of all the other bodies. A formalism to compute this relation was developed by DSX; we simplify their formalism and compute the relation explicitly. (v) The deduction from the previous steps of the explicit translational equations of motion, whose form has not been previously derived

Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies

Science.gov (United States)

Racine, Étienne; Flanagan, Éanna É.

2005-02-01

We give a surface-integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current multipole moments. The derivation requires only that the post-1-Newtonian vacuum field equations are satisfied in weak field regions between the bodies; the bodies' internal gravity can be arbitrarily strong. In particular, black holes are not excluded. The derivation extends previous results due to Damour, Soffel, and Xu (DSX) for weakly self-gravitating bodies in which the post-1-Newtonian field equations are satisfied everywhere. The derivation consists of a number of steps: (i) The definition of each body’s current and mass multipole moments and center-of-mass world line in terms of the behavior of the metric in a weak field region surrounding the body. (ii) The definition for each body of a set of gravitoelectric and gravitomagnetic tidal moments that act on that body, again in terms of the behavior of the metric in a weak field region surrounding the body. For the special case of weakly self-gravitating bodies, our definitions of these multipole and tidal moments agree with definitions given previously by DSX. (iii) The derivation of a formula, for any given body, of the second time derivative of its mass dipole moment in terms of its other multipole and tidal moments and their time derivatives. This formula was obtained previously by DSX for weakly self-gravitating bodies. (iv) A derivation of the relation between the tidal moments acting on each body and the multipole moments and center-of-mass world lines of all the other bodies. A formalism to compute this relation was developed by DSX; we simplify their formalism and compute the relation explicitly. (v) The deduction from the previous steps of the explicit translational equations of motion, whose form has not been previously derived.

An approach to rogue waves through the cnoidal equation

Science.gov (United States)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

A Derivation of Source-based Kinetics Equation with Time Dependent Fission Kernel for Reactor Transient Analyses

International Nuclear Information System (INIS)

Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho; Pyeon, Cheol Ho

2015-01-01

In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r g , E g , t g ) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the neutron sources

Undergraduate Students' Mental Operations in Systems of Differential Equations

Science.gov (United States)

Whitehead, Karen; Rasmussen, Chris

2003-01-01

This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…

Simple equation method for nonlinear partial differential equations and its applications

Directory of Open Access Journals (Sweden)

Taher A. Nofal

2016-04-01

Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

Moment equation approach to neoclassical transport theory

International Nuclear Information System (INIS)

Hirshman, S.P.

1978-01-01

The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory unifies the numerous complex expressions for the transport coefficients, previously obtained by solving the Fokker--Planck equation, and elucidates their physical basis. In the large aspect ratio limit, the continuous transition in the scaling of the diffusion coefficient throughout various collisionality regimes is shown to depend on the ratio of parallel viscosity coefficients of the plasma species. Comparison of the present results with the kinetic theory expressions for the neoclassical fluxes determines the parallel viscosity coefficients for a multispecies plasma in the long-mean-free-path regime

Filters in topology optimization based on Helmholtz‐type differential equations

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Sigmund, Ole

2011-01-01

The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology...... from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation...

Efficient traveltime solutions of the acoustic TI eikonal equation

KAUST Repository

Waheed, Umair bin

2015-02-01

Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.

Equations based on anthropometry to predict body fat measured by absorptiometry in schoolchildren and adolescents.

Science.gov (United States)

Ortiz-Hernández, Luis; Vega López, A Valeria; Ramos-Ibáñez, Norma; Cázares Lara, L Joana; Medina Gómez, R Joab; Pérez-Salgado, Diana

To develop and validate equations to estimate the percentage of body fat of children and adolescents from Mexico using anthropometric measurements. A cross-sectional study was carried out with 601 children and adolescents from Mexico aged 5-19 years. The participants were randomly divided into the following two groups: the development sample (n=398) and the validation sample (n=203). The validity of previously published equations (e.g., Slaughter) was also assessed. The percentage of body fat was estimated by dual-energy X-ray absorptiometry. The anthropometric measurements included height, sitting height, weight, waist and arm circumferences, skinfolds (triceps, biceps, subscapular, supra-iliac, and calf), and elbow and bitrochanteric breadth. Linear regression models were estimated with the percentage of body fat as the dependent variable and the anthropometric measurements as the independent variables. Equations were created based on combinations of six to nine anthropometric variables and had coefficients of determination (r 2 ) equal to or higher than 92.4% for boys and 85.8% for girls. In the validation sample, the developed equations had high r 2 values (≥85.6% in boys and ≥78.1% in girls) in all age groups, low standard errors (SE≤3.05% in boys and ≤3.52% in girls), and the intercepts were not different from the origin (p>0.050). Using the previously published equations, the coefficients of determination were lower, and/or the intercepts were different from the origin. The equations developed in this study can be used to assess the percentage of body fat of Mexican schoolchildren and adolescents, as they demonstrate greater validity and lower error compared with previously published equations. Copyright © 2017 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.

Development and application of a three-parameter RK-PR equation of state

DEFF Research Database (Denmark)

Cismondi, Martin; Mollerup, Jørgen

2005-01-01

In this work, we confirm the somehow previously expressed but not widespread idea that the limitations of cubic equations of state like Soave-Redlich-Kwong equation (SRK) or Peng-Robinson equation (PR) are a consequence of their two-parameter density dependence rather than of their empiric......-PR) equation offers the best performance among cubic three-parameter density functionalities. A simple temperature dependence was developed and a straightforward parameterization procedure established. This simple - and optimized from pure compound data - three-parameter equation of state (3P-EoS) will allow...... in a later stage, by systematic study and comparison to other types of 3P-EoS, to find out what the actual possibilities and limitations of cubic EoS are in the modelling of phase equilibria for asymmetric systems. (c) 2005 Elsevier B.V. All rights reserved....

Planck constant as spectral parameter in integrable systems and KZB equations

OpenAIRE

Levin, A.NRU HSE, Department of Mathematics, Myasnitskaya str. 20, Moscow, 101000, Russia; Olshanetsky, M.(ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218, Russia); Zotov, A.(ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218, Russia)

2014-01-01

We construct special rational ${\\rm gl}_N$ Knizhnik-Zamolodchikov-Bernard (KZB) equations with $\\tilde N$ punctures by deformation of the corresponding quantum ${\\rm gl}_N$ rational $R$-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is $\\tau$. At the level of classical mechanics the deformation parameter $\\tau$ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Ne...

Validation of equations for pleural effusion volume estimation by ultrasonography.

Science.gov (United States)

Hassan, Maged; Rizk, Rana; Essam, Hatem; Abouelnour, Ahmed

2017-12-01

To validate the accuracy of previously published equations that estimate pleural effusion volume using ultrasonography. Only equations using simple measurements were tested. Three measurements were taken at the posterior axillary line for each case with effusion: lateral height of effusion ( H ), distance between collapsed lung and chest wall ( C ) and distance between lung and diaphragm ( D ). Cases whose effusion was aspirated to dryness were included and drained volume was recorded. Intra-class correlation coefficient (ICC) was used to determine the predictive accuracy of five equations against the actual volume of aspirated effusion. 46 cases with effusion were included. The most accurate equation in predicting effusion volume was ( H  +  D ) × 70 (ICC 0.83). The simplest and yet accurate equation was H  × 100 (ICC 0.79). Pleural effusion height measured by ultrasonography gives a reasonable estimate of effusion volume. Incorporating distance between lung base and diaphragm into estimation improves accuracy from 79% with the first method to 83% with the latter.

Extended rate equations

International Nuclear Information System (INIS)

Shore, B.W.

1981-01-01

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

The roots to an equation in particle slowing down theory

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1979-08-01

Previous work on the roots to an equation arising in studies on anisotropic neutron scattering has been extended to include parameter values of interest for a problem put forward by M.M.R. Williams. Detailed numerical results are given. (author)

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.

On integrability of a noncommutative q-difference two-dimensional Toda lattice equation

Energy Technology Data Exchange (ETDEWEB)

Li, C.X., E-mail: trisha_li2001@163.com [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Department of Mathematics, College of Charleston, Charleston, SC 29401 (United States); Nimmo, J.J.C., E-mail: jonathan.nimmo@glasgow.ac.uk [School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Shen, Shoufeng, E-mail: mathssf@zjut.edu.cn [Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023 (China)

2015-12-18

In our previous work (C.X. Li and J.J.C. Nimmo, 2009 [18]), we presented a generalized type of Darboux transformations in terms of a twisted derivation in a unified form. The twisted derivation includes ordinary derivatives, forward difference operators, super derivatives and q-difference operators as its special cases. This result not only enables one to recover the known Darboux transformations and quasideterminant solutions to the noncommutative KP equation, the non-Abelian two-dimensional Toda lattice equation, the non-Abelian Hirota–Miwa equation and the super KdV equation, but also inspires us to investigate quasideterminant solutions to q-difference soliton equations. In this paper, we first construct the bilinear Bäcklund transformations for the known bilinear q-difference two-dimensional Toda lattice equation (q-2DTL) and then derive a Lax pair whose compatibility gives a formally different nonlinear q-2DTL equation and finally obtain its quasideterminant solutions by iterating its Darboux transformations. - Highlights: • Examples are given to illustrate the extensive applications of twisted derivations. • Bilinear Bäcklund transformation is constructed for the known q-2DTL equation. • Lax pair is obtained for an equivalent q-2DTL equation. • Quasideterminant solutions are found for the nc q-2DTL equation.

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.

Approximating a retarded-advanced differential equation that models human phonation

Science.gov (United States)

Teodoro, M. Filomena

2017-11-01

In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.

On a new series of integrable nonlinear evolution equations

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.

1980-10-01

Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)

Urethrotomy has a much lower success rate than previously reported.

Science.gov (United States)

Santucci, Richard; Eisenberg, Lauren

2010-05-01

We evaluated the success rate of direct vision internal urethrotomy as a treatment for simple male urethral strictures. A retrospective chart review was performed on 136 patients who underwent urethrotomy from January 1994 through March 2009. The Kaplan-Meier method was used to analyze stricture-free probability after the first, second, third, fourth and fifth urethrotomy. Patients with complex strictures (36) were excluded from the study for reasons including previous urethroplasty, neophallus or previous radiation, and 24 patients were lost to followup. Data were available for 76 patients. The stricture-free rate after the first urethrotomy was 8% with a median time to recurrence of 7 months. For the second urethrotomy stricture-free rate was 6% with a median time to recurrence of 9 months. For the third urethrotomy stricture-free rate was 9% with a median time to recurrence of 3 months. For procedures 4 and 5 stricture-free rate was 0% with a median time to recurrence of 20 and 8 months, respectively. Urethrotomy is a popular treatment for male urethral strictures. However, the performance characteristics are poor. Success rates were no higher than 9% in this series for first or subsequent urethrotomy during the observation period. Most of the patients in this series will be expected to experience failure with longer followup and the expected long-term success rate from any (1 through 5) urethrotomy approach is 0%. Urethrotomy should be considered a temporizing measure until definitive curative reconstruction can be planned. 2010 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.

3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations

International Nuclear Information System (INIS)

Carreras, B.A.; Garcia, L.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.; Masden, B.F.

1983-01-01

Numerical studies of the resistive stability of tokamak plasmas in cylindrical geometry have been performed using: (1) the full set of resistive Magnetohydrodynamic (MHD) equations and (2) an extended version of the reduced set of resistive MHD equations including diamagnetic and electron temperature effects. In particular, the nonlinear interaction of tearing modes of many helicities has been investigated. The numerical results confirm many of the features uncovered previously using the simple reduced equations. (author)

A novel method to solve functional differential equations

International Nuclear Information System (INIS)

Tapia, V.

1990-01-01

A method to solve differential equations containing the variational operator as the derivation operation is presented. They are called variational differential equations (VDE). The solution to a VDE should be a function containing the derivatives, with respect to the base space coordinates, of the fields up to a generic order s: a s-th-order function. The variational operator doubles the order of the function on which it acts. Therefore, in order to make compatible the orders of the different terms appearing in a VDE, the solution should be a function containing the derivatives of the fields at all orders. But this takes us again back to the functional methods. In order to avoid this, one must restrict the considerations, in the case of second-order VDEs, to the space of s-th-order functions on which the variational operator acts transitively. These functions have been characterized for a one-dimensional base space for the first- and second-order cases. These functions turn out to be polynomial in the highest-order derivatives of the fields with functions of the lower-order derivatives as coefficients. Then VDEs reduce to a system of coupled partial differential equations for the coefficients above mentioned. The importance of the method lies on the fact that the solutions to VDEs are in a one-to-one correspondence with the solutions of functional differential equations. The previous method finds direct applications in quantum field theory, where the Schroedinger equation plays a central role. Since the Schroedinger equation is reduced to a system of coupled partial differential equations, this provides a nonperturbative scheme for quantum field theory. As an example, the massless scalar field is considered

Universality in an information-theoretic motivated nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R; Tabia, G

2007-01-01

Using perturbative methods, we analyse a nonlinear generalization of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are (i) for nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states; (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions, and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realized

Sandia equation of state data base: seslan File

Energy Technology Data Exchange (ETDEWEB)

Kerley, G.I. [Sandia National Labs., Albuquerque, NM (US); Christian-Frear, T.L. [RE/SPEC Inc., Albuquerque, NM (US)

1993-06-24

Sandia National Laboratories maintains several libraries of equation of state tables, in a modified Sesame format, for use in hydrocode calculations and other applications. This report discusses one of those libraries, the seslan file, which contains 78 tables from the Los Alamos equation of state library. Minor changes have been made to these tables, making them more convenient for code users and reducing numerical difficulties that occasionally arise in hydrocode calculations.

BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows

Science.gov (United States)

Shaing, K. C.

2010-07-01

A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.

Cosmological solutions, p-branes, and the Wheeler-DeWitt equation

International Nuclear Information System (INIS)

Lue, H.; Maharana, J.; Maharana, J.; Mukherji, S.; Pope, C.N.; Pope, C.N.

1998-01-01

The low energy effective actions which arise from string theory or M-theory are considered in the cosmological context, where the graviton, dilaton and antisymmetric tensor field strengths depend only on time. We show that previous results can be extended to include cosmological solutions that are related to the E N Toda equations. The solutions of the Wheeler-DeWitt equation in minisuperspace are obtained for some of the simpler cosmological models by introducing intertwining operators that generate canonical transformations which map the theories into free theories. We study the cosmological properties of these solutions, and also briefly discuss generalized Brans-Dicke models in our framework. The cosmological models are closely related to p-brane solitons, which we discuss in the context of the E N Toda equations. We give the explicit solutions for extremal multi-charge (D-3)-branes in the truncated system described by the D 4 =O(4,4) Toda equations. copyright 1998 The American Physical Society

A step function perturbative numerical method for the solution of coupled differential equations arising from the Schroedinger equation. Pt. 2

International Nuclear Information System (INIS)

Ixaru, G.L.

1978-03-01

The method developed in the previous paper (preprint, C.I.Ph. (Bucharest), MC-2-78, 1978) is here investigated from computational point of view. Special emphasis is paid to the two basic descriptors of the efficiency: the volume of memory required and the computational effort (timing). Next, two experimental cases are reported. They (i) confirm the theoretical estimates for the rate cf convergence of each version of the present method and (ii) show that the present method is substantially faster than the others. Specifically, it is found that for typical physical problems it is faster by a factor of ten up to twenty than the methods commonly used, viz. Numerov and de Vogelaere. The data reported also allow an inUirect comparison with the method of Gordon. I l/ allow an indirect comparison with the method of Gordon. It is shown that, while this exhibits the same rate as our basic, lowest order version, the computational effort for the latter is, in case of systems with nine equations, only half than for the method of Gordon. At the end of the paper some types of physical problems are suggested which should be the most benefitting if solved numerically with the present method. (author)

Unexpected finding of T-cell lymphoma in a previously healthy 16-year-old patient after a thorax trauma: a case report

DEFF Research Database (Denmark)

Bach Okholm-Hansen, Anna; Brorson, Stig

2014-01-01

INTRODUCTION: We describe the clinical course and emphasize the difficulties in diagnosing T-cell lymphoblastic lymphoma. The differential diagnostic difficulties have previously been described in regard to pneumonia, but to the best of the authors' knowledge this is the first case report to desc...... relevant to pediatricians, surgeons, anesthesiologists, and general practitioners....

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

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

A report on the study of algorithms to enhance Vector computer performance for the discretized one-dimensional time-dependent heat conduction equation: EPIC research, Phase 1

International Nuclear Information System (INIS)

Majumdar, A.; Makowitz, H.

1987-10-01

With the development of modern vector/parallel supercomputers and their lower performance clones it has become possible to increase computational performance by several orders of magnitude when comparing to the previous generation of scalar computers. These performance gains are not observed when production versions of current thermal-hydraulic codes are implemented on modern supercomputers. It is our belief that this is due in part to the inappropriateness of using old thermal-hydraulic algorithms with these new computer architectures. We believe that a new generation of algorithms needs to be developed for thermal-hydraulics simulation that is optimized for vector/parallel architectures, and not the scalar computers of the previous generation. We have begun a study that will investigate several approaches for designing such optimal algorithms. These approaches are based on the following concepts: minimize recursion; utilize predictor-corrector iterative methods; maximize the convergence rate of iterative methods used; use physical approximations as well as numerical means to accelerate convergence; utilize explicit methods (i.e., marching) where stability will permit. We call this approach the ''EPIC'' methodology (i.e., Explicit Predictor Iterative Corrector methods). Utilizing the above ideas, we have begun our work by investigating the one-dimensional transient heat conduction equation. We have developed several algorithms based on variations of the Hopscotch concept, which we discuss in the body of this report. 14 refs

Solution of the time-dependent, three-dimensional resistive magnetohydrodynamic equations

International Nuclear Information System (INIS)

Finan, C.H. III; Killeen, J.; California Univ., Davis

1981-01-01

Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are expressed as conservation laws, the momentum and energy equations are nonconservative. This is to: (1) provide enhanced numerical stability by eliminating errors introduced by the nonvanishing of nabla x B on the finite difference mesh; and, (2) allow the simulation of low β plasmas. The resulting finite difference equations are a coupled system of nonlinear algebraic equations which are solved by the Newton-Raphson iteration technique. We apply our model to a number of problems of importance in magnetic fusion research. Ideal and resistive internal kink instabilities are simulated in a Cartesian geometry. Growth rates and nonlinear saturation amplitudes are found to be in agreement with previous analytic and numerical predictions. We also simulate these instabilities in a torus, which demonstrates the versatility of the orthogonal curvilinear coordinate representation. (orig.)

Optimal moving grids for time-dependent partial differential equations

Science.gov (United States)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

International Nuclear Information System (INIS)

Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

2014-01-01

In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

Science.gov (United States)

Edelman, Mark

2015-07-01

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

The Kernel Levine Equipercentile Observed-Score Equating Function. Research Report. ETS RR-13-38

Science.gov (United States)

von Davier, Alina A.; Chen, Haiwen

2013-01-01

In the framework of the observed-score equating methods for the nonequivalent groups with anchor test design, there are 3 fundamentally different ways of using the information provided by the anchor scores to equate the scores of a new form to those of an old form. One method uses the anchor scores as a conditioning variable, such as the Tucker…

Saha equation in Rindler space

Indian Academy of Sciences (India)

Sanchari De

2017-05-31

May 31, 2017 ... scenario, the flat local geometry is called the Rindler space. For an illustration, let us consider two reference ... the local acceleration of the frame. To investigate Saha equation in a uniformly acceler- ... the best of our knowledge, the study of Saha equa- tion in Rindler space has not been reported earlier.

A Derivation of Source-based Kinetics Equation with Time Dependent Fission Kernel for Reactor Transient Analyses

Energy Technology Data Exchange (ETDEWEB)

Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)

2015-10-15

In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the

Nuclear fission with a Langevin equation

International Nuclear Information System (INIS)

Boilley, D.; Suraud, E.; Abe, Yasuhisa

1992-01-01

A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results. (author) 23 refs.; 7 figs

A computational method for direct integration of motion equations of structural systems

International Nuclear Information System (INIS)

Brusa, L.; Ciacci, R.; Creco, A.; Rossi, F.

1975-01-01

The dynamic analysis of structural systems requires the solution of the matrix equations: Md 2 delta/dt(t) + Cddelta/dt(t) + Kdelta(t) = F(t). Many numerical methods are available for direct integration of this equation and their efficiency is due to the fulfillment of the following requirements: A reasonable order of accuracy must be obtained for the approximation of the response relevant to the first modes: the model contributions relevant to the eigenvalues with large real part must be essentially neglected. This paper presents a step-by-step numerical scheme for the integration of this equation which satisfies the requirements previously mentioned. (Auth.)

Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

International Nuclear Information System (INIS)

Kataoka, Isao; Tomiyama, Akio

2004-01-01

The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

Comparison of Kernel Equating and Item Response Theory Equating Methods

Science.gov (United States)

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling: Convergence Analysis

National Research Council Canada - National Science Library

Dupuis, Paul; Wang, Hui

2005-01-01

Previous papers by authors establish the connection between importance sampling algorithms for estimating rare-event probabilities, two-person zero-sum differential games, and the associated Isaacs equation...

Integral equations

CERN Document Server

Moiseiwitsch, B L

2005-01-01

Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

Partial Differential Equations

CERN Document Server

1988-01-01

The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

Nonlinear evolution equations

CERN Document Server

Uraltseva, N N

1995-01-01

This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

Fokker-Planck equation in the presence of a uniform magnetic field

International Nuclear Information System (INIS)

Dong, Chao; Zhang, Wenlu; Li, Ding

2016-01-01

The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

Fokker-Planck equation in the presence of a uniform magnetic field

Energy Technology Data Exchange (ETDEWEB)

Dong, Chao, E-mail: chaodong@iphy.ac.cn [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Nuclear Engineering, Seoul National University, Seoul 151-744 (Korea, Republic of); Zhang, Wenlu [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li, Ding, E-mail: dli@ustc.edu.cn [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Modern Physics, University of Science and Technology of China, Anhui Hefei 230026 (China)

2016-08-15

The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

African Journals Online (AJOL)

eobe

plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

Use of fast Fourier transforms for solving partial differential equations in physics

CERN Document Server

Le Bail, R C

1972-01-01

The use of fast Fourier techniques for the direct solution of an important class of elliptic, parabolic, and hyperbolic partial differential equations in two dimensions is described. Extensions to higher-order and higher-dimension equations as well as to integrodifferential equations are presented, and several numerical examples with their resulting precision and timing are reported. (12 refs).

Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

International Nuclear Information System (INIS)

Fan Hongyi; Wang Yong

2006-01-01

With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.

Placenta Percreta Invading Broad Ligament and Parametrium in a Woman with Two Previous Cesarean Sections: A Case Report

Directory of Open Access Journals (Sweden)

Mansoureh Vahdat

2012-01-01

Full Text Available Introduction. The incidence of placenta accreta has dramatically increased due to increasing caesarean section rate all over the world. Placenta percreta is the most severe form of placenta accretes. It frequently results in maternal morbidity and mortality mainly caused by massive obstetric hemorrhage or emergency hysterectomy. Percreta invading into the broad ligament has rarely been previously reported. Case presenting. We presented a case of placenta percreta invading left broad ligament and parametrium in a woman with two previous cesarean sections, which led to massive intraoperative hemorrhage during hysterectomy and transient ischemic encephalopathy. Conclusion. In cases of parametrial involvement, it would be more difficult to decide whether to remove placenta or leave it in site. In surgical removal neither local excision of placental bed and uterine repair nor traditional hysterectomy is adequate if parametrium invaded by placenta. We suggest delayed elective hysterectomy in such cases. So, pregnancy-induced pelvic congestion would be decreased, we can gather an expert team of gynecologists, urologists, and vascular surgeons, we could get plenty of blood products, and we may have the chance to administer methotrexate.

Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

Energy Technology Data Exchange (ETDEWEB)

Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1968-07-01

In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

A new equation of state for porous materials with ultra-low densities

CERN Document Server

Geng Hua Yun; Wu Qiang

2002-01-01

A thermodynamic equation of state is derived which is appropriate for investigating the thermodynamic variations along isobaric paths to predict compression behaviours of porous materials. This equation-of-state model is tested on porous iron, copper, lead and tungsten with different initial densities. The calculated Hugoniots are in good agreement with the corresponding experimental data published previously. This shows that this model can satisfactorily predict the Hugoniots of porous materials with wide porosity and pressure ranges.

The impact of calcium assay change on a local adjusted calcium equation.

Science.gov (United States)

Davies, Sarah L; Hill, Charlotte; Bailey, Lisa M; Davison, Andrew S; Milan, Anna M

2016-03-01

Deriving and validating local adjusted calcium equations is important for ensuring appropriate calcium status classification. We investigated the impact on our local adjusted calcium equation of a change in calcium method by the manufacturer from cresolphthalein complexone to NM-BAPTA. Calcium and albumin results from general practice requests were extracted from the Laboratory Information Management system for a three-month period. Results for which there was evidence of disturbance in calcium homeostasis were excluded leaving 13,482 sets of results for analysis. The adjusted calcium equation was derived following least squares regression analysis of total calcium on albumin and normalized to the mean calcium concentration of the data-set. The revised equation (NM-BAPTA calcium method) was compared with the previous equation (cresolphthalein complexone calcium method). The switch in calcium assay resulted in a small change in the adjusted calcium equation but was not considered to be clinically significant. The calcium reference interval differed from that proposed by Pathology Harmony in the UK. Local adjusted calcium equations should be re-assessed following changes in the calcium method. A locally derived reference interval may differ from the consensus harmonized reference interval. © The Author(s) 2015.

A New Understanding of Particles by G-Flow Interpretation of Differential Equation

Directory of Open Access Journals (Sweden)

Mao L.

2015-07-01

Full Text Available Applying mathematics to the understanding of particles classically with an assumption that if the variables t and x 1 , x 2 , x 3 hold with a system of dynamical equations (1.4, then they are a point ( t , x 1 , x 2 , x 3 in R 4 . However, if we put off this assumption, how can we interpret the solution space of equations? And are the se resultants important for understanding the world? Recently, the author extended Ban ach and Hilbert spaces on a topological graph to introduce −→ G -flows and showed that all such flows on a topological graph −→ G also form a Banach or Hilbert space, which enables one to find t he multiverse solution of these equations on −→ G . Applying this result, this paper discusses the −→ G -flow solutions on Schrödinger equation, Klein-Gordon equation and Dirac equation, i.e., the field equations of particles, bosons or fermions, answers previous questions by ”yes“, and establishes the many world interpretation of quantum mechanics of H. Everett by purely mathematics in logic, i.e., mathematical combinatorics.

equate: An R Package for Observed-Score Linking and Equating

Directory of Open Access Journals (Sweden)

Anthony D. Albano

2016-10-01

Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

Iterative solution of linear equations in ODE codes. [Krylov subspaces

Energy Technology Data Exchange (ETDEWEB)

Gear, C. W.; Saad, Y.

1981-01-01

Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

A Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials

International Nuclear Information System (INIS)

Minelli, T.A.

1976-01-01

A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation

Generalized multiscale finite element methods. nonlinear elliptic equations

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

2013-01-01

In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.

Ginsburg-Landau equation around the superconductor-insulator transition

International Nuclear Information System (INIS)

Ng, T.K.

1991-01-01

Based on the scaling theory of localization, we construct a Ginsburg-Landau (GL) equation for superconductors in an arbitrary strength of disordered potential. Using this GL equation, we reexamine the criteria for the superconductor-insulator transition and find that the transition to a localized superconductor can happen on both sides of the (normal) metal-insulator transition, in contrast to a previous prediction by Ma and Lee [Phys. Rev. B 32, 5658 (1985)] that the transition can only be on the insulator side. Furthermore, by comparing our theory with a recent scaling theory of dirty bosons by Fisher et al. [Phys. Rev. Lett. 64, 587 (1990)], we conclude that nontrivial crossover behavior in transport properties may occur in the vicinity of the superconductor-insulator transition

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz

2014-04-24

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.

Prediction equations of forced oscillation technique: the insidious role of collinearity.

Science.gov (United States)

Narchi, Hassib; AlBlooshi, Afaf

2018-03-27

Many studies have reported reference data for forced oscillation technique (FOT) in healthy children. The prediction equation of FOT parameters were derived from a multivariable regression model examining the effect of age, gender, weight and height on each parameter. As many of these variables are likely to be correlated, collinearity might have affected the accuracy of the model, potentially resulting in misleading, erroneous or difficult to interpret conclusions.The aim of this work was: To review all FOT publications in children since 2005 to analyze whether collinearity was considered in the construction of the published prediction equations. Then to compare these prediction equations with our own study. And to analyse, in our study, how collinearity between the explanatory variables might affect the predicted equations if it was not considered in the model. The results showed that none of the ten reviewed studies had stated whether collinearity was checked for. Half of the reports had also included in their equations variables which are physiologically correlated, such as age, weight and height. The predicted resistance varied by up to 28% amongst these studies. And in our study, multicollinearity was identified between the explanatory variables initially considered for the regression model (age, weight and height). Ignoring it would have resulted in inaccuracies in the coefficients of the equation, their signs (positive or negative), their 95% confidence intervals, their significance level and the model goodness of fit. In Conclusion with inaccurately constructed and improperly reported models, understanding the results and reproducing the models for future research might be compromised.

One-way spatial integration of hyperbolic equations

Science.gov (United States)

Towne, Aaron; Colonius, Tim

2015-11-01

In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.

Iodine-131 induced hepatotoxicity in previously healthy patients with Grave's disease.

Science.gov (United States)

Jhummon, Navina Priya; Tohooloo, Bhavna; Qu, Shen

2013-01-01

To describe the association of the rare and serious complication of liver toxicity in previously healthy Grave's disease (GD) patients after the treatment with radioactive iodine (131)I (RAI). We report the clinical, laboratory and pathologic findings of 2 cases of severe liver toxicity associated with the treatment with RAI in previously healthy patients with GD. Clinical examination and laboratory investigations excluded viral hepatitis, autoimmune hepatitis, granulomatous disease, primary biliary disease, extrahepatic biliary obstruction, and heart failure. Case 1: A previously healthy 52-years old man reportedly having a typical GD but following RAI treatment, concomitantly developed severe liver toxicity that required 1 week of treatment in hospital. Case 2: A previously healthy 34-years old woman is reported as having a typical GD but developed jaundice following RAI treatment that required several weeks of in hospital treatment in the hepato-biliary department. In both cases, the liver dysfunction resolved after intensive treatment with hepato-protective agents. In this report the therapeutic considerations as well as the pathogenetic possibilities are reviewed. To the best of our knowledge, this is the first description of the association observed, which is rare but may be severe and should be considered in any case of thyrotoxicosis where a liver dysfunction develops after the treatment with radioactive iodine (131)I.

Chemical Equation Balancing.

Science.gov (United States)

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Current use of equations for estimating glomerular filtration rate in Spanish laboratories.

Science.gov (United States)

Gràcia-Garcia, Sílvia; Montañés-Bermúdez, Rosario; Morales-García, Luis J; Díez-de Los Ríos, M José; Jiménez-García, Juan Á; Macías-Blanco, Carlos; Martínez-López, Rosalina; Ruiz-Altarejos, Joaquín; Ruiz-Martín, Guadalupe; Sanz-Hernández, Sonia; Ventura-Pedret, Salvador

2012-07-17

In 2006 the Spanish Society of Clinical Biochemistry and Molecular Pathology (SEQC) and the Spanish Society of Nephrology (S.E.N.) developed a consensus document in order to facilitate the diagnosis and monitoring of chronic kidney disease with the incorporation of equations for estimating glomerular filtration rate (eGFR) into laboratory reports. The current national prevalence of eGFR reporting and the degree of adherence to these recommendations among clinical laboratories is unknown. We administered a national survey in 2010-11 to Spanish clinical laboratories. The survey was through e-mail or telephone to laboratories that participated in the SEQC’s Programme for External Quality Assurance, included in the National Hospitals Catalogue 2010, including both primary care and private laboratories. A total of 281 laboratories answered to the survey. Of these, 88.2% reported on the eGFR, with 61.9% reporting on the MDRD equation and 31.6% using the MDRD-IDMS equation. A total of 42.5% of laboratories always reported serum creatinine values, and other variables only when specifically requested. Regarding the way results were presented, 46.2% of laboratories reported the exact numerical value only when the filtration rate was below 60mL/min/1.73m2, while 50.6% reported all values regardless. In 56.3% of the cases reporting eGFR, an interpretive commentary of it was enclosed. Although a high percentage of Spanish laboratories have added eGFR in their reports, this metric is not universally used. Moreover, some aspects, such as the equation used and the correct expression of eGFR results, should be improved.

Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

Energy Technology Data Exchange (ETDEWEB)

Gregoire, O

2008-07-01

In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

Some Further Results on Traveling Wave Solutions for the ZK-BBM( Equations

Directory of Open Access Journals (Sweden)

Shaoyong Li

2013-01-01

Full Text Available We investigate the traveling wave solutions for the ZK-BBM( equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2 equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2 equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.

Picard-Fuchs equations of dimensionally regulated Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Zayadeh, Raphael

2013-12-15

the two-loop sunrise integral with arbitrary fixed masses and varying momentum. It was previously known not to evaluate to multiple polylogarithms, but an analytic answer could not be obtained. Its geometric and number theoretic content is governed by a family of elliptic curves. We provide an inhomogeneous Picard-Fuchs equation which in the meantime lead to an analytic answer of the two-loop sunrise integral. We give a three-loop example where we find a family of K3-surfaces.

Picard-Fuchs equations of dimensionally regulated Feynman integrals

International Nuclear Information System (INIS)

Zayadeh, Raphael

2013-12-01

-loop sunrise integral with arbitrary fixed masses and varying momentum. It was previously known not to evaluate to multiple polylogarithms, but an analytic answer could not be obtained. Its geometric and number theoretic content is governed by a family of elliptic curves. We provide an inhomogeneous Picard-Fuchs equation which in the meantime lead to an analytic answer of the two-loop sunrise integral. We give a three-loop example where we find a family of K3-surfaces.

Some New Integrable Equations from the Self-Dual Yang-Mills Equations

International Nuclear Information System (INIS)

Ivanova, T.A.; Popov, A.D.

1994-01-01

Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

Auxiliary equation method for solving nonlinear partial differential equations

International Nuclear Information System (INIS)

Sirendaoreji,; Jiong, Sun

2003-01-01

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

Periodic and solitary-wave solutions of the Degasperis-Procesi equation

International Nuclear Information System (INIS)

Vakhnenko, V.O.; Parkes, E.J.

2004-01-01

Travelling-wave solutions of the Degasperis-Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis-Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered

Adjustment of pipe flow explicit friction factor equations for application to tube bundles

International Nuclear Information System (INIS)

Wiltz, Christopher L.; Bowen, Mike D.; Von Olnhausen, Wayne A.

2005-01-01

Full text of publication follows: The accurate determination of single phase friction losses or friction pressure drop in tube bundles is essential in the thermal-hydraulic analyses of components such as nuclear fuel assemblies, heat exchangers and steam generators. Such friction losses are normally calculated using a friction factor, f, along with the experimental observation that the friction pressure drop in a pipe is proportional to the dynamic pressure (1/2 ρV 2 ) of the flow: ΔP = 1/2 ρV 2 (fL/D). In this equation L is the pipe or tube bundle length and D is the hydraulic diameter of the pipe or tube bundle. The friction factor is normally calculated using one of a number of explicit friction factor equations. A significant amount of work has been accomplished in developing explicit friction factor equations. These explicit equations range from approximations, which were developed for ease of numerical evaluation, to those which are mathematically complex but yield very good fits to the test data. These explicit friction factor equations are based on a large experimental data base, nearly all of which comes from pipe flow geometry information, and have been historically applied to tube bundles. This paper presents an adjustment method which may be applied to various explicit friction factor equations developed for pipe flow to accurately predict the friction factor for tube bundles. The characteristic of the adjustment is based on experimental friction pressure loss data obtained by Framatome ANP through flow testing of a nuclear fuel assembly (tube bundle) at its Richland Test Facility (RTF). Through adjustment of previously developed explicit friction factor equations for pipe flow, the vast amount of historical development and experimentation in the area of single phase pipe flow friction loss may be incorporated into the evaluation of single phase friction losses within tube bundles. Comparisons of the application of one or more of the previously

The equationally-defined commutator a study in equational logic and algebra

CERN Document Server

Czelakowski, Janusz

2015-01-01

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.  An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras.  The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

Enthalpy of dissociation and hydration number of methane hydrate from the Clapeyron equation

International Nuclear Information System (INIS)

Anderson, Graydon K.

2004-01-01

The enthalpies of the reactions in which methane hydrate is dissociated to methane vapor and either (1) water, or (2) ice are determined by a new analysis using the Clapeyron equation. The difference in enthalpies of the two reactions is used to infer the hydration number at the quadruple point where hydrate, ice, liquid water, and methane vapor coexist. By appropriate corrections, the hydration number at points removed from the quadruple point is also determined. The most important feature of the new analysis is the direct use of the Clapeyron equation. The method avoids the use of certain simplifying assumptions that have compromised the accuracy of previous analyses in which the Clausius-Clapeyron equation was used. The analysis takes into account the finite volumes of all phases, the non-ideality of the vapor phase, and the solubility of methane in water. The results show that the enthalpy of dissociation and hydration number are constant within experimental error over the entire (hydrate, liquid, vapor) coexistence region. The results are more accurate than but entirely consistent with almost all previous studies

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

Science.gov (United States)

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations

Directory of Open Access Journals (Sweden)

Rong Cheng

2010-01-01

Full Text Available The existence of multiple periodic solutions of the following differential delay equation (=−((− is established by applying variational approaches directly, where ∈ℝ, ∈(ℝ,ℝ and >0 is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique to reduce the existence problem of the above equation to an existence problem for a related coupled system. Such a reduction method introduced first by Kaplan and Yorke in (1974 is often employed in previous papers to study the existence of periodic solutions for the above equation and its similar ones by variational approaches.

Measuring the equations of state in a relaxed magnetohydrodynamic plasma

Science.gov (United States)

Kaur, M.; Barbano, L. J.; Suen-Lewis, E. M.; Shrock, J. E.; Light, A. D.; Brown, M. R.; Schaffner, D. A.

2018-01-01

We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.

Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

Science.gov (United States)

Abdelaziz, Y.; Maillard, J.-M.

2017-05-01

We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same {}_2F1 hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus {}_2F1 hypergeometric function example. We then focus on identities relating the same {}_2F1 hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to {}_3F2 , hypergeometric functions, and show that one just reduces to the previous {}_2F1 cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a _2F1 hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or {}_2F1 hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to

Two-fluid equations for a nuclear system with arbitrary motions

Energy Technology Data Exchange (ETDEWEB)

Kim, Byoung Jae [Chungnam National University, Daejeon (Korea, Republic of); Kim, Kyung Doo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2016-10-15

Ocean nuclear systems include a seabed-type plant, a floating-type plant, and a nuclear-propulsion ship. We asked ourselves, 'What governing equations should be used for ocean nuclear systems?' Since ocean nuclear systems are apt to move arbitrarily, the two-fluid model must be formulated in the non-inertial frame of reference that is undergoing acceleration with respect to an inertial frame. Two-phase flow systems with arbitrary motions are barely reported. Kim et al. (1996) added the centripetal and Euler acceleration forces to the homogeneous equilibrium momentum equation embedded in the RETRAN code. However, they did not look into the mass and energy equations. The purpose of this study is to derive general two-fluid equations in the non-inertial frame of reference, which can be used for safety analysis of ocean nuclear systems. The two-fluid equation forms for scalar properties such as mass, internal energy, and enthalpy equation in the moving frame are the same as those in the absolute frame. On the other hand, the fictitious effect must be included in the momentum equation.

Lectures on the practical solution of differential equations

International Nuclear Information System (INIS)

Dresner, L.

1979-11-01

This report comprises lectures on the practical solution of ordinary and partial differential equations given in the In-Hours Continuing Education Program for Scientific and Technical Personnel at Oak Ridge National Laboratory

Stable estimation of two coefficients in a nonlinear Fisher–KPP equation

International Nuclear Information System (INIS)

Cristofol, Michel; Roques, Lionel

2013-01-01

We consider the inverse problem of determining two non-constant coefficients in a nonlinear parabolic equation of the Fisher–Kolmogorov–Petrovsky–Piskunov type. For the equation u t = DΔu + μ(x) u − γ(x)u 2 in (0, T) × Ω, which corresponds to a classical model of population dynamics in a bounded heterogeneous environment, our results give a stability inequality between the couple of coefficients (μ, γ) and some observations of the solution u. These observations consist in measurements of u: in the whole domain Ω at two fixed times, in a subset ω⊂⊂Ω during a finite time interval and on the boundary of Ω at all times t ∈ (0, T). The proof relies on parabolic estimates together with the parabolic maximum principle and Hopf’s lemma which enable us to use a Carleman inequality. This work extends previous studies on the stable determination of non-constant coefficients in parabolic equations, as it deals with two coefficients and with a nonlinear term. A consequence of our results is the uniqueness of the couple of coefficients (μ, γ), given the observation of u. This uniqueness result was obtained in a previous paper but in the one-dimensional case only. (paper)

Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method

International Nuclear Information System (INIS)

Suescun D, D.; Oviedo T, M.

2017-09-01

In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

Science.gov (United States)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

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

OpenAIRE

Kihara, Hironobu

2008-01-01

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

Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates

International Nuclear Information System (INIS)

Brizard, A.

1988-09-01

A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

Science.gov (United States)

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1991-05-01

MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

Differential equations a dynamical systems approach ordinary differential equations

CERN Document Server

Hubbard, John H

1991-01-01

This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.

Differential equations

CERN Document Server

Barbu, Viorel

2016-01-01

This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

Shunt malfunction causing acute neurological deterioration in 2 patients with previously asymptomatic Chiari malformation Type I. Report of two cases.

Science.gov (United States)

Elliott, Robert; Kalhorn, Stephen; Pacione, Donato; Weiner, Howard; Wisoff, Jeffrey; Harter, David

2009-08-01

Patients with symptomatic Chiari malformation Type I (CM-I) typically exhibit a chronic, slowly progressive disease course with evolution of symptoms. However, some authors have reported acute neurological deterioration in the setting of CM-I and acquired Chiari malformations. Although brainstem dysfunction has been documented in patients with CM-II and hydrocephalus or shunt malfunction, to the authors' knowledge only 1 report describing ventriculoperitoneal (VP) shunt malfunction causing neurological deterioration in a patient with CM-I exists. The authors report on their experience with the treatment of previously asymptomatic CM-I in 2 children who experienced quite different manifestations of acute neurological deterioration secondary to VP shunt malfunction. Presumably, VP shunt malfunction created a positive rostral pressure gradient across a stenotic foramen magnum, resulting in tetraparesis from foramen magnum syndrome in 1 patient and acute ataxia and cranial nerve deficits from syringobulbia in the other. Although urgent shunt revisions yielded partial recovery of neurological function in both patients, marked improvement occurred only after posterior fossa decompression.

Single-site Green function of the Dirac equation for full-potential electron scattering

Energy Technology Data Exchange (ETDEWEB)

Kordt, Pascal

2012-05-30

I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

Single-site Green function of the Dirac equation for full-potential electron scattering

International Nuclear Information System (INIS)

Kordt, Pascal

2012-01-01

I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

Science.gov (United States)

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

The impact of the implementations of the Sysrust’s framework upon the quality of financial reporting: structural equation modelling approach

Directory of Open Access Journals (Sweden)

Ahmed Al-Dmour

2018-03-01

Full Text Available The purpose of this research is to examine empirically, validate, and predict the reliability of the proposed relationship between the reliability of AIS process in the context of SysTrust' framework (principles and criteria and the quality of financial reporting in shareholdings companies in Jordan. For this purpose, a primary data was used that was collected through a self-structured questionnaire from 239 of shareholdings companies. The extent of SysTrust's framework (principles and criteria and the quality of financial reporting were also measured. The data were analyzed using structural equation modeling. The results showed that the magnitude and significance of the loading estimate and they indicated that all of the main five principles of SysTrust's framework are relevant in predicting the quality of financial reporting. Moreover, the reliability of AIS by the implementation of these five principles of SysTrust's framework were positively impacting the quality of financial reporting, as the structural coefficient for these paths are significant.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Science.gov (United States)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Relations between nonlinear Riccati equations and other equations in fundamental physics

International Nuclear Information System (INIS)

Schuch, Dieter

2014-01-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

Meson spectra from two-body dirac equations with minimal interactions

International Nuclear Information System (INIS)

Crater, H.W.; Becker, R.L.; Wong, C.Y.

1991-01-01

Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

Science.gov (United States)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

Least-squares finite element discretizations of neutron transport equations in 3 dimensions

Energy Technology Data Exchange (ETDEWEB)

Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)

1996-12-31

The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices

International Nuclear Information System (INIS)

Sechin, Ivan; Zotov, Andrei

2016-01-01

In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.

Student Perceptions of Writing Projects in a University Differential-Equations Course

Science.gov (United States)

Latulippe, Christine; Latulippe, Joe

2014-01-01

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits…

Partial differential equations

CERN Document Server

Evans, Lawrence C

2010-01-01

This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

Rate equation modelling of erbium luminescence dynamics in erbium-doped silicon-rich-silicon-oxide

Energy Technology Data Exchange (ETDEWEB)

Shah, Miraj, E-mail: m.shah@ee.ucl.ac.uk [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Wojdak, Maciej; Kenyon, Anthony J. [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Halsall, Matthew P.; Li, Hang; Crowe, Iain F. [Photon Science Institute and School of Electrical and Electronic Engineering, University of Manchester, Sackville St Building, Manchester M13 9PL (United Kingdom)

2012-12-15

Erbium doped silicon-rich silica offers broad band and very efficient excitation of erbium photoluminescence (PL) due to a sensitization effect attributed to silicon nanocrystals (Si-nc), which grow during thermal treatment. PL decay lifetime measurements of sensitised Er{sup 3+} ions are usually reported to be stretched or multi exponential, very different to those that are directly excited, which usually show a single exponential decay component. In this paper, we report on SiO{sub 2} thin films doped with Si-nc's and erbium. Time resolved PL measurements reveal two distinct 1.54 {mu}m Er decay components; a fast microsecond component, and a relatively long lifetime component (10 ms). We also study the structural properties of these samples through TEM measurements, and reveal the formation of Er clusters. We propose that these Er clusters are responsible for the fast {mu}s decay component, and we develop rate equation models that reproduce the experimental transient observations, and can explain some of the reported transient behaviour in previously published literature.

Process cells dismantling of EUREX pant: previous activities

International Nuclear Information System (INIS)

Gili, M.

1998-01-01

In the '98-'99 period some process cells of the EUREX pant will be dismantled, in order to place there the liquid wastes conditioning plant 'CORA'. This report resumes the previous activities (plant rinsing campaigns and inactive Cell 014 dismantling), run in the past three years and the drawn experience [it

Functional equations with causal operators

CERN Document Server

Corduneanu, C

2003-01-01

Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

Electron and ion transport equations in computational weakly-ionized plasmadynamics

International Nuclear Information System (INIS)

Parent, Bernard; Macheret, Sergey O.; Shneider, Mikhail N.

2014-01-01

A new set of ion and electron transport equations is proposed to simulate steady or unsteady quasi-neutral or non-neutral multicomponent weakly-ionized plasmas through the drift–diffusion approximation. The proposed set of equations is advantaged over the conventional one by being considerably less stiff in quasi-neutral regions because it can be integrated in conjunction with a potential equation based on Ohm's law rather than Gauss's law. The present approach is advantaged over previous attempts at recasting the system by being applicable to plasmas with several types of positive ions and negative ions and by not requiring changes to the boundary conditions. Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms. Further, several grid convergence studies indicate that the present approach exhibits a higher resolution (and hence requires fewer nodes to reach a given level of accuracy) when ambipolar diffusion is present. Because the proposed equations are not intrinsically linked to specific discretization or integration schemes and exhibit substantial advantages with no apparent disadvantage, they are generally recommended as a substitute to the fluid models in which the electric field is obtained from Gauss's law as long as the plasma remains weakly-ionized and unmagnetized

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

Science.gov (United States)

Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

2012-01-01

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

Science.gov (United States)

Kudryashov, Nikolay A.; Volkov, Alexandr K.

2017-01-01

We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

Handbook of integral equations

CERN Document Server

Polyanin, Andrei D

2008-01-01

This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

[Double mutant alleles in the EXT1 gene not previously reported in a teenager with hereditary multiple exostoses].

Science.gov (United States)

Cammarata-Scalisi, Francisco; Cozar, Mónica; Grinberg, Daniel; Balcells, Susana; Asteggiano, Carla G; Martínez-Domenech, Gustavo; Bracho, Ana; Sánchez, Yanira; Stock, Frances; Delgado-Luengo, Wilmer; Zara-Chirinos, Carmen; Chacín, José Antonio

2015-04-01

Hereditary forms of multiple exostoses, now called EXT1/EXT2-CDG within Congenital Disorders of Glycosylation, are the most common benign bone tumors in humans and clinical description consists of the formation of several cartilage-capped bone tumors, usually benign and localized in the juxta-epiphyseal region of long bones, although wide body dissemination in severe cases is not uncommon. Onset of the disease is variable ranging from 2-3 years up to 13-15 years with an estimated incidence ranging from 1/18,000 to 1/50,000 cases in European countries. We present a double mutant alleles in the EXT1 gene not previously reported in a teenager and her family with hereditary multiple exostoses.

CORE-COLLAPSE SUPERNOVA EQUATIONS OF STATE BASED ON NEUTRON STAR OBSERVATIONS

International Nuclear Information System (INIS)

Steiner, A. W.; Hempel, M.; Fischer, T.

2013-01-01

Many of the currently available equations of state for core-collapse supernova simulations give large neutron star radii and do not provide large enough neutron star masses, both of which are inconsistent with some recent neutron star observations. In addition, one of the critical uncertainties in the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully explored by the currently available equations of state. In this article, we construct two new equations of state which match recent neutron star observations and provide more flexibility in studying the dependence on nuclear matter properties. The equations of state are also provided in tabular form, covering a wide range in density, temperature, and asymmetry, suitable for astrophysical simulations. These new equations of state are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics with three-flavor Boltzmann neutrino transport. The results are compared with commonly used equations of state in supernova simulations of 11.2 and 40 M ☉ progenitors. We consider only equations of state which are fitted to nuclear binding energies and other experimental and observational constraints. We find that central densities at bounce are weakly correlated with L and that there is a moderate influence of the symmetry energy on the evolution of the electron fraction. The new models also obey the previously observed correlation between the time to black hole formation and the maximum mass of an s = 4 neutron star

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

Science.gov (United States)

Li, Bing; Li, Yongkun; Zhang, Xuemei

2016-01-01

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

Equations of motion of higher-spin gauge fields as a free differential algebra

International Nuclear Information System (INIS)

Vasil'ev, M.A.

1988-01-01

It is shown that the introduction of auxiliary dynamical variables that generalize the gravitational Weyl tensor permits one to reduce the equations of motion of free massless fields of all spins in the anti-de Sitter O(3,2) space to a form characteristic of free differential algebras. The equations of motion of auxiliary gauge fields introduced previously are modified analogously. Arguments are presented to the effect that the equations of motion of interacting massless fields of all spins should be described in terms of a free differential algebra which is a deformation of a known free differential algebra generated by 1- and 0-forms in the adjoint representation of a nonabelian superalgebra of higher spins and auxiliary fields

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

Energy Technology Data Exchange (ETDEWEB)

EL Safadi, M

2007-03-15

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

Performance equations of proton exchange membrane fuel cells with feeds of varying degrees of humidification

International Nuclear Information System (INIS)

Hsuen, Hsiao-Kuo; Yin, Ken-Ming

2012-01-01

Performance equations that describe the dependence of cell potential on current density for proton exchange membrane fuel cells (PEMFCs) with feeds of varying degrees of humidification have been formulated in algebraic form. The equations are developed by the reduction of a one-dimensional multi-domain model that takes into account, in details, the transport limitations of gas species, proton migration and electron conduction, electrochemical kinetics, as well as liquid water flow within the cathode, anode, and membrane. The model equations for the anode and membrane were integrated with those of the cathode developed in the previous studies to form a complete set of equations for one-dimensional single cell model. Because the transport equations for the anode diffuser can be solved analytically, calculations of integrals are only needed in the membrane and the two-phase region of cathode diffuser. The proposed approach greatly reduces the complexity of the model equations, and only iterations of a single algebraic equation are required to obtain final solutions. Since the performance equations are originated from a mechanistic one-dimensional model, all the parameters appearing in the equations are endowed with a precise physical significance.

Validity of Miles Equation in Predicting Propellant Slosh Damping in Baffled Tanks at Variable Slosh Amplitude

Science.gov (United States)

Yang, H. Q.; West, Jeff

2018-01-01

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Ordinary differential equations

CERN Document Server

Greenberg, Michael D

2014-01-01

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

An Eulerian description of the streaming process in the lattice Boltzmann equation

CERN Document Server

Lee Tae Hun

2003-01-01

This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...

Iodine-131 induced hepatotoxicity in previously healthy patients with Grave’s disease

Science.gov (United States)

2013-01-01

Objective To describe the association of the rare and serious complication of liver toxicity in previously healthy Grave’s disease (GD) patients after the treatment with radioactive iodine 131I (RAI). Case presentation We report the clinical, laboratory and pathologic findings of 2 cases of severe liver toxicity associated with the treatment with RAI in previously healthy patients with GD. Clinical examination and laboratory investigations excluded viral hepatitis, autoimmune hepatitis, granulomatous disease, primary biliary disease, extrahepatic biliary obstruction, and heart failure. Case 1: A previously healthy 52-years old man reportedly having a typical GD but following RAI treatment, concomitantly developed severe liver toxicity that required 1 week of treatment in hospital. Case 2: A previously healthy 34-years old woman is reported as having a typical GD but developed jaundice following RAI treatment that required several weeks of in hospital treatment in the hepato-biliary department. In both cases, the liver dysfunction resolved after intensive treatment with hepato-protective agents. In this report the therapeutic considerations as well as the pathogenetic possibilities are reviewed. Conclusion To the best of our knowledge, this is the first description of the association observed, which is rare but may be severe and should be considered in any case of thyrotoxicosis where a liver dysfunction develops after the treatment with radioactive iodine 131I. PMID:23497434

From convolutionless generalized master to Pauli master equations

International Nuclear Information System (INIS)

Capek, V.

1995-01-01

The paper is a continuation of previous work within which it has been proved that time integrals of memory function (i.e. Markovian transfer rates from Pauli Master Equations, PME) in Time-Convolution Generalized Master Equations (TC-GME) for probabilities of finding a state of an asymmetric system interacting with a bath with a continuous spectrum are exactly zero, provided that no approximation is involved, irrespective of the usual finite-perturbation-order correspondence with the Golden Rule transition rates. In this paper, attention is paid to an alternative way of deriving the rigorous PME from the TCL-GME. Arguments are given in favor of the proposition that the long-time limit of coefficients in TCL-GME for the above probabilities, under the same assumption and presuming that this limit exists, is equal to zero. 11 refs

Cut cancellation in the planar integral equation for the Reggeon

International Nuclear Information System (INIS)

Bishari, M.; Veneziano, G.

1975-01-01

Planar unitarity for the Reggeon, analyticity and the multi-Regge assumption with cluster production lead to integral equations of the Chew-Goldberger-Low type with separable self-consistent kernel. Contrary to common prejudice, the authors show the existence of solutions exhibiting moving poles and exact, non-perturbative cancellation of the cut. Previously studied consistency conditions are rederived. (Auth.)

Relationship between the public's belief in recovery, level of mental illness stigma, and previous contact.

Science.gov (United States)

Barczyk, Amanda N

2015-01-01

Disbelief exits that individuals who have a mental health condition are able to recover and fully function in life. This study analyzed 1,437 adults from the 2006 General Social Survey. Structural equation modeling (1) examined the relationship between respondents' level of prejudicial attitudes and social distance (i.e., stigma) toward individuals who have a mental health condition and their belief in the potential of recovery (2) tested whether previous contact with an individual who received treatment was a mediator. Findings indicated that the belief in recovery led to lower levels of social distance. Prejudicial attitudes were found to be a predictor of one's level of social distance. Previous contact was not a mediator however; males, minorities and those with less education were less likely to have had previous contact. Results indicated a need to emphasize the probability of recovering from a mental health condition when developing target-specific stigma reducing strategies.

Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Chowdury, A.R.; Naskar, M.

1986-01-01

Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli

Quantum master equation for collisional dynamics of massive particles with internal degrees of freedom

International Nuclear Information System (INIS)

Smirne, Andrea; Vacchini, Bassano

2010-01-01

We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom, interacting through collisions with a background ideal gas. When either internal or center-of-mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of internal degrees of freedom on center-of-mass decoherence is considered in this framework.

Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates

Science.gov (United States)

Wilson, F.; Neukirch, T.

2018-01-01

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the "pseudo-potential" (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a "fractional multipole" nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.

PREFACE: Symmetries and Integrability of Difference Equations

Science.gov (United States)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of

Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods; Calculo Numerico de Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Metodos Numericos

Energy Technology Data Exchange (ETDEWEB)

Reynolds, J. M.; Lopez-Bruna, D.

2009-10-12

In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.

Bilateral orbital infarction and retinal detachment in a previously undiagnosed sickle cell hemoglobinopathy African child

Science.gov (United States)

Helen, Onakpoya Oluwatoyin; Ajite, K. O.; Oyelami, O. A.; Asaleye, C. M.; Adeoye, A. O.

2013-01-01

Bone infarction involving the orbit in sickle cell disease is not common. Bilateral orbital infarction in a previously undiagnosed sickle cell hemoglobinopathy has not been previously reported. In this report, we present a case of an 11-year-old previously undiagnosed sickle cell disease Nigerian girl with severe acute bilateral orbital infarction and retinal detachment to highlight that hemoglobinopathy induced orbital infarction should be considered in African children with acute onset proptosis with or without previous history of sickle cell hemoglobinopathy. PMID:23901183

Fractional Schroedinger equation

International Nuclear Information System (INIS)

Laskin, Nick

2002-01-01

Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

Semiconservative quasispecies equations for polysomic genomes: The general case

Science.gov (United States)

Itan, Eran; Tannenbaum, Emmanuel

2010-06-01

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analog of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for noncomplementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

Introduction to differential equations

CERN Document Server

Taylor, Michael E

2011-01-01

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

A case report: mixed thrombus formation in a previously sutured right atrium.

Science.gov (United States)

Yunfei, Ling; Dongxu, Li; Shuhua, Luo; Yabo, Wang; San, Deep; Changping, Gan; Ke, Lin; Qi, An

2014-08-01

We describe the case of a 19-year-old Chinese woman who nine months prior underwent repair of an atrial septal defect and came to our hospital with a right atrial mass attached to the anterior wall of the right atrium on transthoracic echocardiography. Pathologic examination revealed the mass was a mixed-type thrombosis with some unusual organization, which previously was not described in literature.

Introducing time-dependent molecular fields: a new derivation of the wave equations

Science.gov (United States)

Baer, Michael

2018-02-01

This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

A maximum principle for the first-order Boltzmann equation, incorporating a potential treatment of voids

International Nuclear Information System (INIS)

Schofield, S.L.

1988-01-01

Ackroyd's generalized least-squares method for solving the first-order Boltzmann equation is adapted to incorporate a potential treatment of voids. The adaptation comprises a direct least-squares minimization allied with a suitably-defined bilinear functional. The resulting formulation gives rise to a maximum principle whose functional does not contain terms of the type that have previously led to difficulties in treating void regions. The maximum principle is derived without requiring continuity of the flux at interfaces. The functional of the maximum principle is concluded to have an Euler-Lagrange equation given directly by the first-order Boltzmann equation. (author)

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

2016-07-01

The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

Averaged RMHD equations

International Nuclear Information System (INIS)

Ichiguchi, Katsuji

1998-01-01

A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)

Final Technical Report for Year 5 Early Career Research Project "Viscosity and equation of state of hot and dense QCD matter"

Energy Technology Data Exchange (ETDEWEB)

Molnar, Denes [Purdue Univ., West Lafayette, IN (United States)

2016-05-25

The Section below summarizes research activities and achievements during the fifth (last) year of the PI’s Early Career Research Project (ECRP). Unlike the first four years of the project, the last year was not funded under the American Recovery and Reinvestment Act (ARRA). The ECRP advanced two main areas: i) radiative 3 ↔ 2 radiative transport, via development of a new computer code MPC/Grid that solves the Boltzmann transport equation in full 6+1D (3X+3V+time); and ii) application of relativistic hydrodynamics, via development of a self-consistent framework to convert viscous fluids to particles. In Year 5 we finalized thermalization studies with radiative gg ↔ ggg transport (Sec. 1.1.1) and used nonlinear covariant transport to assess the accuracy of fluid-to-particle conversion models (Sec. 1.1.2), calculated observables with self-consistent fluid-to-particle conversion from realistic viscous hydrodynamic evolution (Secs. 1.2.1 and 1.2.2), extended the covariant energy loss formulation to heavy quarks (Sec. 1.4.1) and studied energy loss in small systems (Sec. 1.4.2), and also investigated how much of the elliptic flow could have non-hydrodynamic origin (Sec 1.3). Years 1-4 of the ECRP were ARRA-funded and, therefore, they have their own report document ’Final Technical Report for Years 1-4 of the Early Career Research Project “Viscosity and equation of state of hot and dense QCD matter”’ (same award number DE-SC0004035). The PI’s group was also part of the DOE JET Topical Collaboration, a multi-institution project that overlapped in time significantly with the ECRP. Purdue achievements as part of the JET Top- ical Collaboration are in a separate report “Final Technical Report summarizing Purdue research activities as part of the DOE JET Topical Collaboration” (award DE-SC0004077).

Journal: A Review of Some Tracer-Test Design Equations for ...

Science.gov (United States)

Determination of necessary tracer mass, initial sample-collection time, and subsequent sample-collection frequency are the three most difficult aspects to estimate for a proposed tracer test prior to conducting the tracer test. To facilitate tracer-mass estimation, 33 mass-estimation equations are reviewed here, 32 of which were evaluated using previously published tracer-test design examination parameters. Comparison of the results produced a wide range of estimated tracer mass, but no means is available by which one equation may be reasonably selected over the others. Each equation produces a simple approximation for tracer mass. Most of the equations are based primarily on estimates or measurements of discharge, transport distance, and suspected transport times. Although the basic field parameters commonly employed are appropriate for estimating tracer mass, the 33 equations are problematic in that they were all probably based on the original developers' experience in a particular field area and not necessarily on measured hydraulic parameters or solute-transport theory. Suggested sampling frequencies are typically based primarily on probable transport distance, but with little regard to expected travel times. This too is problematic in that tends to result in false negatives or data aliasing. Simulations from the recently developed efficient hydrologic tracer-test design methodology (EHTD) were compared with those obtained from 32 of the 33 published tracer-

A note on Verhulst's logistic equation and related logistic maps

International Nuclear Information System (INIS)

Gutierrez, M Ranferi; Reyes, M A; Rosu, H C

2010-01-01

We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following results. For the map x n+1 = rx n (1 - x n ) we propose a new way to write the solution for r = -2 which allows better precision of the iterative terms, while for the map x n+1 - x n = rx n (1 - x n+1 ) we show that it behaves identically to the logistic equation from the standpoint of the general Riccati solution, which is also provided herein for any value of the parameter r.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

Science.gov (United States)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

International Nuclear Information System (INIS)

EL Safadi, M.

2007-03-01

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

Differential equations

CERN Document Server

Tricomi, FG

2013-01-01

Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

How to obtain the covariant form of Maxwell's equations from the continuity equation

International Nuclear Information System (INIS)

Heras, Jose A

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

Direct and iterative algorithms for the parallel solution of the one-dimensional macroscopic Navier-Stokes equations

International Nuclear Information System (INIS)

Doster, J.M.; Sills, E.D.

1986-01-01

Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required

Semiconductor device simulation by a new method of solving poisson, Laplace and Schrodinger equations

International Nuclear Information System (INIS)

Sharifi, M. J.; Adibi, A.

2000-01-01

In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as poisson, Laplace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in several cases including the problem of finding electron concentration profile in the channel of a HEMT. In another section, we solve the Poisson equation by this method, choosing the problem of SBD as an example. Finally we solve the Laplace equation in two dimensions and as an example, we focus on the VED. In this paper, we have shown that, the method can get stable and precise results in solving all of these problems. Also the programs which have been written based on this method become considerably faster, more clear, and more abstract

Differential equations in airplane mechanics

Science.gov (United States)

Carleman, M T

1922-01-01

In the following report, we will first draw some conclusions of purely theoretical interest, from the general equations of motion. At the end, we will consider the motion of an airplane, with the engine dead and with the assumption that the angle of attack remains constant. Thus we arrive at a simple result, which can be rendered practically utilizable for determining the trajectory of an airplane descending at a constant steering angle.

Integrability of N=3 super Yang-Mills equations

International Nuclear Information System (INIS)

Devchand, C.; Ogievetsky, V.

1993-10-01

We describe the harmonic superspace formulation of the Witten-Manin supertwistor correspondence for N=3 extended super Yang-Mills theories. The essence in that on being sufficiently supersymmetrised (up to the N=3 extension), the Yang-Mills equations of motion can be recast in the form of Cauchy-Riemann-like holomorphicity conditions for a pair of prepotentials in the appropriate harmonic superspace. This formulation makes the explicit construction of solutions a rather more tractable proposition than previous attempts. (orig.)

Planck constant as spectral parameter in integrable systems and KZB equations

Science.gov (United States)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Loop equations and bootstrap methods in the lattice

Directory of Open Access Journals (Sweden)

Peter D. Anderson

2017-08-01

Full Text Available Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator, it becomes a well defined equation for a discrete set of loops. In this paper we study different numerical approaches to solving this equation. Previous ideas gave good results in the strong coupling region. Here we propose an alternative method based on the observation that certain matrices ρˆ of Wilson loop expectation values are positive definite. They also have unit trace (ρˆ⪰0,Trρˆ=1, in fact they can be defined as reduced density matrices in the space of open loops after tracing over color indices and can be used to define an entropy associated with the loss of information due to such trace SWL=−Tr[ρˆln⁡ρˆ]. The condition that such matrices are positive definite allows us to study the weak coupling region which is relevant for the continuum limit. In the exactly solvable case of two dimensions this approach gives very good results by considering just a few loops. In four dimensions it gives good results in the weak coupling region and therefore is complementary to the strong coupling expansion. We compare the results with standard Monte Carlo simulations.

An axisymmetric evolution code for the Einstein equations on hyperboloidal slices

International Nuclear Information System (INIS)

Rinne, Oliver

2010-01-01

We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational cost. The formulation is based on an earlier axisymmetric evolution scheme, adapted to time slices of constant mean curvature. Ideas from a previous study by Moncrief and the author are applied in order to regularize the formally singular evolution equations at future null infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime are obtained, including a gravitational perturbation. The Bondi news function is evaluated at future null infinity.

On an integrable discretization of the modified Korteweg-de Vries equation

Science.gov (United States)

Suris, Yuri B.

1997-02-01

We find time discretizations for the two “second flows” of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.

Previous induced abortion among young women seeking abortion-related care in Kenya: a cross-sectional analysis.

Science.gov (United States)

Kabiru, Caroline W; Ushie, Boniface A; Mutua, Michael M; Izugbara, Chimaraoke O

2016-05-14

Unsafe abortion is a leading cause of death among young women aged 10-24 years in sub-Saharan Africa. Although having multiple induced abortions may exacerbate the risk for poor health outcomes, there has been minimal research on young women in this region who have multiple induced abortions. The objective of this study was therefore to assess the prevalence and correlates of reporting a previous induced abortion among young females aged 12-24 years seeking abortion-related care in Kenya. We used data on 1,378 young women aged 12-24 years who presented for abortion-related care in 246 health facilities in a nationwide survey conducted in 2012. Socio-demographic characteristics, reproductive and clinical histories, and physical examination assessment data were collected from women during a one-month data collection period using an abortion case capture form. Nine percent (n = 98) of young women reported a previous induced abortion prior to the index pregnancy for which they were receiving care. Statistically significant differences by previous history of induced abortion were observed for area of residence, religion and occupation at bivariate level. Urban dwellers and unemployed/other young women were more likely to report a previous induced abortion. A greater proportion of young women reporting a previous induced abortion stated that they were using a contraceptive method at the time of the index pregnancy (47 %) compared with those reporting no previous induced abortion (23 %). Not surprisingly, a greater proportion of young women reporting a previous induced abortion (82 %) reported their index pregnancy as unintended (not wanted at all or mistimed) compared with women reporting no previous induced abortion (64 %). Our study results show that about one in every ten young women seeking abortion-related care in Kenya reports a previous induced abortion. Comprehensive post-abortion care services targeting young women are needed. In particular, post

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

Science.gov (United States)

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

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

Directory of Open Access Journals (Sweden)

M. P. Markakis

2010-01-01

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

On separable Pauli equations

International Nuclear Information System (INIS)

Zhalij, Alexander

2002-01-01

We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Science.gov (United States)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Standardization of equations for radiochemical calculations

International Nuclear Information System (INIS)

Danahy, R.J.; Dugan, T.A.; Tomlinson, F.K.; Jones, H.W.

1994-01-01

In mid 1993, the Fernald Environmental Restoration Management Corporation (FERMCO), with USEPA approval implemented a project quality assurance plan containing performance-based specifications for radiochemical sample analyses conducted in support of the Fernald site remediation activities. FERMCO's initial approach to acquiring performance-based radioanalytical services was to provide limited guidance regarding equations for computation of the quantities required in each analysis report. It became evident that there was a significant divergence of opinion on how to compute some very basic radiochemical quantities. The use of a standardized set of equations was needed in order to ensure comparability of data from different laboratories. In a remediation project of this magnitude, use of multiple laboratories is a virtual necessity. Consequently comparability of data becomes an extremely important issue. A critical issue in the Remedial Investigation/Feasibility Study (RI/FS) phase of the dean up project is to avoid the occurrence of excessive false positive sample results. Such results could lead to unnecessary clean up and significant additional cost. This paper describes the specific formulas FERMCO is currently using to define such quantities as net sample count rate, sample radionuclide concentration, radiometric tracer and gravimetric carrier recovery. Equations have also been produced to define the uncertainty in each of the above quantities. Equations for the Total Propagated Uncertainty (TPU) and for a sample-specific Minimum Detectable Concentration (MDC) have also been specified. Generalized equations have been reformulated to address the specific conditions which apply to the analysis of FERMCO samples. In particular, FERMCO requires results which have been corrected for the radioactivity in the blank while in other instances, sample results without blank correction are required

Recursive approach for non-Markovian time-convolutionless master equations

Science.gov (United States)

Gasbarri, G.; Ferialdi, L.

2018-02-01

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.

Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

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Jishan Fan

2013-04-01

Full Text Available Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.

Adomian decomposition method for solving the telegraph equation in charged particle transport

International Nuclear Information System (INIS)

Abdou, M.A.

2005-01-01

In this paper, the analysis for the telegraph equation in case of isotropic small angle scattering from the Boltzmann transport equation for charged particle is presented. The Adomian decomposition is used to solve the telegraph equation. By means of MAPLE the Adomian polynomials of obtained series (ADM) solution have been calculated. The behaviour of the distribution function are shown graphically. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solution of linear and nonlinear problems

New numerical method for solving the solute transport equation

International Nuclear Information System (INIS)

Ross, B.; Koplik, C.M.

1978-01-01

The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

Sensitivity of Equated Aggregate Scores to the Treatment of Misbehaving Common Items

Science.gov (United States)

Michaelides, Michalis P.

2010-01-01

The delta-plot method (Angoff, 1972) is a graphical technique used in the context of test equating for identifying common items with aberrant changes in their item difficulties across administrations or alternate forms. This brief research report explores the effects on equated aggregate scores when delta-plot outliers are either retained in or…

On the classification of scalar evolution equations with non-constant separant

Science.gov (United States)

Hümeyra Bilge, Ayşe; Mizrahi, Eti

2017-01-01

The ‘separant’ of the evolution equation u t   =  F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order

Bioelectrical impedance analysis (BIA) equations validation against hydrodensitometry in a Colombian population

International Nuclear Information System (INIS)

Caicedo-Eraso, J C; Gonzalez-Correa, C A; Gonzalez-Correa, C H

2013-01-01

Several studies have shown that the accuracy of BIA results depends of ethnicity, age, gender, hormonal and genetic variations and, so far, there are not specific equations for Colombian population. The purpose was to evaluate reported BIA equations to determine their usefulness in body composition assessment in young females from Colombia using hydrodensitometry as the reference method. A sample of 30 young females was evaluated. Inclusion and exclusion criteria were defined to minimize the variability of BIA. Height, weight, multi-frequency BIA, residual lung volume (RV) and underwater weight (UWW) were measured. Five BIA equations met the inclusion criteria of this study. Three equations overestimated and two equations underestimated body fat (BF). Paired Student t-test and Bland and Altman analysis (p<0.05) showed significant differences in four BIA equations. However, all standard error of estimate (SEE) to BF was greater than 2.7 kg. This study showed that the five selected BIA equations are not valid for estimation of body composition in young females from Colombia. It is recommended to develop BIA equations to improve BF fat assessment in our population.

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Directory of Open Access Journals (Sweden)

Vitanov Nikolay K.

2018-03-01

Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

Science.gov (United States)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Antiflow of nucleons at the softest point of the equation of state

International Nuclear Information System (INIS)

Brachmann, J.; Soff, S.; Dumitru, A.; Stoecker, H.; Maruhn, J. A.; Greiner, W.; Bravina, L. V.; Rischke, D. H.

2000-01-01

We investigate flow in semiperipheral nuclear collisions at Alternating Gradient Synchrotron and Super Proton Synchrotron energies within macroscopic as well as microscopic transport models. The hot and dense zone assumes the shape of an ellipsoid which is tilted by an angle Θ with respect to the beam axis. If matter is close to the softest point of the equation of state, this ellipsoid expands predominantly orthogonal to the direction given by Θ. This antiflow component is responsible for the previously predicted reduction of the directed transverse momentum around the softest point of the equation of state. (c) 2000 The American Physical Society

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

2013-09-02

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

KAUST Repository

Zygalakis, K. C.

2011-01-01

In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.

An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

International Nuclear Information System (INIS)

Fujita, Y.

2001-01-01

In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

KAUST Repository

Pathmanathan, Pras

2010-06-01

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

KAUST Repository

Pathmanathan, Pras; Bernabeu, Miguel O.; Bordas, Rafel; Cooper, Jonathan; Garny, Alan; Pitt-Francis, Joe M.; Whiteley, Jonathan P.; Gavaghan, David J.

2010-01-01

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

Science.gov (United States)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Evolution of the cosmological horizons in a universe with countably infinitely many state equations

Energy Technology Data Exchange (ETDEWEB)

Margalef-Bentabol, Berta; Cepa, Jordi [Departamento de Astrofísica, Universidad de la Laguna, E-38205 La Laguna, Tenerife (Spain); Margalef-Bentabol, Juan, E-mail: bmb@cca.iac.es, E-mail: juanmargalef@estumail.ucm.es, E-mail: jcn@iac.es [Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, E-28040 Madrid (Spain)

2013-02-01

This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider a general accelerated universe with countably infinitely many constant state equations, and we obtain simple expressions in terms of their respective recession velocities that generalize the previous results for one and two state equations. We also provide a qualitative study of the values of the horizons and their velocities at the origin of the universe and at the far future, and we prove that these values only depend on one dominant state equation. Finally, we compare both horizons and determine when one is larger than the other.

Symbolic computation and solitons of the nonlinear Schroedinger equation in inhomogeneous optical fiber media

International Nuclear Information System (INIS)

Li Biao; Chen Yong

2007-01-01

In this paper, the inhomogeneous nonlinear Schroedinger equation with the loss/gain and the frequency chirping is investigated. With the help of symbolic computation, three families of exact analytical solutions are presented by employing the extended projective Riccati equation method. From our results, many previous known results of nonlinear Schroedinger equation obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Of optical and physical interests, soliton propagation and soliton interaction are discussed and simulated by computer, which include snake-soliton propagation and snake-solitons interaction, boomerang-like soliton propagation and boomerang-like solitons interaction, dispersion managed (DM) bright (dark) soliton propagation and DM solitons interaction

Covariant field equations in supergravity

Energy Technology Data Exchange (ETDEWEB)

Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

2017-12-15

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Covariant field equations in supergravity

International Nuclear Information System (INIS)

Vanhecke, Bram; Proeyen, Antoine van

2017-01-01

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Reduction of lattice equations to the Painlevé equations: PIV and PV

Science.gov (United States)

Nakazono, Nobutaka

2018-02-01

In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

Modified cable equation incorporating transverse polarization of neuronal membranes for accurate coupling of electric fields.

Science.gov (United States)

Wang, Boshuo; Aberra, Aman S; Grill, Warren M; Peterchev, Angel V

2018-04-01

We present a theory and computational methods to incorporate transverse polarization of neuronal membranes into the cable equation to account for the secondary electric field generated by the membrane in response to transverse electric fields. The effect of transverse polarization on nonlinear neuronal activation thresholds is quantified and discussed in the context of previous studies using linear membrane models. The response of neuronal membranes to applied electric fields is derived under two time scales and a unified solution of transverse polarization is given for spherical and cylindrical cell geometries. The solution is incorporated into the cable equation re-derived using an asymptotic model that separates the longitudinal and transverse dimensions. Two numerical methods are proposed to implement the modified cable equation. Several common neural stimulation scenarios are tested using two nonlinear membrane models to compare thresholds of the conventional and modified cable equations. The implementations of the modified cable equation incorporating transverse polarization are validated against previous results in the literature. The test cases show that transverse polarization has limited effect on activation thresholds. The transverse field only affects thresholds of unmyelinated axons for short pulses and in low-gradient field distributions, whereas myelinated axons are mostly unaffected. The modified cable equation captures the membrane's behavior on different time scales and models more accurately the coupling between electric fields and neurons. It addresses the limitations of the conventional cable equation and allows sound theoretical interpretations. The implementation provides simple methods that are compatible with current simulation approaches to study the effect of transverse polarization on nonlinear membranes. The minimal influence by transverse polarization on axonal activation thresholds for the nonlinear membrane models indicates that

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

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Thomas Gomez

2018-04-01

Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

Test equating methods and practices

CERN Document Server

Kolen, Michael J

1995-01-01

In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

Fronts from integrodifference equations and persistence effects on the Neolithic transition

Science.gov (United States)

Fort, Joaquim; Pérez-Losada, Joaquim; Isern, Neus

2007-09-01

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%).

Integration of Chandrasekhar's integral equation

International Nuclear Information System (INIS)

Tanaka, Tasuku

2003-01-01

We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness

Development and validation of GFR-estimating equations using diabetes, transplant and weight

DEFF Research Database (Denmark)

Stevens, L.A.; Schmid, C.H.; Zhang, Y.L.

2009-01-01

interactions. Equations were developed in a pooled database of 10 studies [2/3 (N = 5504) for development and 1/3 (N = 2750) for internal validation], and final model selection occurred in 16 additional studies [external validation (N = 3896)]. RESULTS: The mean mGFR was 68, 67 and 68 ml/min/ 1.73 m(2......BACKGROUND: We have reported a new equation (CKD-EPI equation) that reduces bias and improves accuracy for GFR estimation compared to the MDRD study equation while using the same four basic predictor variables: creatinine, age, sex and race. Here, we describe the development and validation...... of this equation as well as other equations that incorporate diabetes, transplant and weight as additional predictor variables. METHODS: Linear regression was used to relate log-measured GFR (mGFR) to sex, race, diabetes, transplant, weight, various transformations of creatinine and age with and without...

Handbook of structural equation modeling

CERN Document Server

Hoyle, Rick H

2012-01-01

The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu

The pathogenicity of genetic variants previously associated with left ventricular non-compaction

DEFF Research Database (Denmark)

Abbasi, Yeganeh; Jabbari, Javad; Jabbari, Reza

2016-01-01

BACKGROUND: Left ventricular non-compaction (LVNC) is a rare cardiomyopathy. Many genetic variants have been associated with LVNC. However, the number of the previous LVNC-associated variants that are common in the background population remains unknown. The aim of this study was to provide...... an updated list of previously reported LVNC-associated variants with biologic description and investigate the prevalence of LVNC variants in healthy general population to find false-positive LVNC-associated variants. METHODS AND RESULTS: The Human Gene Mutation Database and PubMed were systematically...... searched to identify all previously reported LVNC-associated variants. Thereafter, the Exome Sequencing Project (ESP) and the Exome Aggregation Consortium (ExAC), that both represent the background population, was searched for all variants. Four in silico prediction tools were assessed to determine...

On generalized fractional vibration equation

International Nuclear Information System (INIS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-01-01

Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

Differential equations for dummies

CERN Document Server

Holzner, Steven

2008-01-01

The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

Science.gov (United States)

Caplan-Auerbach, Jacqueline

2009-01-01

Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

A systematic iterative approach to the equations of low type

International Nuclear Information System (INIS)

Znojil, M.

1987-01-01

Nonlinear singular integral equations of the Low type appear in the description of π-N scattering amplitude at relativistic energies. The standard iteration solution differs and does not give sufficiently exact results even using the Pade approximation. A new approach is proposed. Its essence lies in a repeated formal simplification of the equation accompanied by a representation of the simplified amplitude in a generalized continued-fractional form. A simple example demonstrate that the new method improves the convergence of previous approach and essentially expands the region of its convergence. From the other side, its nonequivalence to a more complicate Newton-Kantorovich method is shown. In the future more realistic applications of the method one can expect increasing of result reliability

Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian

Directory of Open Access Journals (Sweden)

A. Zabrodin

2018-02-01

Full Text Available We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable glN Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.

Block-pulse functions approach to numerical solution of Abel’s integral equation

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Monireh Nosrati Sahlan

2015-12-01

Full Text Available This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

Science.gov (United States)

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

How do western abyssal currents cross the equator?

Science.gov (United States)

Nof, Doron; Olson, Donald B.

1993-02-01

Previous investigations of upper ocean currents on a β-plane have shown that it is quite difficult for a parcel of fluid to cross the equator in the open ocean. Boundary currents sometimes can cross the equator, but even this crossing is not easily achieved. The main barrier for equatorial crossing of inviscid western boundary currents is the presence of a front on the open ocean side ( NOF, 1990, Deep-Sea Research, 37, 853-875). One-and-a-half and 2 1/2 layer models are used to examine how this frontal blocking constraint is modified by bottom topography. Both models show that some topographic features, such as the Mid-Atlantic Ridge, may entirely relax the frontal blocking constraint. The single layer crossing is modeled in terms of a heavy double-fronted inertial current (overlaid by a stagnant infinitely deep upper layer) flowing northward in a parabolic channel. Analytic solutions show that the current's position "flips" as it crosses the equator, it is situated next to the left flank of the channel (i.e. the western boundary) in the southern hemisphere and next to the right flank (i.e. the eastern part of the channel corresponding to the western side of the the mid-ocean ridge) in the northern hemisphere. With the aid of the above model, a 2 1/2 layer model, which contains an additional intermediate current above the core, is considered. It is found that the nonfrontal southward (or northward) intermediate flow crosses the equator and remains adjacent to the western boundary. In contrast, the deep frontal flow underneath again "flips" from the left to the right boundary as it crosses the equator. Possible application of this theory to the dense Antarctic Bottom Water (AABW) and the Lower North Atlantic Deep Water (LNADW) is discussed.

Calculation of crystalline lens power in chickens with a customized version of Bennett's equation.

Science.gov (United States)

Iribarren, Rafael; Rozema, Jos J; Schaeffel, Frank; Morgan, Ian G

2014-03-01

This paper customizes Bennett's equation for calculating lens power in chicken eyes from refraction, keratometry and biometry. Previously published data on refraction, corneal power, anterior chamber depth, lens thickness, lens radii of curvature, axial length and eye power in chickens aged 10-90 days were used to estimate Gullstrand's lens power and Bennett's lens power for chicken eyes, and to calculate the lens equivalent refractive index. Bennett's A and B constants for the front and back surface powers of the lens were calculated for data measured from day 10 to 90 at 10 day intervals, and mean customized constants were calculated. The mean customized constants for Bennett's equation for chicks were A=0.574±0.023 and B=0.379±0.021. As found previously, lens power decreases with age in chicks, while corneal power decreases and axial length increases. The lens equivalent refractive index decreases with age from 10 to 90 days after hatching. Bennett's equation can be used to calculate lens power in chicken eyes for studies on animal myopia, using standard biometry. Copyright © 2014 Elsevier B.V. All rights reserved.

The sl (2 n|2 n) (1) super-Toda lattices and the heavenly equations as continuum limit

International Nuclear Information System (INIS)

Kuznetsova, Zhanna; Popowicz, Ziemowit; Toppan, Francesco.

2005-04-01

The n → ∞ continuum limit of super-Toda models associated with the affine sl (2 n|2 n) (1) (super)algebra series produces (2 + 1)-dimensional integrable equations in the S 1 versus R 2 spacetimes. The equations of motion of the (super)Toda hierarchies depend not only on the chosen (super)algebras but also on the specific presentation of their Cartan matrices. Four distinct series of integrable hierarchies in relation with symmetric-versus-antisymmetric, null-versus-non null presentations of the corresponding Cartan matrices are investigated. In the continuum limit we derive four classes of integrable equations of heavenly type, generalizing the results previously obtained in the literature. The systems are manifestly N = 1 supersymmetric and, for specific choices of the Cartan matrix preserving the complex structure, admit a hidden N = 2 supersymmetry. The coset reduction of the (super)-heavenly equation to the I versus R (2) (S 1 /Z 2 ) versus R 2 spacetime (with I a line segment) is illustrated. Finally, integrable N = 2,4 super symmetrically extended models in (1 + 1) dimensions are constructed through dimensional reduction of the previous systems. (author)

Rigid particle revisited: Extrinsic curvature yields the Dirac equation

Energy Technology Data Exchange (ETDEWEB)

Deriglazov, Alexei, E-mail: alexei.deriglazov@ufjf.edu.br [Depto. de Matemática, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation); Nersessian, Armen, E-mail: arnerses@ysu.am [Yerevan State University, 1 Alex Manoogian St., Yerevan 0025 (Armenia); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation)

2014-03-01

We reexamine the model of relativistic particle with higher-derivative linear term on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so(3.2)-algebra yields massive Dirac equation. -- Highlights: •New way of canonical quantization of relativistic rigid particle is proposed. •Quantization made in terms of so(3.2) angular momentum algebra. •Quantization yields massive Dirac equation.

Solving polynomial differential equations by transforming them to linear functional-differential equations

OpenAIRE

Nahay, John Michael

2008-01-01

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

International Nuclear Information System (INIS)

Rodriguez D, R.

2007-01-01

In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

Differential Equation over Banach Algebra

OpenAIRE

Kleyn, Aleks

2018-01-01

In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Linander, Hampus; Nilsson, Bengt E.W. [Department of Physics, Theoretical PhysicsChalmers University of Technology, S-412 96 Göteborg (Sweden)

2016-07-05

In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 “translation”, “Lorentz” and “dilatation”) properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.

Action principles for the Vlasov equation: Four old, one new

International Nuclear Information System (INIS)

Ye, Huanchun; Morrison, P.J.

1991-01-01

Action principles for the Vlasov equation are presented. Four previously known action principles, which differ by the choice of dynamical variables, are described and the interrelationship between them discussed. A new action principle called the leaf action, which manifestly preserves the Casimir invariants and possess a single function as the dynamical variable, is presented. The relationship to the noncanonical Hamiltonian formalism is also explored. 21 refs

All static spherically symmetric perfect-fluid solutions of Einstein's equations

International Nuclear Information System (INIS)

Lake, Kayll

2003-01-01

An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by nontrivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions

Quantum molecular dynamics of warm dense iron and a five-phase equation of state

Science.gov (United States)

Sjostrom, Travis; Crockett, Scott

2018-05-01

Through quantum molecular dynamics (QMD), utilizing both Kohn-Sham (orbital-based) and orbital-free density functional theory, we calculate the equation of state of warm dense iron in the density range 7 -30 g/cm 3 and temperatures from 1 to 100 eV. A critical examination of the iron pseudopotential is made, from which we find a significant improvement at high pressure to the previous QMD calculations of Wang et al. [Phys. Rev. E 89, 023101 (2014), 10.1103/PhysRevE.89.023101]. Our results also significantly extend the ranges of density and temperature that were attempted in that prior work. We calculate the shock Hugoniot and find very good agreement with experimental results to pressures over 20 TPa. These results are then incorporated with previous studies to generate a five-phase equation of state for iron.

Quantifying Ab Initio Equation of State Errors for Hydrogen-Helium Mixtures

Science.gov (United States)

Clay, Raymond; Morales, Miguel

2017-06-01

In order to produce predictive models of Jovian planets, an accurate equation of state for hydrogen-helium mixtures is needed over pressure and temperature ranges spanning multiple orders of magnitude. While extensive theoretical work has been done in this area, previous controversies regarding the equation of state of pure hydrogen have demonstrated exceptional sensitivity to approximations commonly employed in ab initio calculations. To this end, we present the results of our quantum Monte Carlo based benchmarking studies for several major classes of density functionals. Additionally, we expand upon our published results by considering the impact that ionic finite size effects and density functional errors translate to errors in the equation of state. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Elements of partial differential equations

CERN Document Server

Sneddon, Ian Naismith

1957-01-01

Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

International Nuclear Information System (INIS)

Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

2009-01-01

In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

Introduction to partial differential equations

CERN Document Server

Greenspan, Donald

2000-01-01

Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

International Nuclear Information System (INIS)

Yao Ruo-Xia; Wang Wei; Chen Ting-Hua

2014-01-01

Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)

Eternal inflation and a thermodynamic treatment of Einstein's equations

Energy Technology Data Exchange (ETDEWEB)

Ghersi, José Tomás Gálvez [Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima, Perú (Peru); Geshnizjani, Ghazal; Shandera, Sarah [Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada); Piazza, Federico, E-mail: jotogalgher@gmail.com, E-mail: ggeshnizjani@perimeterinstitute.ca, E-mail: fpiazza@apc.univ-paris7.fr, E-mail: sshandera@perimeterinstitute.ca [PCCP and APC, CNRS (UMR7164), Université Denis Diderot Paris 7, Batiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris (France)

2011-06-01

In pursuing the intriguing resemblance of the Einstein equations to thermodynamic equations, most sharply seen in systems possessing horizons, we suggest that eternal inflation of the stochastic type may be a fruitful phenomenon to explore. We develop a thermodynamic first law for quasi-de Sitter space, valid on the horizon of a single observer's Hubble patch and explore consistancy with previous proposals for horizons of various types in dynamic and static situations. We use this framework to demonstrate that for the local observer fluctuations of the type necessary for stochastic eternal inflation fall within the regime where the thermodynamic approach is believed to apply. This scenario is interesting because of suggestive parallels with black hole evaporation.

Study on the creep constitutive equation of Hastelloy X, (1)

International Nuclear Information System (INIS)

Suzuki, Kazuhiko; Mutoh, Yasushi

1983-01-01

In order to carry out the structural design of high temperature pipings, intermediate heat exchangers and isolating valves for a multipurpose high temperature gas-cooled reactor, in which coolant temperature reaches 1000 deg C, the creep characteristics of Hastelloy X used as the heat resistant material must be clarified. In addition to usual creep rupture life and the time to reach a specified creep strain, the dependence of creep strain curves on time, temperature and stress must be determined and expressed with equations. Therefore, using the creep data of Hastelloy X given in the literatures, the creep constitutive equation was made. Since the creep strain curves under the same test condition were different according to heats, the sensitivity analysis of the creep constitutive equation was performed. The form of the creep constitutive equation was determined to be Garofalo type. The result of the sensitivity analysis is reported. (Kako, I.)

Invariant quantum mechanical equations of motion

Energy Technology Data Exchange (ETDEWEB)

Wigner, E. P. [Princeton University, Princeton, NJ (United States)

1963-01-15

One of the last few years’ most important developments in theoretical physics is the recognition that it is useful to extend to complex numbers the definition domain of intrinsically real variables, such as energy or angular momentum. This leads one to review many subjects which were considered to be closed. It should not have surprised me, therefore, when Dr. Salam asked me to report, at this seminar, on equations for elementary particles which are not believed to exist in nature, such as particles with imaginary mass. Even though the equations which describe such particles will play no role in the theory as long as the variables such as energy or angular momentum have physically meaningful values, that is, as long as they are real, they may play a significant role when the definition domain of these variables is extended.

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

Solution of underdetermined systems of equations with gridded a priori constraints.

Science.gov (United States)

Stiros, Stathis C; Saltogianni, Vasso

2014-01-01

The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy. The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an R(n) grid containing an approximation of the real solution. The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the R(n) containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

Contribution to the study of the Fokker-planck equation; Contribution a l'etude de l'equation de Fokker-planck

Energy Technology Data Exchange (ETDEWEB)

Blaquiere, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1963-07-01

In the first paragraphs of this report, the Fokker-Planck equation is presented using the presentation method due to S. Chandrasekhar. Certain conventional resolution methods are given, and then a consideration of the physical interpretation of its various terms leads to a new study method based on the use of Campbell's theorems. This gives a solution to the equation in an integral form. The integral kernel of the solution is a normal centred distribution. Finally, the use of the Laplace transformation leads to a simple determination of the parameters of this integral kernel and connects the present theory to the characteristic function method used in particular in the field of nuclear reactors. The method also makes it possible to calculate the moments of the different orders of the probability distribution without the necessity of solving the Fokker-Planck equation. (author) [French] Dans les premiers paragraphes de ce rapport, l'equation de FOKKER-PLANCK est introduite en utilisant le mode d'expose de S. CHANDRASEKHAR. Puis, apres avoir rappele certaines methodes classiques de resolution, l'interpretation physique de ses differents termes nous conduit a une nouvelle methode d'etude qui repose sur l'utilisation des theoremes de CAMPBELL. On est ainsi conduit a la solution de l'equation sous forme integrale. Le noyau integral de la solution est une distribution normale centree. Enfin l'emploi de la transformation de LAPLACE conduit a une determination simple des parametres de ce noyau integral, et relie la theorie actuelle a la methode de la fonction caracteristique associee, utilisee en particulier dans le domaine des reacteurs nucleaires. Finalement cette methode permet le calcul des moments des differents ordres de la distribution de probabilites, sans passer par la resolution souvent laborieuse de l'equation de FOKKER-PLANCK. (auteur)

Limited-diffraction solutions to Maxwell and Schroedinger equations

International Nuclear Information System (INIS)

Lu, Jian-yu; Greenleaf, J.F.

1996-10-01

The authors have developed a new family of limited diffraction electromagnetic X-shaped waves based on the scalar X-shaped waves discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain their shape as they propagate to an infinite distance. The 'X waves' possess (theoretically) infinitely extended 'arms' and - at least, the ones studied in this paper - have an infinite total energy: therefore, they are not physically realizable. However, they can be truncated in both space and time and 'approximated' by means of a finite aperture radiator so to get a large enough depth of interest (depth of field). In addition to the Maxwell equations, X wave solutions to the free Schroedinger equation are also obtained. Possible applications of these new waves are discussed. Finally, the authors discuss the appearance of the X-shaped solutions from the purely geometric point of view of the special relativity theory

Integral equations with difference kernels on finite intervals

CERN Document Server

Sakhnovich, Lev A

2015-01-01

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful...

Spurious Solutions Of Nonlinear Differential Equations

Science.gov (United States)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1992-01-01

Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

Reactimeter dispersion equation

OpenAIRE

A.G. Yuferov

2016-01-01

The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

Science.gov (United States)

2018-03-14

UNIVERSITY OF TECHNOLOGY Final Report 03/14/2018 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR...optimal control problems involving fractional-order differential equations Wang, Song Curtin University of Technology Kent Street, Bentley WA6102...Article history : Received 3 October 2016 Accepted 26 March 2017 Available online 29 April 2017 Keywords: Hamilton–Jacobi–Bellman equation Financial

Equation of State of Fe3C and Implications for the Carbon Content of Earth's Core

Science.gov (United States)

Davis, A.; Brauser, N.; Thompson, E. C.; Chidester, B.; Greenberg, E.; Prakapenka, V. B.; Campbell, A.

2017-12-01

Carbon is a common component in protoplanetary cores, as represented by iron meteorites. Therefore, along with silicon, oxygen, and other light elements, it is likely to be an alloying component with iron in Earth's core. Previous studies of the densities of iron carbides have not reached the combined pressure and temperature conditions relevant to Earth's core. To better understand the geophysical implications of carbon addition to Earth's core, we report P-V-T measurements of Fe3C to pressures and temperatures exceeding 110 GPa and 2500 K, using synchrotron X-ray diffraction in a laser heated diamond anvil cell. Fitting these measurements to an equation of state and assuming 1.5% density change upon melting and a 4000 K core-mantle boundary temperature, we report a value of 6 wt% carbon necessary to match the PREM density in the outer core. This value should be considered an upper bound due to the likely presence of other light elements.

Enhancing the Equating of Item Difficulty Metrics: Estimation of Reference Distribution. Research Report. ETS RR-14-07

Science.gov (United States)

Ali, Usama S.; Walker, Michael E.

2014-01-01

Two methods are currently in use at Educational Testing Service (ETS) for equating observed item difficulty statistics. The first method involves the linear equating of item statistics in an observed sample to reference statistics on the same items. The second method, or the item response curve (IRC) method, involves the summation of conditional…

Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

CERN Document Server

Qin, Hong

2005-01-01

Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations

Energy Technology Data Exchange (ETDEWEB)

Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares

2015-07-01

This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)

Secondary recurrent miscarriage is associated with previous male birth.

LENUS (Irish Health Repository)

Ooi, Poh Veh

2012-01-31

Secondary recurrent miscarriage (RM) is defined as three or more consecutive pregnancy losses after delivery of a viable infant. Previous reports suggest that a firstborn male child is associated with less favourable subsequent reproductive potential, possibly due to maternal immunisation against male-specific minor histocompatibility antigens. In a retrospective cohort study of 85 cases of secondary RM we aimed to determine if secondary RM was associated with (i) gender of previous child, maternal age, or duration of miscarriage history, and (ii) increased risk of pregnancy complications. Fifty-three women (62.0%; 53\\/85) gave birth to a male child prior to RM compared to 32 (38.0%; 32\\/85) who gave birth to a female child (p=0.002). The majority (91.7%; 78\\/85) had uncomplicated, term deliveries and normal birth weight neonates, with one quarter of the women previously delivered by Caesarean section. All had routine RM investigations and 19.0% (16\\/85) had an abnormal result. Fifty-seven women conceived again and 33.3% (19\\/57) miscarried, but there was no significant difference in failure rates between those with a previous male or female child (13\\/32 vs. 6\\/25, p=0.2). When patients with abnormal results were excluded, or when women with only one previous child were considered, there was still no difference in these rates. A previous male birth may be associated with an increased risk of secondary RM but numbers preclude concluding whether this increases recurrence risk. The suggested association with previous male birth provides a basis for further investigations at a molecular level.

Secondary recurrent miscarriage is associated with previous male birth.

LENUS (Irish Health Repository)

Ooi, Poh Veh

2011-01-01

Secondary recurrent miscarriage (RM) is defined as three or more consecutive pregnancy losses after delivery of a viable infant. Previous reports suggest that a firstborn male child is associated with less favourable subsequent reproductive potential, possibly due to maternal immunisation against male-specific minor histocompatibility antigens. In a retrospective cohort study of 85 cases of secondary RM we aimed to determine if secondary RM was associated with (i) gender of previous child, maternal age, or duration of miscarriage history, and (ii) increased risk of pregnancy complications. Fifty-three women (62.0%; 53\\/85) gave birth to a male child prior to RM compared to 32 (38.0%; 32\\/85) who gave birth to a female child (p=0.002). The majority (91.7%; 78\\/85) had uncomplicated, term deliveries and normal birth weight neonates, with one quarter of the women previously delivered by Caesarean section. All had routine RM investigations and 19.0% (16\\/85) had an abnormal result. Fifty-seven women conceived again and 33.3% (19\\/57) miscarried, but there was no significant difference in failure rates between those with a previous male or female child (13\\/32 vs. 6\\/25, p=0.2). When patients with abnormal results were excluded, or when women with only one previous child were considered, there was still no difference in these rates. A previous male birth may be associated with an increased risk of secondary RM but numbers preclude concluding whether this increases recurrence risk. The suggested association with previous male birth provides a basis for further investigations at a molecular level.

Test equating, scaling, and linking methods and practices

CERN Document Server

Kolen, Michael J

2014-01-01

This book provides an introduction to test equating, scaling, and linking, including those concepts and practical issues that are critical for developers and all other testing professionals.  In addition to statistical procedures, successful equating, scaling, and linking involves many aspects of testing, including procedures to develop tests, to administer and score tests, and to interpret scores earned on tests. Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably.  Test scaling is the process of developing score scales that are used when scores on standardized tests are reported. In test linking, scores from two or more tests are related to one another. Linking has received much recent attention, due largely to investigations of linking similarly named tests from different test publishers or tests constructed for different purposes. In recent years, researchers from the education, psychology, and...

Ordinary Differential Equation Models for Adoptive Immunotherapy.

Science.gov (United States)

Talkington, Anne; Dantoin, Claudia; Durrett, Rick

2018-05-01

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Solving the Schroedinger equation using Smolyak interpolants

International Nuclear Information System (INIS)

Avila, Gustavo; Carrington, Tucker Jr.

2013-01-01

In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased

A generalized fractional sub-equation method for fractional differential equations with variable coefficients

International Nuclear Information System (INIS)

Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

2012-01-01

In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

True amplitude wave equation migration arising from true amplitude one-way wave equations

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Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

Science.gov (United States)

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation

International Nuclear Information System (INIS)

Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste

2005-07-01

The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)

Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

International Nuclear Information System (INIS)

Dzhamay, Anton

2009-01-01

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

Fractional neutron point kinetics equations for nuclear reactor dynamics

International Nuclear Information System (INIS)

Espinosa-Paredes, Gilberto; Polo-Labarrios, Marco-A.; Espinosa-Martinez, Erick-G.; Valle-Gallegos, Edmundo del

2011-01-01

The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.