An application of the decomposition method for the generalized KdV and RLW equations
Kaya, D
2003-01-01
We consider solitary-wave solutions of the generalized regularized long-wave (RLW) and Korteweg-de Vries (KdV) equations. We prove the convergence of Adomian decomposition method applied to the generalized RLW and KdV equations. Then we obtain the exact solitary-wave solutions and numerical solutions of the generalized RLW and KdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the generalized RLW and KdV equations.
New exact solutions for a generalized variable coefficients 2D KdV equation
Energy Technology Data Exchange (ETDEWEB)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A. E-mail: m_zahran1@mans.edu.eg; Sabry, R. E-mail: refaatsabry@mans.edu.eg
2004-03-01
Using homogeneous balance method an auto-Baecklund transformation for a generalized variable coefficients 2D KdV equation is obtained. Then new exact solutions are found which include solitary one. Also, we have found certain new analytical soliton-typed solution in terms of the variable coefficients of the studied 2D KdV equation.
New exact solutions to the generalized KdV equation with ...
Indian Academy of Sciences (India)
Keywords. Improved Fan subequation method; bifurcation method; generalized KdV equation; soliton solution; kink solution; periodic solution. ... Shengqiang Tang1 Dahe Feng1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, People's Republic of China ...
Interactions of Soliton Waves for a Generalized Discrete KdV Equation
International Nuclear Information System (INIS)
Zhou Tong; Zhu Zuo-Nong
2017-01-01
It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. (paper)
Interactions of Soliton Waves for a Generalized Discrete KdV Equation
Zhou, Tong; Zhu, Zuo-Nong
2017-07-01
It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. Supported by the National Natural Science Foundation of China under Grant Nos. 11501353, 11271254, 11428102, and 11671255, also supported by the Ministry of Economy and Competitiveness of Spain under contracts MTM2012-37070 and MTM2016-80276-P (AEI/FEDER, EU)
Indian Academy of Sciences (India)
is to study the interaction properties between the periodic waves. Here, we take the (2+1)-dimensional KdV equation .... In fact, such limit for the present family of doubly periodic waves is especially rich, since one can proceed with the long .... ematical Society, Providence, 1997). [11] K Chandrasekharan, Elliptic functions ...
An approximate solution for a generalized Hirota-Satsom coupled (Kdv equation
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H.A. Wahab
2017-03-01
Full Text Available In this paper the Homotopy Analysis Method (HAM, is applied to find the approximate solution of Hirota-Satsuma coupled (KdV equations, which don't need a small parameter for solution. The results obtained by HAM is compared with exact solution, the results divulge that the Homotopy Analysis Method are most accurate, closed and suitable to exact solution of the equation, as compare to Homotopy Perturbation Method. It is predicated that the HAM can be found usually.
Directory of Open Access Journals (Sweden)
Xiangrong Wang
2015-01-01
Full Text Available A generalized (2+1-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1-dimensional KdV equation. The N-soliton solutions of the (2+1-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method.
Energy Technology Data Exchange (ETDEWEB)
Sabry, R.; Zahran, M.A.; Fan Engui
2004-05-31
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found.
New exact solutions to the generalized KdV equation with ...
Indian Academy of Sciences (India)
Mathematically, these physical structures have been studied by using various analytical methods, such as inverse scattering method Hirota bilinear method and so on. [1–3]. Practically, there is no unified technique that can be employed to handle all types of nonlinear differential equations. Recently, Fan [4] presented a Fan ...
KdV Equation with Self-consistent Sources in Non-uniform Media
International Nuclear Information System (INIS)
Hao Honghai; Zhang Dajun; Wang Guangsheng
2009-01-01
Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources (corresponding to λ t = -2aλ) and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota's method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated. (general)
Adiabatic invariants of the extended KdV equation
Energy Technology Data Exchange (ETDEWEB)
Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)
2017-01-30
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.
The fractional coupled KdV equations: Exact solutions and white noise functional approach
International Nuclear Information System (INIS)
Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah
2013-01-01
Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)
On complexly coupled modified KdV equations
Indian Academy of Sciences (India)
Abstract. We introduced complexly coupled modified KdV (ccmKdV) equations, which could be derived from a two-layer fluid model [Yang and Mao, Chin. Phys. Lett. 25, 1527. (2008); Hu, J. Phys. A: Math. Theor. 43, 185207 (2009)], and used the Miura transforma- tion to construct expressions for their alternative Lax pair ...
New Numerical Treatment for Solving the KDV Equation
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khalid ali
2017-01-01
Full Text Available In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using collocation method with the modified exponential cubic B-spline. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.
A motion of spacelike curves in the Minkowski 3-space and the KdV equation
International Nuclear Information System (INIS)
Ding Qing; Wang Wei; Wang Youde
2010-01-01
This Letter shows that soliton solutions to KdV equation describe a motion of spacelike curves in R 2,1 with initial data being suitably restricted. This gives a different geometric interpretation of KdV from that given recently by Musso and Nicolodi, and gives a unified geometric explanation for KdV and MKdV.
A finite element method for extended KdV equations
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Karczewska Anna
2016-09-01
Full Text Available The finite element method (FEM is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
The Lax operator approach for the Virasoro and the W-constraints in the generalized KdV hierarchy
International Nuclear Information System (INIS)
Panda, S.; Roy, S.
1992-08-01
We show directly in the Lax operator approach how the Virasoro and W-constraints on the τ-function arise in the p-reduced KP hierarchy or Generalized KdV hierarchy. In particular, we consider the KdV and the Boussinesq hierarchy to show that the Virasoro and the W-constraints follow from the string equation by expanding the ''additional symmetry'' operator in terms of the Lax operator. We also mention how this method could be generalized for higher KdV hierarchies. (author). 34 refs
Painleve Property and Complexiton Solutions of a Special Coupled KdV Equation
International Nuclear Information System (INIS)
Yang Jianrong; Mao Jiejian
2008-01-01
A special coupled KdV equation is proved to be the Painleve property by the Kruskal's simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota's bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical complexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically
International Nuclear Information System (INIS)
Yang Zonghang
2007-01-01
We find new exact travelling wave solutions for two potential KdV equations which are presented by Foursov [Foursov MV. J Math Phys 2000;41:6173-85]. Compared with the extended tanh-function method, the algorithm used in our paper can obtain some new kinds of exact travelling wave solutions. With the aid of symbolic computation, some novel exact travelling wave solutions of the potential KdV equations are constructed
International Nuclear Information System (INIS)
Khater, H.; Sayed, S. M.; Callebaut, D. K.
2005-01-01
The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to Burgers' type, two-dimensional sine-Gordon, generalized Korteweg-de Vries-type, (2+1)- and the original (3+1)- dimensional Liouville equations are considered. On the one hand, the Backlund transformations are implemented to obtain several classes of exact solutions for the reduced Burgers-type and two-dimensional sine-Gordon equations. On the other hand, other methods and transformations are developed to obtain exact for the original two-dimensional generalized Korteweg-de Vries-type, (2+1)- and the original (3+1)-dimensional Liouville equations. The corresponding gauge potential A, and the gauge strenghts F μν are also obtained
Revisitation of the localized excitations of the (2+1)-dimensional KdV equation
Lou, Sen-yue; Ruan, H.-y.
2001-01-01
In a previous paper (Lou S-y 1995 J. Phys. A: Math. Gen. 28 7227), a generalized dromion structure was revealed for the (2+1)-dimensional KdV equation, which was first derived by Boiti et al (Boiti M, Leon J J P, Manna M and Pempinelli F 1986 Inverse Problems 2 271) using the idea of the weak Lax pair. In this paper, using a Bäcklund transformation and the variable separation approach, we find there exist much more abundant localized structures for the (2+1)-dimensional KdV equation. The abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution. Some special types of dromion solution, lumps, breathers, instantons and the ring type of soliton, are discussed by selecting the arbitrary functions appropriately. The dromion solutions can be driven by sets of straight-line and curved-line ghost solitons. The dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves. The breathers may breathe both in amplitude and in shape.
Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations
Directory of Open Access Journals (Sweden)
S.A. El-Wakil
2016-02-01
Full Text Available A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics.
Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method
International Nuclear Information System (INIS)
Saddique, I.; Nazar, K.
2009-01-01
In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)
An extended K-dV equation for nonlinear magnetosonic wave in a multi-ion plasma
Energy Technology Data Exchange (ETDEWEB)
Ida, A. [Nagoya Univ. (Japan). School of Engineering; Sanuki, H.; Todoroki, J.
1995-06-01
Nonlinear magnetosonic waves propagating perpendicularly to a magnetic field are studied in two-ion plasma. It is shown that high frequency magnetosonic wave under the influence of finite cut-off frequency is described by an extended K-dV equation, rather than conventional K-dV equation. Modulational stability of this mode is strongly affected by the finite cut-off frequency in two-ion plasma. (author).
Perturbative expansion and the initial value problem of the K.d.V. equations
International Nuclear Information System (INIS)
Turchetti, G.
1980-01-01
For the potential K.d.V. equation is considered a perturbation expansion in which the initial condition is imposed on the zeroth order term. The N soliton solutions turn out to be rational functions in the expansion parameter so that the perturbation series can be exactly summed by the [N-1/N] Pade approximants; moreover the [n-1/n] and [n/n] Pade approximants for n [pt
Exact periodic and solitary waves and their interactions for the (2+1)-dimensional KdV equation
International Nuclear Information System (INIS)
Peng Yanze
2006-01-01
A general solution involving three arbitrary functions is first obtained for a (2+1)-dimensional KdV equation by means of WTC truncation method. Then exact periodic wave solutions are expressed in terms of rational functions of the Jacobi elliptic functions. Limit cases are studied and some interesting, new solitary structures are revealed. The interaction properties between Jacobi elliptic waves (various limit cases) are investigated numerically. The fusion and fission of y-periodic solitary waves is for the first time reported
Modulating functions method for parameters estimation in the fifth order KdV equation
Asiri, Sharefa M.
2017-07-25
In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a system of linear algebraic equations of the unknowns. The statistical properties of the modulating functions solution are described in this paper. In addition, guidelines for choosing the number of modulating functions, which is an important design parameter, are provided. The effectiveness and robustness of the proposed method are shown through numerical simulations in both noise-free and noisy cases.
New binary travelling-wave periodic solutions for the modified KdV equation
International Nuclear Information System (INIS)
Yan Zhenya
2008-01-01
In this Letter, the modified Korteweg-de Vries (mKdV) equations with the focusing (+) and defocusing (-) branches are investigated, respectively. Many new types of binary travelling-wave periodic solutions are obtained for the mKdV equation in terms of Jacobi elliptic functions such as sn(ξ,m)cn(ξ,m)dn(ξ,m) and their extensions. Moreover, we analyze asymptotic properties of some solutions. In addition, with the aid of the Miura transformation, we also give the corresponding binary travelling-wave periodic solutions of KdV equation
Saha Ray, S.
2013-12-01
In this paper, the modified fractional reduced differential transform method (MFRDTM) has been proposed and it is implemented for solving fractional KdV (Korteweg-de Vries) equations. The fractional derivatives are described in the Caputo sense. In this paper, the reduced differential transform method is modified to be easily employed to solve wide kinds of nonlinear fractional differential equations. In this new approach, the nonlinear term is replaced by its Adomian polynomials. Thus the nonlinear initial-value problem can be easily solved with less computational effort. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of the solutions, several fractional KdV equations with different types of nonlinearities are considered. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional KdV equations.
An outline of cellular automaton universe via cosmological KdV equation
Christianto, V.; Smarandache, F.; Umniyati, Y.
2018-03-01
It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kuruczs hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion [4][5]. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.
Kersten, P.H.M.
1988-01-01
By the introduction of nonlocal basonic and fermionic variables we construct a recursion symmetry of the super KdV equation, leading to a hierarchy of bosonic symmetries and one of fermionic symmetries. The hierarchies of bosonic and fermionic conservation laws arise in a natural way in the
Lou, Sen-yue; Tang, Xiao-yan; Lin, Ji
2000-12-01
To get the similarity solutions of a nonlinear physical equation, one may use the classical Lie group approach, nonclassical Lie group approach and the Clarkson and Kruskal (CK) direct method. In this paper the direct method is modified to get the similarity and conditional similarity reductions of a (2+1) dimensional KdV-type equation. Ten types of usual similarity reductions [including the (1+1)-dimensional shallow water wave equation and the variable KdV equation] and six types of conditional similarity reductions of the (2+1)-dimensional KdV equation are obtained. Some special solutions of the conditional similarity reduction equations are found to show the nontriviality of the conditional similarity reduction approach. The conditional similarity solutions cannot be obtained by using the nonclassical Lie group approach in its present form. How to modify the nonclassical Lie group approach to obtain the conditional similarity solutions is still open.
symmetric generalized Korteweg–de Vries equations
Indian Academy of Sciences (India)
and Hyman [3]. This Lagrangian gives rise to a general class of KdV equations ut + ul−2ux + α[2upuxxx + 4pup−1uxuxx + p(p − 1)up−2(ux)3]=0, (2) where u(x, t) = ϕx(x, t). For 0 2 the derivatives of the solution ...
Ali, Rustam; Saha, Asit; Chatterjee, Prasanta
2017-12-01
Analytical electron acoustic solitary wave (EASW) solution is investigated in the presence of periodic force for an unmagnetized plasma consisting of cold electron fluid, superthermal hot electrons, and stationary ions. Employing the reductive perturbation technique, the forced Korteg-de Vries (KdV) equation is derived for electron acoustic waves. For the first time, an analytical solution for EASWs is derived in the presence of periodic force. The effects of the ratio between hot electron and cold electron number densities at equilibrium (α), spectral index (κ), speed of the traveling wave (M), strength (f0), and frequency (ω) of the periodic force are studied on the analytical solution of EASWs. It is observed that the parameters α, κ, M, f0, and ω affect significantly the structures of the electron acoustic solitary waves. The results may have relevance in laboratory plasmas as well as in space plasma environments.
Infinitely many conservation laws for the discrete KdV equation
International Nuclear Information System (INIS)
Rasin, Alexander G; Schiff, Jeremy
2009-01-01
Rasin and Hydon (2007 J. Phys. A: Math. Theor. 40 12763-73) suggested a way to construct an infinite number of conservation laws for the discrete KdV equation (dKdV), by repeated application of a certain symmetry to a known conservation law. It was not decided, however, whether the resulting conservation laws were distinct and nontrivial. In this paper we obtain the following results: (1) we give an alternative method to construct an infinite number of conservation laws using a discrete version of the Gardner transformation. (2) We give a direct proof that the conservation laws obtained by the method of Rasin and Hydon are indeed distinct and nontrivial. (3) We consider a continuum limit in which the dKdV equation becomes a first-order eikonal equation. In this limit the two sets of conservation laws become the same, and are evidently distinct and nontrivial. This proves the nontriviality of the conservation laws constructed by the Gardner method, and gives an alternative proof of the nontriviality of the conservation laws constructed by the method of Rasin and Hydon
Mohammed, K. Elboree
2015-10-01
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.
Generalized Miura transformations, two-bosons KP hierarchies and their reduction to KdV hierarchies
International Nuclear Information System (INIS)
Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Medeiros, R.T.; Zimerman, A.H.
1993-02-01
Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies. (author). 16 refs
Tang, Xiao-yan; Qian, Xian-min; Lin, Ji; Lou, S. Y.
2004-06-01
The classical and nonclassical Lie group approaches are extended and applied to construct new conditional similarity reductions for nonlinear systems. The application of the method to a simple (2+1)-dimensional KdV equation results in not only the known conditional similarity reductions obtained by the modified Clarkson and Kruskal’s direct method but also a great diversity of classical and nonclassical conditional similarity reductions.
Numerical simulation of a solitonic gas in KdV and KdV–BBM equations
Energy Technology Data Exchange (ETDEWEB)
Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex (France); Pelinovsky, Efim, E-mail: pelinovsky@hydro.appl.sci-nnov.ru [Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod (Russian Federation); Department of Applied Mathematics, Nizhny Novgorod State Technical University (Russian Federation); National Research University – Higher School of Economics (Russian Federation)
2014-08-28
The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes–Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term. - Highlights: • High-resolution simulations of a solitonic gas are presented. • Integrable and non-integrable cases are considered. • The effect of integrability was shown to be negligible. • Dependence of the statistical characteristics on the model parameters was studied.
Well-posedness and ill-posedness of the fifth-order modified KdV equation
Directory of Open Access Journals (Sweden)
Soonsik Kwon
2008-01-01
Full Text Available We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. $$displaylines{ partial_t u - partial_x^5u + c_1partial_x^3(u^3 + c_2upartial_x upartial_x^2 u + c_3uupartial_x^3 u =0cr u(x,0= u_0(x }$$ where $u:mathbb{R}imesmathbb{R} o mathbb{R} $ and $c_j$'s are real. We show the local well-posedness in $H^s(mathbb{R}$ for $sgeq 3/4$ via the contraction principle on $X^{s,b}$ space. Also, we show that the solution map from data to the solutions fails to be uniformly continuous below $H^{3/4}(mathbb{R}$. The counter example is obtained by approximating the fifth order mKdV equation by the cubic NLS equation.
Compactons in PT-symmetric generalized Korteweg-de Vries equations
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Mihaila, Bogdan [Los Alamos National Laboratory; Bender, Carl M [WASHINGTON UNIV; Cooper, Fred [SANTA FE INSTITUTE; Khare, Avinash [INSTITUTE OF PHYSICS
2008-01-01
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.
Yan ze, PENG; Department of Mathematics, Huazhong University of Science and Technology
2005-01-01
An exact periodic wave solution, which represents the interaction between the waves with different speeds, is first given by the rational function of the Jacobi elliptic functions with different moduli for a (2+1)-dimensional KdV equation. Under different limit conditions, some new types of solitary structures called periodic solitons are then revealed. The interaction properties between periodic waves and between periodic solitons are studied numerically and found to be nonelastic. But a lon...
A nonstandard numerical method for the modified KdV equation
Indian Academy of Sciences (India)
Ayhan Aydin
2017-10-25
Oct 25, 2017 ... where r and q are real parameters. Here u = u(x,t) is a function of the space variable x and time variable t. In most applications, u(x,t) represents the amplitude of the relevant wave mode (e.g., u may represent the vertical displacement of the pycnocline). Equation (1) is a nonlinear partial differential equation ...
The integrability of an extended fifth-order KdV equation with Riccati ...
Indian Academy of Sciences (India)
Furthermore, the infinitely many conservation laws of the extended Lax equation are found using its Lax pair. ... Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, People's Republic of China; College of Art and Sciences, Shanghai Maritime University, Shanghai 201306, ...
The integrability of an extended fifth-order KdV equation with Riccati ...
Indian Academy of Sciences (India)
2College of Art and Sciences, Shanghai Maritime University, Shanghai 201306,. People's Republic of China. ∗ ... Lax pair, infinitely many conservation laws, Hamiltonian structure and Painlevé test that can characterize the ... the infinitely many conservation laws of the extended Lax equation are found by using its. Lax pair.
A Numerical Solution for Hirota-Satsuma Coupled KdV Equation
Directory of Open Access Journals (Sweden)
M. S. Ismail
2014-01-01
Full Text Available A Petrov-Galerkin method and product approximation technique are used to solve numerically the Hirota-Satsuma coupled Korteweg-de Vries equation, using cubic B-splines as test functions and a linear B-spline as trial functions. The implicit midpoint rule is used to advance the solution in time. Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. The von Neumann stability analysis of the schemes shows that the two schemes are unconditionally stable. The single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitons, three solitons, and birth of solitons is also discussed.
A nonstandard numerical method for the modified KdV equation
Indian Academy of Sciences (India)
Ayhan Aydin
2017-10-25
Oct 25, 2017 ... AYHAN AYDIN1,∗ and CANAN KOROGLU2. 1Department of Mathematics, Atilim University, Ankara 06836, Turkey. 2Department of Mathematics, Hacettepe University, Beytepe, Ankara 06800, Turkey. ∗ .... Denominator functions for the discrete derivatives must, in general, be expressed in terms of more.
DEFF Research Database (Denmark)
Miansari, Mo; Miansari, Me; Barari, Amin
2009-01-01
In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely...
Saberi, Elaheh; Reza Hejazi, S.
2018-02-01
In the present paper, Lie point symmetries of the time-fractional generalized Hirota-Satsuma coupled KdV (HS-cKdV) system based on the Riemann-Liouville derivative are obtained. Using the derived Lie point symmetries, we obtain similarity reductions and conservation laws of the considered system. Finally, some analytic solutions are furnished by means of the invariant subspace method in the Caputo sense.
KdV and kink antikink solitons in car-following models
Ge, H. X.; Cheng, R. J.; Dai, S. Q.
2005-11-01
The jams in the congested traffic are related with various density waves, which might be governed by the nonlinear wave equations, such as the Korteweg-de-Vries (KdV) equation, the Burgers equation and the modified Korteweg-de-Vries (mKdV) equation. Three different versions of optimal velocity models are examined. The stability conditions of the models are obtained by using the linear stability theory. The KdV equation near the neutral stability line and the mKdV equation around the critical point are derived by applying the reductive perturbation method, respectively. The traffic jams could be thus described by the KdV and kink-antikink soliton solutions for the two kinds of equations. The general solutions are given for, which can lead to specific solutions in previous work. Moreover, they are applied to solve a new model-the full velocity difference model and the corresponding KdV and kink-antikink soliton solutions could be quickly obtained, which demonstrates the general solutions presented herein are useful.
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
International Nuclear Information System (INIS)
Horii, Zene
2002-01-01
By generalization of the Kawasaki-Ohta equation representing the interface dynamics, we report formulation of equations, which express mass transports, deterministic and stochastic, for nonlinear lattices. The equations are written characteristically by flow variable representations defined in the Letter. We found that the KdV equation and the Burgers equation, formulated by the flow variables, express mass transports in hydrodynamics and in stochastic processes, respectively. The representations lead to the conclusion that in nonequilibria we should observe a change not in a concentration but in concentration flows
Lagrangian Approach to Dispersionless KdV Hierarchy
Directory of Open Access Journals (Sweden)
Amitava Choudhuri
2007-09-01
Full Text Available We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether's theorem, provides a method to make the relation between symmetries and conserved quantities more precise. We have exploited this fact to study the variational symmetries of the dispersionless KdV equation.
Energy Technology Data Exchange (ETDEWEB)
Trogdon, Thomas, E-mail: trogdon@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Deconinck, Bernard [Department of Applied Mathematics, University of Washington, Campus Box 352420, Seattle, WA 98195 (United States)
2014-01-31
All solutions of the Korteweg–de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi-)periodic. In this paper, we discuss a class of solutions that is a nonlinear superposition of these two cases: their asymptotic state for large |x| is (quasi-)periodic, but they may contain solitons, with or without dispersive tails. Such scenarios might occur in the case of localized perturbations of previously present sea swell, for instance. Such solutions have been discussed from an analytical point of view only recently. We numerically demonstrate different features of these solutions.
Computing generalized Langevin equations and generalized Fokker-Planck equations.
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.
The generalized Airy diffusion equation
Directory of Open Access Journals (Sweden)
Frank M. Cholewinski
2003-08-01
Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.
New exact solutions to the generalized KdV equation with ...
Indian Academy of Sciences (India)
4c4 , 0). Notice that we need only consider the case c3 ≥ 0 because of the invariance of eq. (3.8) under the transformation φ → −φ, y → −y, c3 → −c3. Using the bifurcation theory of dynamical systems [9–11], we can obtain the bifurca- tion curves and phase portraits under various parameter conditions shown as follows.
Generalized quantal equation of motion
International Nuclear Information System (INIS)
Morsy, M.W.; Embaby, M.
1986-07-01
In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)
Completely integrable operator evolutionary equations
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)
Travelling wave solutions in a class of generalized Korteweg-de Vries equation
International Nuclear Information System (INIS)
Shen Jianwei; Xu Wei
2007-01-01
In this paper, we consider a new generalization of KdV equation u t = u x u l-2 + α[2u xxx u p + 4pu p-1 u x u xx + p(p - 1)u p-2 (u x ) 3 ] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory
Application of the trial equation method for solving some nonlinear ...
Indian Academy of Sciences (India)
the trial equation method. Also a more general trial equation method is proposed. Keywords. Trial equation method; KdV equation; K(m, n) equation; dual-power law; soliton solution. PACS Nos 02.30.Jr; 02.70.Wz; 04.20.Jb. 1. Introduction. Nonlinear phenomena exist in all the fields such as fluid mechanics, plasma physics, ...
Application of the trial equation method for solving some nonlinear ...
Indian Academy of Sciences (India)
In this paper some exact solutions including soliton solutions for the KdV equation with dual power law nonlinearity and the (, ) equation with generalized evolution are obtained using the trial equation method. Also a more general trial equation method is proposed.
The auxiliary elliptic-like equation and the exp-function method
Indian Academy of Sciences (India)
exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. As examples, the RKL models, the high-order nonlinear Schrödinger equation, the Hamilton amplitude equation, the generalized Hirota–Satsuma coupled KdV system and the generalized ZK–BBM equation are ...
Soliton solutions for some x-dependent nonlinear evolution equations
International Nuclear Information System (INIS)
Wang, Pan
2014-01-01
Under investigation in this paper are two x-dependent nonlinear evolution equations: the generalized x-dependent nonlinear Schrödinger (NLS) equation and the modified Korteweg–de Vries (KdV) equation. With the help of Hirota method and symbolic computation, the one- and two-soliton solutions have been obtained for the generalized x-dependent NLS and KdV equations. Propagation and evolution of one soliton have been investigated through the physical quantities of amplitude, width and velocity. The effects of the parameters in the equations on the interaction of two solitons have been studied analytically and graphically. (paper)
On linear equations with general polynomial solutions
Laradji, A.
2018-04-01
We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation.
Generalization of Einstein's gravitational field equations
Moulin, Frédéric
2017-12-01
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.
A generalized advection dispersion equation
Indian Academy of Sciences (India)
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
General and exact pressure evolution equation
Toutant, Adrien
2017-11-01
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. This new pressure equation is valid for all real dense fluids for which the pressure tensor is isotropic. It is argued that this new pressure equation allows unifying compressible, low-Mach and incompressible approaches. Moreover, this equation should be able to replace the Poisson equation in isothermal incompressible fluids. For computational fluid dynamics, it can be seen as an alternative to Lattice Boltzmann methods and as the physical justification of artificial compressibility.
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Multiplication. If ux, f (x) and g(x) are differentiable in the opened interval D, then: D ux [f(x) · g(x)]=g(x)f (x) + f(x)g (x). + (gf + fg )(x)ux + u x. (f(x)g(x)). (2.5) ..... for solution of various nonlinear problems without usual restrictive assumptions. To solve equation. (4.2) by means of variational iteration method, we put (4.2) as ...
Energy Technology Data Exchange (ETDEWEB)
Ganguly, A., E-mail: gangulyasish@rediffmail.com, E-mail: aganguly@maths.iitkgp.ernet.in; Das, A., E-mail: amiya620@gmail.com [Department of Mathematics, IIT Kharagpur, Kharagpur, 721302 West Bengal (India)
2014-11-15
We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Generalized Harnack Inequality for Nonhomogeneous Elliptic Equations
Julin, Vesa
2015-05-01
This paper is concerned with nonlinear elliptic equations in nondivergence form where F has a drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative solutions do not satisfy the classical Harnack inequality. This paper presents a new generalization of the Harnack inequality for such equations. As a corollary we obtain the optimal Harnack type of inequality for p( x)-harmonic functions which quantifies the strong minimum principle.
Compacton-like solutions for modified KdV and nonlinear ...
Indian Academy of Sciences (India)
through asymmetric twin-core fibres, we hope that the newly found compacton may be launched in a long-haul telecommunication network utilizing asymmetric twin-core fibres. Keywords. Compacton-like solutions; modified KdV equation; nonlinear Schrödinger equation; fractional transform. PACS Nos 42.81.Dp; 42.65.
Compacton-like solutions for modified KdV and nonlinear ...
Indian Academy of Sciences (India)
2014-07-18
Jul 18, 2014 ... ... case of modified KdV equation. Keeping in mind the significance of nonlinear Schrödinger equation with external source, for pulse propagation through asymmetric twin-core fibres, we hope that the newly found compacton may be launched in a long-haul telecommunication network utilizing asymmetric ...
Generalization of the Knizhnik-Zamolodchikov-equations
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Recknagel, A.; Schomerus, V.
1996-09-01
In this letter we introduce a generalization of the Knizhnik-Zamolodchikov equations from affine Lie algebras to a wide class of conformal field theories (not necessarily rational). The new equations describe correlation functions of primary fields and of a finite number of their descendents. Our proposal is based on Nahm's concept of small spaces which provide adequate substitutes for the lowest energy subspaces in modules of affine Lie algebras. We explain how to construct the first order differential equations and investigate properties of the associated connections, thereby preparing the grounds for an analysis of quantum symmetries. The general considerations are illustrated in examples of Virasoro minimal models. (orig.)
N = 4 super KdV hierarchy in N = 4 and N = 2 superspaces
International Nuclear Information System (INIS)
Delduc, F.
1995-10-01
The results of further analysis of the integrability properties of the N = 4 supersymmetric KdV equation deduced earlier as a Hamiltonian flow on N 4 SU(2) superconformal algebra in the harmonic N = 4 superspace are presented. To make this equation and the relevant Hamiltonian structures more tractable, it is reformulated in the ordinary N = 4 and further in N = 2 superspaces. These results provide a strong evidence that the unique N = 4 SU(2) super KdV hierarchy exists. (author)
General particle transport equation. Final report
International Nuclear Information System (INIS)
Lafi, A.Y.; Reyes, J.N. Jr.
1994-12-01
The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence
Bihamiltonian Cohomology of KdV Brackets
Carlet, G.; Posthuma, H.; Shadrin, S.
2016-01-01
Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular, this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups.
The solution of the generalized Kepler's equation
López, Rosario; Hautesserres, Denis; San-Juan, Juan Félix
2018-01-01
In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in closed form of the eccentricity is produced. During the evaluation of the theory, it is necessary to solve a generalization of the classical Kepler's equation. In this work, the application of a numerical technique and three initial guesses to the generalized Kepler's equation are discussed.
Some Remarks on Stability of Generalized Equations
Czech Academy of Sciences Publication Activity Database
Outrata, Jiří; Henrion, R.; Kruger, A.Y.
2013-01-01
Roč. 159, č. 3 (2013), s. 681-697 ISSN 0022-3239 R&D Projects: GA AV ČR IAA100750802; GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : Parameterized generalized equation * Regular and limiting coderivative * Constant rank CQ * Mathematical program with equilibrium constraints Subject RIV: BA - General Mathematics Impact factor: 1.406, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-some remarks on stability of generalized equations.pdf
Generalized Langevin Equation Description of Stochastic ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Astrophysics and Astronomy; Volume 35; Issue 3. Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks. Chun Sing Leung Gabriela Mocanu Tiberiu Harko. Part VI: Combined Multi-Waveband Observations Volume 35 Issue 3 September 2014 pp 449- ...
General Reducibility and Solvability of Polynomial Equations ...
African Journals Online (AJOL)
General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...
Two dimensional generalizations of the Newcomb equation
International Nuclear Information System (INIS)
Dewar, R.L.; Pletzer, A.
1989-11-01
The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs
Unsteady Stokes equations: Some complete general solutions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
making use of eq. (2), it is easy to see that the pressure is harmonic. Hence, on operating the Laplace operator on eq. (3), we find that the velocity vector satisfies the equation. ∇2. (. ∇2 −. 1 ν. ∂. ∂t. ) V = 0. (4). 1.1 A complete general solution of unsteady Stokes equations. Let (V, p) be any solution of (2) and (3). We define.
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
Generalized Langevin Equation Description of Stochastic ...
Indian Academy of Sciences (India)
Generalized Langevin equation for stochastic oscillations of accretion disks. We consider that the particles in the disk are in contact with an isotropic and homoge- neous external medium. The interaction of the particles with the cosmic environment is described by a friction force and a random force. The vertical oscillations ...
Soliton multidimensional equations and integrable evolutions preserving Laplace's equation
International Nuclear Information System (INIS)
Fokas, A.S.
2008-01-01
The KP equation, which is an integrable nonlinear evolution equation in 2+1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the KP equation, I obtain an integrable nonlinear evolution equation in 4+2. The requirement that real initial conditions remain real under this evolution, implies that the dependent variable satisfies a nonlinear evolution equation in 3+1 coupled with Laplace's equation. A reduction of this system of equations to a single equation in 2+1 contains as particular cases certain singular integro-differential equations which appear in the theory of water waves
Yan, Zhen-Ya
2001-11-01
In this paper,eight types of (1+1)-dimensional similarity reductions which contain variable coefficient equation,are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensional isospectral flows associated with the second-order scalar operators by using the direct method.In addition,the cnoidal wave solution and dromion-like solution are also derived by using the reduced nonlinear ordinary differential equations.The (1+1) dromion obtained by Lou [J.Phys.A28 (1995) 7227] and Zhang [Chin.Phys.9 (2000) 1] is only a special case of our results.Moreover,some properties of the dromion-like solutions are analyzed. The project supported by National Natural Science Foundation of China under Grant No. 10072013, the National Key Basic Research Development Project Program of China under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119
The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2018-02-01
Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.
International Nuclear Information System (INIS)
Montano, D.; Rivlis, G.
1991-01-01
In this paper we explicitly compute the correlation functions of the (1, q) series of the KdV hierarchy, i.e. models with q-1 primary fields. We also find from algebraic considerations a ghost number conservation law for the (1, q) models. All the results in this paper follow from the algebraic properties of the KdV hierarchy without using any extraneous information from a field theory interpretation. We find the interesting result that some correlation functions vanish even when they conserve ghost number. This is an indication for further selection rules. (orig.)
Partial Differential Equations in General Relativity
International Nuclear Information System (INIS)
Choquet-Bruhat, Yvonne
2008-01-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Partial Differential Equations in General Relativity
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne
2008-09-07
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Exact solutions to the generalized Lienard equation and its ...
Indian Academy of Sciences (India)
and the solutions of the equation are applied to solve nonlinear wave equations with nonlin- ... Lienard equation (1) corresponds to the p = 2 case of the generalized Lienard equation. Some exact solutions of the generalized Lienard equation (2) and their applications have been ...... In order to make the left-hand side of eq.
Generalized Ideal Gas Equations for Structureful Universe
Directory of Open Access Journals (Sweden)
Khalid Khan
2006-09-01
Full Text Available We have derived generalized ideal gas equations for a structureful universe consistingof all forms of matters. We have assumed a universe that contains superclusters. Superclusters arethen made of clusters. Each cluster can be further divided into smaller ones and so on. We havederived an expression for the entropy of such a universe. Our model is rather independent of thegeometry of the intermediate clusters. Our calculations are valid for a non-interacting universewithin non-relativistic limits. We suggest that structure formation can reduce the expansion rateof the universe.
Generalized Maxwell equations and charge conservation censorship
Modanese, G.
2017-02-01
The Aharonov-Bohm electrodynamics is a generalization of Maxwell theory with reduced gauge invariance. It allows to couple the electromagnetic field to a charge which is not locally conserved, and has an additional degree of freedom, the scalar field S = ∂αAα, usually interpreted as a longitudinal wave component. By reformulating the theory in a compact Lagrangian formalism, we are able to eliminate S explicitly from the dynamics and we obtain generalized Maxwell equation with interesting properties: they give ∂μFμν as the (conserved) sum of the (possibly non-conserved) physical current density jν, and a “secondary” current density iν which is a nonlocal function of jν. This implies that any non-conservation of jν is effectively “censored” by the observable field Fμν, and yet it may have real physical consequences. We give examples of stationary solutions which display these properties. Possible applications are to systems where local charge conservation is violated due to anomalies of the Adler-Bell-Jackiw (ABJ) kind or to macroscopic quantum tunnelling with currents which do not satisfy a local continuity 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
Dichotomies for generalized ordinary differential equations and applications
Bonotto, E. M.; Federson, M.; Santos, F. L.
2018-03-01
In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.
Exact solution for the generalized Telegraph Fisher's equation
International Nuclear Information System (INIS)
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
KdV cnoidal waves in a traffic flow model with periodic boundaries
Hattam, L.
2017-06-01
An optimal-velocity (OV) model describes car motion on a single lane road. In particular, near to the boundary signifying the onset of traffic jams, this model reduces to a perturbed Korteweg-de Vries (KdV) equation using asymptotic analysis. Previously, the KdV soliton solution has then been found and compared to numerical results (see Muramatsu and Nagatani [1]). Here, we instead apply modulation theory to this perturbed KdV equation to obtain at leading order, the modulated cnoidal wave solution. At the next order, the Whitham equations are derived, which have been modified due to the equation perturbation terms. Next, from this modulation system, a family of spatially periodic cnoidal waves are identified that characterise vehicle headway distance. Then, for this set of solutions, we establish the relationship between the wave speed, the modulation term and the driver sensitivity. This analysis is confirmed with comparisons to numerical solutions of the OV model. As well, the long-time behaviour of these solutions is investigated.
An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy
Matsushima, Masatomo; Ohmiya, Mayumi
2009-09-01
The stationary KdV hierarchy is constructed using a kind of recursion operator called Λ-operator. The notion of the maximal solution of the n-th stationary KdV equation is introduced. Using this maximal solution, a specific differential polynomial with the auxiliary spectral parameter called the spectral M-function is constructed as the quadratic form of the fundamental system of the eigenvalue problem for the 2-nd order linear ordinary differential equation which is related to the linearizing operator of the hierarchy. By calculating a perfect square condition of the quadratic form by an elementary algebraic method, the complete set of first integrals of this hierarchy is constructed.
General Equations for the Bubble Point Formation Volume Factor of ...
African Journals Online (AJOL)
General equations for calculating the bubble point formation volume factor of all types of crude oil have been developed. Unlike present equation used in the oil industry, these new equations do not require the gas gravity of gas that is associated with the crude oil. The new equations are intended to complement the recent ...
General solution of the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Dolan, Louise [Department of Physics, University of North Carolina,Chapel Hill, NC 27599 (United States); Goddard, Peter [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)
2016-10-26
The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension, have been reformulated in polynomial form. The scattering equations for N particles are equivalent to N−3 polynomial equations h{sub m}=0, 1≤m≤N−3, in N−3 variables, where h{sub m} has degree m and is linear in the individual variables. Facilitated by this linearity, elimination theory is used to construct a single variable polynomial equation, Δ{sub N}=0, of degree (N−3)! determining the solutions. Δ{sub N} is the sparse resultant of the system of polynomial scattering equations and it can be identified as the hyperdeterminant of a multidimensional matrix of border format within the terminology of Gel’fand, Kapranov and Zelevinsky. Macaulay’s Unmixedness Theorem is used to show that the polynomials of the scattering equations constitute a regular sequence, enabling the Hilbert series of the variety determined by the scattering equations to be calculated, independently showing that they have (N−3)! solutions.
A general polynomial solution to convection–dispersion equation ...
Indian Academy of Sciences (India)
Jiao Wang
s12040-017-0820-4. A general polynomial solution to convection–dispersion equation using ... water pollution of groundwater, numerical models are increasingly used in .... to convective transport by water flow is negligi- ble. Equation (4) is ...
Generalized Callan-Symanzik equations and the Renormalization Group
International Nuclear Information System (INIS)
MacDowell, S.W.
1975-01-01
A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg
Unsteady Stokes equations: Some complete general solutions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes flow in the absence of body forces is derived. Keywords. Complete ...
Generalization of Einstein's gravitational field equations
International Nuclear Information System (INIS)
Moulin, Frederic
2017-01-01
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)
Generalization of Einstein's gravitational field equations
Energy Technology Data Exchange (ETDEWEB)
Moulin, Frederic [Ecole Normale Superieure Paris-Saclay, Departement de Physique, Cachan (France)
2017-12-15
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)
The transport equation in general geometry
International Nuclear Information System (INIS)
Pomraning, G.C.
1990-01-01
As stated in the introduction to the paper, the motivation for this work was to obtain an explicit form for the streaming operator in the transport equation, which could be used to compute curvature effects in an asymptotic analysis leading to diffusion theory. This sign error was discovered while performing this analysis
Generalized Fokker-Planck equation: Derivation and exact solutions
Denisov, S. I.; Horsthemke, W.; Hänggi, P.
2009-04-01
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.
Trial equation method for solving the generalized Fisher equation with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Triki, Houria [Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba (Algeria); Wazwaz, Abdul-Majid, E-mail: wazwaz@sxu.edu [Department of Mathematics, Saint Xavier University, Chicago, IL 60655 (United States)
2016-03-22
We investigate a generalized Fisher equation with temporally varying coefficients, describing the dynamics of a field in inhomogeneous media. A class of exact soliton solutions of this equation is presented, and some of which are derived for the first time. The trial equation method is applied to obtain these soliton solutions. The constraint conditions for the existence of these solutions are also exhibited.
An implicit spectral formula for generalized linear Schroedinger equations
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan
2009-01-01
We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)
Traveling wave behavior for a generalized fisher equation
International Nuclear Information System (INIS)
Feng Zhaosheng
2008-01-01
There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation
Tisdell, C. C.
2017-01-01
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…
Generalized Smoluchowski equation with correlation between clusters
International Nuclear Information System (INIS)
Sittler, Lionel
2008-01-01
In this paper we compute new reaction rates of the Smoluchowski equation which takes into account correlations. The new rate K = K MF + K C is the sum of two terms. The first term is the known Smoluchowski rate with the mean-field approximation. The second takes into account a correlation between clusters. For this purpose we introduce the average path of a cluster. We relate the length of this path to the reaction rate of the Smoluchowski equation. We solve the implicit dependence between the average path and the density of clusters. We show that this correlation length is the same for all clusters. Our result depends strongly on the spatial dimension d. The mean-field term K MF i,j = (D i + D j )(r j + r i ) d-2 , which vanishes for d = 1 and is valid up to logarithmic correction for d = 2, is the usual rate found with the Smoluchowski model without correlation (where r i is the radius and D i is the diffusion constant of the cluster). We compute a new rate: the correlation rate K i,j C = (D i +D j )(r j +r i ) d-1 M((d-1)/d f ) is valid for d ≥ 1(where M(α) = Σ +∞ i=1 i α N i is the moment of the density of clusters and d f is the fractal dimension of the cluster). The result is valid for a large class of diffusion processes and mass-radius relations. This approach confirms some analytical solutions in d = 1 found with other methods. We also show Monte Carlo simulations which illustrate some exact new solvable models
Directory of Open Access Journals (Sweden)
Hongxia Wu
2016-01-01
Full Text Available Two kinds of Darboux-Bäcklund transformations (DBTs are constructed for the q-deformed Nth KdV hierarchy with self-consistent sources (q-NKdVHSCS by using the q-deformed pseudodifferential operators. Note that one of the DBTs provides a nonauto Bäcklund transformation for two q-deformed Nth KdV equations with self-consistent sources (q-NKdVESCS with different degree. In addition, the soliton solution to the first nontrivial equation of q-KdVHSCS is also obtained.
Automatic computation and solution of generalized harmonic balance equations
Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.
2018-02-01
Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.
Generalized Langevin Equation Description of Stochastic ...
Indian Academy of Sciences (India)
general retarded effects of the frictional force, and on the fluctuation– dissipation theorems. The vertical displacements ... modelled via a friction force and a random force, respectively. By taking into account the presence of a .... Kubo, R. 1966, Report on Progress in Phys., 29, 255. Leung, C. S., Wei, J. Y., Harko, T., Kovacs, ...
BOOK REVIEW: Equations of Motion in General Relativity Equations of Motion in General Relativity
Schäfer, Gerhard
2012-03-01
Devoted exclusively to the problem of motion in general relativity, this book by H. Asada, T. Futamase, and P. A. Hogan is highly welcome to close up a gap in the book sector presenting a concise account of theoretical developments and results on gravitational equations of motion achieved since the discovery of the binary neutron star system PSR 1913+16 in 1974. For the most part, the book is concerned with the development and application of the important post-Newtonian approximation (PNA) framework which allows for highly efficient approximate analytic solutions of the Einstein field equations for many-body systems in terms of a slow-motion and weak-field ordering parameter. That approximation scheme is shown to be applicable also to the external motion of strongly self-gravitating objects if their internal dynamics is frozen in (strong field point particle limit) and the external conditions fit. Relying on the expertise of the authors, the PNA framework is presented in a form which, at the 1PNA level, had become famous through the work by Einstein, Infeld and Hoffmann in 1938; therein, surface integrals over gravitational field expressions in the outside-body regime play a crucial role. Other approaches which also succeeded with the highest achieved PNA level so far are mentioned too, if not fully exhaustively with respect to the highest, the 3.5PNA level which contains the inverse power of the speed of light to the seventh order. Regarding the 3PNA, the reader gains a clear understanding of how the equations of motion for binary systems with compact components come about. Remarkably, no deviation from four-dimensional space-time is needed. Various explicit analytic expressions are derived for binary systems: the periastron advance and the orbital period at the 2PNA, the orbital decay through gravitational radiation reaction at the 2.5PNA, and effects of the gravitational spin-orbit and spin-spin couplings on the orbital motion. Also the propagation of light
Ion-acoustic K-dV and mK-dV solitons in a degenerate electron-ion dense plasma
Nahar, L.; Zobaer, M. S.; Roy, N.; Mamun, A. A.
2013-02-01
A theoretical investigation has been made of the nonlinear propagation of ion-acoustic waves associated with a dense plasma system consisting degenerate electron and ion fluids. This fluid model, which is valid for both the non-relativistic and ultra-relativistic limits, has been employed with the reductive perturbation method. The K-dV and modified K-dV (mK-dV) equations have been derived and numerically analyzed. The basic features of solitons have been observed. It has been shown that the plasma system under consideration supports the propagation of solitons (electrostatic solitary structures) obtained from the solutions of K-dV and mK-dV equations. The implications of our results obtained from this investigation in compact astrophysical objects have been briefly discussed.
General method for reducing the two-body Dirac equation
International Nuclear Information System (INIS)
Galeao, A.P.; Ferreira, P.L.
1992-01-01
A semi relativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schroedinger-type equations is also discussed. (author)
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Generalized Freud's equation and level densities with polynomial ...
Indian Academy of Sciences (India)
The generalized Freud's equations for = 3, 4 and 5 are derived and using this R = h / h − 1 is obtained, where h is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of R , are obtained using Freud's equation and using this, explicit ...
Generalized Freud's equation and level densities with polynomial
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.
CHARTS STRUTT-INCE FOR GENERALIZED MATHIEU EQUATION
Directory of Open Access Journals (Sweden)
R.I. Parovik
2012-06-01
Full Text Available We have investigated the solution of the generalized Mathieu equation. With the aid of diagrams Stratton-Ince built the instability region, the condition can occur when the parametric resonance.
Generalized heat-transport equations: parabolic and hyperbolic models
Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio
2018-03-01
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.
Singular inflation from generalized equation of state fluids
Energy Technology Data Exchange (ETDEWEB)
Nojiri, S., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, S.D., E-mail: odintsov@ieec.uab.es [Institut de Ciencies de lEspai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Cerdanyola del Valles, Barcelona (Spain); ICREA, Passeig Lluîs Companys, 23, 08010 Barcelona (Spain); National Research Tomsk State University, 634050 Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 Tomsk (Russian Federation); Oikonomou, V.K., E-mail: v.k.oikonomou1979@gmail.com [Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece); National Research Tomsk State University, 634050 Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 Tomsk (Russian Federation)
2015-07-30
We study models with a generalized inhomogeneous equation of state fluids, in the context of singular inflation, focusing to so-called Type IV singular evolution. In the simplest case, this cosmological fluid is described by an equation of state with constant w, and therefore a direct modification of this constant w fluid is achieved by using a generalized form of an equation of state. We investigate from which models with generalized phenomenological equation of state, a Type IV singular inflation can be generated and what the phenomenological implications of this singularity would be. We support our results with illustrative examples and we also study the impact of the Type IV singularities on the slow-roll parameters and on the observational inflationary indices, showing the consistency with Planck mission results. The unification of singular inflation with singular dark energy era for specific generalized fluids is also proposed.
Geometric Procedures for Graphing the General Quadratic Equation.
DeTemple, Duane W.
1984-01-01
How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)
Food Web Assembly Rules for Generalized Lotka-Volterra Equations
DEFF Research Database (Denmark)
Härter, Jan Olaf Mirko; Mitarai, Namiko; Sneppen, Kim
2016-01-01
In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this...
Generalized latent variable modeling multilevel, longitudinal, and structural equation models
Skrondal, Anders; Rabe-Hesketh, Sophia
2004-01-01
This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models.
Generalized bootstrap equations and possible implications for the NLO Odderon
Energy Technology Data Exchange (ETDEWEB)
Bartels, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Vacca, G.P. [INFN, Sezione di Bologna (Italy)
2013-07-15
We formulate and discuss generalized bootstrap equations in nonabelian gauge theories. They are shown to hold in the leading logarithmic approximation. Since their validity is related to the self-consistency of the Steinmann relations for inelastic production amplitudes they can be expected to be valid also in NLO. Specializing to the N=4 SYM, we show that the validity in NLO of these generalized bootstrap equations allows to find the NLO Odderon solution with intercept exactly at one.
Symmetries of the Euler compressible flow equations for general equation of state
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-10-15
The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.
Symmetries of the Euler compressible flow equations for general equation of state
International Nuclear Information System (INIS)
Boyd, Zachary M.; Ramsey, Scott D.; Baty, Roy S.
2015-01-01
The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS's to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2015-01-01
Full Text Available By using Frobenius’ idea together with integral bifurcation method, we study a third order nonlinear equation of generalization form of the modified KdV equation, which is an important water wave model. Some exact traveling wave solutions such as smooth solitary wave solutions, nonsmooth peakon solutions, kink and antikink wave solutions, periodic wave solutions of Jacobian elliptic function type, and rational function solution are obtained. And we show their profiles and discuss their dynamic properties aim at some typical solutions. Though the types of these solutions obtained in this work are not new and they are familiar types, they did not appear in any existing literatures because the equation ut+ux+νuxxt+βuxxx + αuux+1/3να(uuxxx+2uxuxx+3μα2u2ux+νμα2(u2uxxx+ux3+4uuxuxx + ν2μα2(ux2uxxx+2uxuxx2 = 0 is very complex. Particularly, compared with the cited references, all results obtained in this paper are new.
Generalized Gel'fand-Levitan equation and variational relations of the Kaup-Newell equation
International Nuclear Information System (INIS)
Kawata, T.; Sakai, J.
1980-05-01
The generalized Gel'fand-Levitan integral equation is derived for solving the inverse problem of Kaup-Newell eigenvalue problem, which makes it possible to solve the derivative nonlinear Schroedinger equation etc. by the inverse Fourier Spectral transform. By this integral equation we obtained the variation of potentials as a functional of that of scattering data. The inverse functional relation is also given by perturbing the Kaup-Newell equation as to potentials. For both functionals the contribution from the discrete spectrum is obtained and the completeness of squared eigenfunctions is naturally derived. These functional relations play the important role for studying the dynamical property and the perturbational technique related to the nonlinear evolution equations solved by the Kaup-Newell equation. (author)
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F.
2015-09-30
Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
On the General Equation of the Second Degree
Indian Academy of Sciences (India)
IAS Admin
We give a unified treatment of the general equa- tion of second degree in two real variables in terms of the eigenvalues of the matrix associated to the quadratic terms and describe the solution sets in all cases. 1. Introduction. The study of the general equation of second degree in two variables was a major chapter in a ...
Sketching the General Quadratic Equation Using Dynamic Geometry Software
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
Anisotropic charged physical models with generalized polytropic equation of state
Nasim, A.; Azam, M.
2018-01-01
In this paper, we found the exact solutions of Einstein-Maxwell equations with generalized polytropic equation of state (GPEoS). For this, we consider spherically symmetric object with charged anisotropic matter distribution. We rewrite the field equations into simple form through transformation introduced by Durgapal (Phys Rev D 27:328, 1983) and solve these equations analytically. For the physically acceptability of these solutions, we plot physical quantities like energy density, anisotropy, speed of sound, tangential and radial pressure. We found that all solutions fulfill the required physical conditions. It is concluded that all our results are reduced to the case of anisotropic charged matter distribution with linear, quadratic as well as polytropic equation of state.
Equation of state and general relativity in supernovae
International Nuclear Information System (INIS)
Baron, E.A.
1985-01-01
The results of an extensive numerical study of the outcome of massive star collapse and subsequent shock formation and propagation are presented. The stiffness of the equation of state at high density is shown to play a crucial role, a softer equation of state being helpful to shock production and propagation. The effect of neutrinos is investigated in a simple manner by varying the neutrino transport from a simple trapping density to a simple leakage scheme. With a softer equation of state, the maximum central densities reached are high enough that general relativity may become important. The effects of general relativity are investigated in detail. It is shown that while general relativity is generally harmful to the shock, once the equation of state becomes soft enough, general relativistic effects may conspire to transfer large amounts of energy from the gravitational field to the shock, resulting in powerful explosions. This is first investigated using simplified initial conditions, the initial models being constructed in an ad hoc fashion to facilitate numerical investigation. Finally, results are presented for detailed pre-supernovae initial models of 12 and 15 M/sub sun/. These models do explode, with explosion energies varying from approx.1 - 3 x 10 51 ergs depending on the degree of softness of the high density equation of state
Superstability of the generalized orthogonality equation on restricted ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
(n ≥ 2) satisfies the functional inequality. ||〈f (x), f (y)〉| − |〈x,y〉|| ≤ ε for some ε ≥ 0 and for all x,y ∈ Rn. , then f is a solution of the generalized orthogonality equation (1). We will refer the reader to [3,6,8,12] for detailed definitions of stability and superstability of functional equations. By using ideas of Skof and Rassias [8,11], ...
General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2009-01-01
Roč. 193, č. 2 (2009), s. 109-129 ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172
Novel loop-like solitons for the generalized Vakhnenko equation
International Nuclear Information System (INIS)
Zhang Min; Ma Yu-Lan; Li Bang-Qing
2013-01-01
A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation
Charged cylindrical polytropes with generalized polytropic equation of state
Energy Technology Data Exchange (ETDEWEB)
Azam, M. [University of Education, Division of Science and Technology, Lahore (Pakistan); Mardan, S.A.; Noureen, I.; Rehman, M.A. [University of the Management and Technology, Department of Mathematics, Lahore (Pakistan)
2016-09-15
We study the general formalism of polytropes in the relativistic regime with generalized polytropic equations of state in the vicinity of cylindrical symmetry. We take a charged anisotropic fluid distribution of matter with a conformally flat condition for the development of a general framework of the polytropes. We discuss the stability of the model by the Whittaker formula and conclude that one of the models developed is physically viable. (orig.)
BOOK REVIEW: Partial Differential Equations in General Relativity
Halburd, Rodney G.
2008-11-01
Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed
Generalized Fokker-Planck equation, Brownian motion, and ergodicity.
Plyukhin, A V
2008-06-01
Microscopic theory of Brownian motion of a particle of mass M in a bath of molecules of mass mforce, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In the general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order (m/M)2 and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented.
Volume transport and generalized hydrodynamic equations for monatomic fluids.
Eu, Byung Chan
2008-10-07
In this paper, the effects of volume transport on the generalized hydrodynamic equations for a pure simple fluid are examined from the standpoint of statistical mechanics and, in particular, kinetic theory of fluids. First, we derive the generalized hydrodynamic equations, namely, the constitutive equations for the stress tensor and heat flux for a single-component monatomic fluid, from the generalized Boltzmann equation in the presence of volume transport. Then their linear steady-state solutions are derived and examined with regard to the effects of volume transport on them. The generalized hydrodynamic equations and linear constitutive relations obtained for nonconserved variables make it possible to assess Brenner's proposition [Physica A 349, 11 (2005); Physica A 349, 60 (2005)] for volume transport and attendant mass and volume velocities as well as the effects of volume transport on the Newtonian law of viscosity, compression/dilatation (bulk viscosity) phenomena, and Fourier's law of heat conduction. On the basis of study made, it is concluded that the notion of volume transport is sufficiently significant to retain in irreversible thermodynamics of fluids and fluid mechanics.
Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang
2006-01-01
This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…
Towards a general equation for frequency domain reflectometers
Rüdiger, Christoph; Western, Andrew W.; Walker, Jeffrey P.; Smith, Adam B.; Kalma, Jetse D.; Willgoose, Garry R.
2010-03-01
SummaryIt is well documented that capacitance-based soil moisture sensor measurements are particularly influenced by particle size distribution, density, salinity, and temperature of a soil, in addition to its moisture content. Moreover, the equations provided by manufacturers of soil moisture sensors are often only applicable to a limited number of soil types, thus yielding significant errors when compared with gravimetric measurements for observations in real soils. This limitation makes site-specific calibrations of such sensors necessary. Consequently, development of a general equation provides the possibility to derive the needed parameters from information such as soil type or particle size distribution. This paper describes the development of a general equation for the Campbell Scientific CS616 Water Content Reflectometers using data from sensors installed throughout the Goulburn River experimental catchment. It is subsequently tested using monitoring sites in the Murrumbidgee Soil Moisture Monitoring Network, which were not part of the original development; both monitoring networks are located in south-eastern Australia. Previously developed equations for temperature correction and soil moisture estimation using the Campbell Scientific CS615 Water Content Reflectometer are adapted to the new CS616 sensor. Moreover, relationships between readily available soil properties and the parameters of the general equations are derived. It is shown that the general equations developed here can be applied to data collected in the field using only information on the soil particle size distribution with an RMSE of around 6% m 3/m 3 (<1% m 3/m 3 under laboratory conditions; which is a significant improvement in comparison to 14% m 3/m 3 when using the manufacturer's equations).
Multi wave method for the generalized form of BBM equation
Bildik, Necdet; Tandogan, Yusuf Ali
2014-12-01
In this paper, we apply the multi-wave method to find new multi wave solutions for an important nonlinear physical model. This model is well known as generalized form of Benjamin Bona Mahony (BBM) equation. Using the mathematics software Mathematica, we compute the traveling wave solutions. Then, the multi wave solutions including periodic wave solutions, bright soliton solutions and rational function solutions are obtained by the multi wave method. It is seen that this method is very useful mathematical approach for generalized form of BBM equation.
Thermodynamic framework for a generalized heat transport equation
Directory of Open Access Journals (Sweden)
Guo Yangyu
2016-06-01
Full Text Available In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.
On the non-stationary generalized Langevin equation
Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja
2017-12-01
In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.
The generalized Burgers equation with and without a time delay
Directory of Open Access Journals (Sweden)
Nejib Smaoui
2004-01-01
Full Text Available We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut=vuxx−uux+u+h(x, 0
Generalized isothermal models with strange equation of state
Indian Academy of Sciences (India)
Sri Lanka. *Corresponding author. E-mail: maharaj@ukzn.ac.za. MS received 30 October 2008; revised 5 December 2008; accepted 16 December 2008. Abstract. We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact.
An improved generalized Newton method for absolute value equations.
Feng, Jingmei; Liu, Sanyang
2016-01-01
In this paper, we suggest and analyze an improved generalized Newton method for solving the NP-hard absolute value equations [Formula: see text] when the singular values of A exceed 1. We show that the global and local quadratic convergence of the proposed method. Numerical experiments show the efficiency of the method and the high accuracy of calculation.
On the General Equation of the Second Degree
Indian Academy of Sciences (India)
IAS Admin
inequalities. He has authored four books covering topics in functional analysis and its applications to partial differential equations. We give a unified treatment of the general equa- tion of second degree in two real variables in terms of the eigenvalues of the matrix associated to the quadratic terms and describe the solution.
Survey on Dirac equation in general relativity theory
International Nuclear Information System (INIS)
Paillere, P.
1984-10-01
Starting from an infinitesimal transformation expressed with a Killing vector and using systematically the formalism of the local tetrades, we show that, in the area of the general relativity, the Dirac equation may be formulated only versus the four local vectors which determine the gravitational potentials, their gradients and the 4-vector potential of the electromagnetic field [fr
Nuclear equation of state, general relativity and supernovae explosions
International Nuclear Information System (INIS)
Kahana, S.
1985-01-01
Prompt explosions are obtained in hydrodynamic simulations for the 12 Msub solar and 15 Msub solar type II supernova initial models of Weaver and Woosley, when the nuclear equation of state is sufficiently soft and when general relativity is included. 12 refs
The Neumann Problem for the Laplace Equation on General Domains
Czech Academy of Sciences Publication Activity Database
Medková, Dagmar
2007-01-01
Roč. 57, č. 4 (2007), s. 1107-1139 ISSN 0011-4642 Institutional research plan: CEZ:AV0Z10190503 Keywords : Laplace equation * Neumann problem * potential Subject RIV: BA - General Mathematics Impact factor: 0.155, year: 2007
Generalized Stability of Euler-Lagrange Quadratic Functional Equation
Directory of Open Access Journals (Sweden)
Hark-Mahn Kim
2012-01-01
Full Text Available The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation f(ax+by+af(x-by=(a+1b2f(y+a(a+1f(x, in (β,p-Banach space, where a,b are fixed rational numbers such that a≠-1,0 and b≠0.
Exact solutions of the Bach field equations of general relativity
Fiedler, B.; Schimming, R.
1980-02-01
Conformally invariant gravitational field equations on the hand and fourth order field equations on the other were discussed in the early history of general relativity (Weyl Einstein, Bach et al.) and have recently gained some new interest (Deser, P. Günther, Treder, et al.). The equations Bαβ=0 or Bαβ= ϰTαβ, where Bαβ denotes the Bach tensor and Tαβ a suitable energy-momentum tensor, possess both the mentioned properties. We construct exact solutions ds2= gαβdxαdxβ of the Bach equations: (2, 2)-decomposable, centrally symmetric and pp-wave solutions. The gravitational field gαβ is coupled by Bαβ= ϰTαβ to an electromagnetic field Fαβ=- Fαβ obeying the Maxwell equations or to a neutrino field ϕ A obeying the Weyl equations respectively. Among interesting new metrics ds2 there appear some physically well-known ones, such as the De Sitter universe, the Weyl-Trefftz metric. and the plane-fronted gravitational waves with parallel rays (pp-waves) known from Einstein's theory. The solutions are built up by means of special techniques: A separation method for (2, 2)-decomposable solutions, simplification of centrally symmetric metrics by a suitable conformal transformation, and complex function methods for pp-wave solutions.
Generalized nonlinear Proca equation and its free-particle solutions
Nobre, F. D.; Plastino, A. R.
2016-06-01
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schrödinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ ^{μ }(ěc {x},t), involves an additional field Φ ^{μ }(ěc {x},t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E2 = p2c2 + m2c4 for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed.
Generalized nonlinear Proca equation and its free-particle solutions
Energy Technology Data Exchange (ETDEWEB)
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
Developing a generalized allometric equation for aboveground biomass estimation
Xu, Q.; Balamuta, J. J.; Greenberg, J. A.; Li, B.; Man, A.; Xu, Z.
2015-12-01
A key potential uncertainty in estimating carbon stocks across multiple scales stems from the use of empirically calibrated allometric equations, which estimate aboveground biomass (AGB) from plant characteristics such as diameter at breast height (DBH) and/or height (H). The equations themselves contain significant and, at times, poorly characterized errors. Species-specific equations may be missing. Plant responses to their local biophysical environment may lead to spatially varying allometric relationships. The structural predictor may be difficult or impossible to measure accurately, particularly when derived from remote sensing data. All of these issues may lead to significant and spatially varying uncertainties in the estimation of AGB that are unexplored in the literature. We sought to quantify the errors in predicting AGB at the tree and plot level for vegetation plots in California. To accomplish this, we derived a generalized allometric equation (GAE) which we used to model the AGB on a full set of tree information such as DBH, H, taxonomy, and biophysical environment. The GAE was derived using published allometric equations in the GlobAllomeTree database. The equations were sparse in details about the error since authors provide the coefficient of determination (R2) and the sample size. A more realistic simulation of tree AGB should also contain the noise that was not captured by the allometric equation. We derived an empirically corrected variance estimate for the amount of noise to represent the errors in the real biomass. Also, we accounted for the hierarchical relationship between different species by treating each taxonomic level as a covariate nested within a higher taxonomic level (e.g. species equations, the plant's taxonomy, and their biophysical environment.
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Dynamic behavior of a nonlinear rational difference equation and generalization
Directory of Open Access Journals (Sweden)
Shi Qihong
2011-01-01
Full Text Available Abstract This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x n = (x n-k + x n-m + x n-l /(x n-k x n-m + x n-m x n-l +1 with the initial data { x - l , x - l + 1 , … , x - 1 } ∈ ℝ + l and 1 ≤ k ≤ m ≤ l. The convergence of solution to this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et al. Appl. Math. Lett. 20:54-58, 2007; Papaschinopoulos and Schinas J Math Anal Appl 294:614-620, 2004 to a large extent. In addition, some propositions for generalized equations are reported.
A numerical scheme for the generalized Burgers–Huxley equation
Directory of Open Access Journals (Sweden)
Brajesh K. Singh
2016-10-01
Full Text Available In this article, a numerical solution of generalized Burgers–Huxley (gBH equation is approximated by using a new scheme: modified cubic B-spline differential quadrature method (MCB-DQM. The scheme is based on differential quadrature method in which the weighting coefficients are obtained by using modified cubic B-splines as a set of basis functions. This scheme reduces the equation into a system of first-order ordinary differential equation (ODE which is solved by adopting SSP-RK43 scheme. Further, it is shown that the proposed scheme is stable. The efficiency of the proposed method is illustrated by four numerical experiments, which confirm that obtained results are in good agreement with earlier studies. This scheme is an easy, economical and efficient technique for finding numerical solutions for various kinds of (nonlinear physical models as compared to the earlier schemes.
Gradient blow-up in generalized Burgers and Boussinesq equations
Yushkov, E. V.; Korpusov, M. O.
2017-12-01
We study the influence of gradient non-linearity on the global solubility of initial-boundary value problems for a generalized Burgers equation and an improved Boussinesq equation which are used for describing one-dimensional wave processes in dissipative and dispersive media. For a large class of initial data, we obtain sufficient conditions for global insolubility and a bound for blow-up times. Using the Boussinesq equation as an example, we suggest a modification of the method of non-linear capacity which is convenient from a practical point of view and enables us to estimate the blow-up rate. We use the method of contraction mappings to study the possibility of instantaneous blow-up and short-time existence of solutions.
Enhanced group analysis of a semi linear generalization of a general bond-pricing equation
Bozhkov, Y.; Dimas, S.
2018-01-01
The enhanced group classification of a semi linear generalization of a general bond-pricing equation is carried out by harnessing the underlying equivalence and additional equivalence transformations. We employ that classification to unearth the particular cases with a larger Lie algebra than the general case and use them to find non trivial invariant solutions under the terminal and the barrier option condition.
Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations
Kuzemsky, A. L.
2018-01-01
We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.
A general method for enclosing solutions of interval linear equations
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2012-01-01
Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Ram K. Saxena; Zivorad Tomovski; Trifce Sandev
2015-01-01
In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find ...
Generalized Einstein’s Equations from Wald Entropy
Directory of Open Access Journals (Sweden)
Maulik Parikh
2016-03-01
Full Text Available We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.
Generalized isothermal models with strange equation of state
Indian Academy of Sciences (India)
intention to study the Einstein–Maxwell system with a linear equation of state with ... It is our intention to model the interior of a dense realistic star with a general ... The definition m(r) = 1. 2. ∫ r. 0 ω2ρ(ω)dω. (14) represents the mass contained within a radius r which is a useful physical quantity. The mass function (14) has ...
Variational Iteration Method for Solving a Fuzzy Generalized Pantograph Equation
Directory of Open Access Journals (Sweden)
A. Amiri
2014-05-01
Full Text Available A numerical method for solving the fuzzy generalized pantograph equation under fuzzy initial value conditions is presented. This technique provides a sequence of functions which converges to the exact solution to the problem and is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. To display the validity and applicability of the numerical method two illustrative examples are presented.
Multiple Canard Cycles in Generalized Liénard Equations
Dumortier, Freddy; Roussarie, Robert
2001-07-01
The paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of parameters. Proofs are based on the techniques introduced in “Canard Cycles and Center Manifolds” (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. Soc., 121). The presentation is limited to generalized Liénard equations ɛx+α(x, c) x+β(x, c)=0.
Resummed memory kernels in generalized system-bath master equations
Mavros, Michael G.; Van Voorhis, Troy
2014-08-01
Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the "Landau-Zener resummation" of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.
Integrable generalization of the associated Camassa–Holm equation
Energy Technology Data Exchange (ETDEWEB)
Luo, Lin, E-mail: luolin@sspu.edu.cn [Department of Mathematics, Shanghai Second Polytechnic University, Shanghai 201209 (China); Qiao, Zhijun, E-mail: qiao@utpa.edu [Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539 (United States); Lopez, Juan, E-mail: jflopezz@utpa.edu [Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539 (United States)
2014-02-07
In this paper, we study an integrable generalization of the associated Camassa–Holm equation. The generalized system is shown to be integrable in the sense of Lax pair and the bilinear Bäcklund transformations are presented through the Bell polynomial technique. Meanwhile, its infinite conservation laws are constructed, and conserved densities and fluxes are given in explicit recursion formulas. Furthermore, a Darboux transformation for the system is derived with the help of the gauge transformation between two Lax pairs. As an application, soliton and periodic wave solutions are given through the Darboux transformation.
A Generalized Representation Formula for Systems of Tensor Wave Equations
Shao, Arick
2011-08-01
In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski (Hyperbolic Equ. 4(3):401-433, 2007) to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization of (Hyperbolic Equ. 4(3):401-433, 2007) is a key component for extending Klainerman and Rodnianski's breakdown criterion result for Einstein-vacuum spacetimes in (J. Amer. Math. Soc. 23(2):345-382, 2009) to Einstein-Maxwell and Einstein-Yang-Mills spacetimes.
The cluster bootstrap consistency in generalized estimating equations
Cheng, Guang
2013-03-01
The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference. © 2012.
GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS
Directory of Open Access Journals (Sweden)
Túlio Jardim Raad
2006-06-01
Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.
The Generalized Conversion Factor in Einstein's Mass-Energy Equation
Directory of Open Access Journals (Sweden)
Ajay Sharma
2008-07-01
Full Text Available Einstein's September 1905 paper is origin of light energy-mass inter conversion equation ($L = Delta mc^{2}$ and Einstein speculated $E = Delta mc^{2}$ from it by simply replacing $L$ by $E$. From its critical analysis it follows that $L = Delta mc^{2}$ is only true under special or ideal conditions. Under general cases the result is $L propto Delta mc^{2}$ ($E propto Delta mc^{2}$. Consequently an alternate equation $Delta E = A ub c^{2}Delta M$ has been suggested, which implies that energy emitted on annihilation of mass can be equal, less and more than predicted by $Delta E = Delta mc^{2}$. The total kinetic energy of fission fragments of U-235 or Pu-239 is found experimentally 20-60 MeV less than Q-value predicted by $Delta mc^{2}$. The mass of particle Ds (2317 discovered at SLAC, is more than current estimates. In many reactions including chemical reactions $E = Delta mc^{2}$ is not confirmed yet, but regarded as true. It implies the conversion factor than $c^{2}$ is possible. These phenomena can be explained with help of generalized mass-energy equation $Delta E = A ub c^{2}Delta M$.
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Soliton equations and pseudospherical surfaces
International Nuclear Information System (INIS)
Sasaki, R.
1979-03-01
All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)
The generalized effective potential and its equations of motion
International Nuclear Information System (INIS)
Ananikyan, N.S.; Savvidy, G.K.
1980-01-01
By means ot the Legendre transformations a functional GITA(PHI, G, S) is constructed which depends on PHI -a possible expectation value of the quantum field, G -a possible expectation value of the 2-point connected Green function and S= - a possible expectation value of the classical action. The motion equations for the functional GITA are derived on the example of the gPHI 3 theory and an iteration technique is suggested to solve them. A basic equation for GITA which is solved by means of iteration techniques is an ordinary and not a variation one, as it is the case at usual Legendre transformations. The developed formalism can be easily generalized as to other theories
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
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.
Improved dynamic equations for the generally configured Stewart platform manipulator
Energy Technology Data Exchange (ETDEWEB)
Pedrammehr, Siamak; Mahboubkhah, Mehran [University of Tabriz, Tabriz (Iran, Islamic Republic of); Khani, Navid [University of Tehran, Tehran (Iran, Islamic Republic of)
2012-03-15
In this paper, a Newton-Euler approach is utilized to generate the improved dynamic equations of the generally configured Stewart platform. Using the kinematic model of the universal joint, the rotational degree of freedom of the pods around the axial direction is taken into account in the formulation. The justifiable direction of the reaction moment on each pod is specified and considered in deriving the dynamic equations. Considering the theorem of parallel axes, the inertia tensors for different elements of the manipulator are obtained in this study. From a theoretical point, the improved formulation is more accurate in comparison with previous ones, and the necessity of the improvement is clear evident from significant differences in the simulation results for the improved model and the model without improvement. In addition to more feasibility of the structure and higher accuracy, the model is highly compatible with computer arithmetic and suitable for online applications for loop control problems in hardware.
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
Improved dynamic equations for the generally configured Stewart platform manipulator
International Nuclear Information System (INIS)
Pedrammehr, Siamak; Mahboubkhah, Mehran; Khani, Navid
2012-01-01
In this paper, a Newton-Euler approach is utilized to generate the improved dynamic equations of the generally configured Stewart platform. Using the kinematic model of the universal joint, the rotational degree of freedom of the pods around the axial direction is taken into account in the formulation. The justifiable direction of the reaction moment on each pod is specified and considered in deriving the dynamic equations. Considering the theorem of parallel axes, the inertia tensors for different elements of the manipulator are obtained in this study. From a theoretical point, the improved formulation is more accurate in comparison with previous ones, and the necessity of the improvement is clear evident from significant differences in the simulation results for the improved model and the model without improvement. In addition to more feasibility of the structure and higher accuracy, the model is highly compatible with computer arithmetic and suitable for online applications for loop control problems in hardware
A Generalization of the Einstein-Maxwell Equations
Cotton, Fredrick
2016-03-01
The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf
The general class of the vacuum spherically symmetric equations of the general relativity theory
Energy Technology Data Exchange (ETDEWEB)
Karbanovski, V. V., E-mail: Karbanovski_V_V@mail.ru; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N., E-mail: Markov_Victor@mail.ru; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R. [Murmansk State Pedagogical University (Russian Federation)
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
Analytical Solution of Generalized Space-Time Fractional Cable Equation
Directory of Open Access Journals (Sweden)
Ram K. Saxena
2015-04-01
Full Text Available In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.
Topological branes, p-algebras and generalized Nahm equations
Energy Technology Data Exchange (ETDEWEB)
Bonelli, Giulio; Tanzini, Alessandro [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy); Zabzine, Maxim [Theoretical Physics, Department of Physics and Astronomy, Uppsala University, Box 803, SE-751 08 Uppsala (Sweden)], E-mail: maxim.zabzine@teorfys.uu.se
2009-03-02
Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory.
A New Solution for Einstein Field Equation in General Relativity
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.
Herschlag, Gregory J; Mitran, Sorin; Lin, Guang
2015-06-21
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.
Simple Numerical Schemes for the Korteweg-deVries Equation
International Nuclear Information System (INIS)
McKinstrie, C. J.; Kozlov, M.V.
2000-01-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves
Schluchter, Mark D.
2008-01-01
In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by…
David. C. Chojnacky
2012-01-01
An update of the Jenkins et al. (2003) biomass estimation equations for North American tree species resulted in 35 generalized equations developed from published equations. These 35 equations, which predict aboveground biomass of individual species grouped according to a taxa classification (based on genus or family and sometimes specific gravity), generally predicted...
Generalized multiscale finite element method for elasticity equations
Chung, Eric T.
2014-10-05
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.
Stability of the complex generalized Hartree-Fock equations.
Goings, Joshua J; Ding, Feizhi; Frisch, Michael J; Li, Xiaosong
2015-04-21
For molecules with complex and competing magnetic interactions, it is often the case that the lowest energy Hartree-Fock solution may only be obtained by removing the spin and time-reversal symmetry constraints of the exact non-relativistic Hamiltonian. To do so results in the complex generalized Hartree-Fock (GHF) method. However, with the loss of variational constraints comes the greater possibility of converging to higher energy minima. Here, we report the implementation of stability test of the complex GHF equations, along with an orbital update scheme should an instability be found. We apply the methodology to finding the local minima of several spin-frustrated hydrogen rings, as well as the non-collinear molecular magnet Cr3, illustrating the utility of the broken symmetry GHF method and some of its lesser-known nuances.
Particular solutions of generalized Euler-Poisson-Darboux equation
Directory of Open Access Journals (Sweden)
Rakhila B. Seilkhanova
2015-01-01
Full Text Available In this article we consider the generalized Euler-Poisson-Darboux equation $$ {u}_{tt}+\\frac{2\\gamma }{t}{{u}_{t}}={u}_{xx}+{u}_{yy} +\\frac{2\\alpha }{x}{{u}_{x}}+\\frac{2\\beta }{y}{{u}_y},\\quad x>0,\\;y>0,\\;t>0. $$ We construct particular solutions in an explicit form expressed by the Lauricella hypergeometric function of three variables. Properties of each constructed solutions have been investigated in sections of surfaces of the characteristic cone. Precisely, we prove that found solutions have singularity $1/r$ at $r\\to 0$, where ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.
2016-09-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
Explicit estimating equations for semiparametric generalized linear latent variable models
Ma, Yanyuan
2010-07-05
We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.
Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations
International Nuclear Information System (INIS)
Burt, P.B.
1978-01-01
Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references
A General Linear Method for Equating with Small Samples
Albano, Anthony D.
2015-01-01
Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…
Analysis of comparative data using generalized estimating equations.
Paradis, Emmanuel; Claude, Julien
2002-09-21
It is widely acknowledged that the analysis of comparative data from related species should be performed taking into account their phylogenetic relationships. We introduce a new method, based on the use of generalized estimating equations (GEE), for the analysis of comparative data. The principle is to incorporate, in the modelling process, a correlation matrix that specifies the dependence among observations. This matrix is obtained from the phylogenetic tree of the studied species. Using this approach, a variety of distributions (discrete or continuous) can be analysed using a generalized linear modelling framework, phylogenies with multichotomies can be analysed, and there is no need to estimate ancestral character state. A simulation study showed that the proposed approach has good statistical properties with a type-I error rate close to the nominal 5%, and statistical power to detect correlated evolution between two characters which increases with the strength of the correlation. The proposed approach performs well for the analysis of discrete characters. We illustrate our approach with some data on macro-ecological correlates in birds. Some extensions of the use of GEE are discussed.
General-relativistic celestial mechanics. II. Translational equations of motion
International Nuclear Information System (INIS)
Damour, T.; Soffel, M.; Xu, C.
1992-01-01
The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c) 4 in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies
Solutions of Riccati-Abel equation in terms of characteristics of general complex algebra
International Nuclear Information System (INIS)
Yamaleev, R.M.
2012-01-01
The Riccati-Abel differential equation defined as an equation between the first order derivative and the cubic polynomial is explored. In the case of constant coefficients this equation is reduced into an algebraic equation. A method of derivation of a summation formula for solutions of the Riccati-Abel equation is elaborated. The solutions of the Riccati-Abel equation are expressed in terms of the characteristic functions of general complex algebra of the third order
Nonlinear integrodifferential equations as discrete systems
Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.
1999-06-01
We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.
Generalization of DT Equations for Time Dependent Sources
Neri, Lorenzo; Tudisco, Salvatore; Musumeci, Francesco; Scordino, Agata; Fallica, Giorgio; Mazzillo, Massimo; Zimbone, Massimo
2010-01-01
New equations for paralyzable, non paralyzable and hybrid DT models, valid for any time dependent sources are presented. We show how such new equations include the equations already used for constant rate sources, and how it’s is possible to correct DT losses in the case of time dependent sources. Montecarlo simulations were performed to compare the equations behavior with the three DT models. Excellent accordance between equations predictions and Montecarlo simulation was found. We also obtain good results in the experimental validation of the new hybrid DT equation. Passive quenched SPAD device was chosen as a device affected by hybrid DT losses and active quenched SPAD with 50 ns DT was used as DT losses free device. PMID:22163500
Generalization of DT Equations for Time Dependent Sources
Directory of Open Access Journals (Sweden)
Massimo Mazzillo
2010-12-01
Full Text Available New equations for paralyzable, non paralyzable and hybrid DT models, valid for any time dependent sources are presented. We show how such new equations include the equations already used for constant rate sources, and how it’s is possible to correct DT losses in the case of time dependent sources. Montecarlo simulations were performed to compare the equations behavior with the three DT models. Excellent accordance between equations predictions and Montecarlo simulation was found. We also obtain good results in the experimental validation of the new hybrid DT equation. Passive quenched SPAD device was chosen as a device affected by hybrid DT losses and active quenched SPAD with 50 ns DT was used as DT losses free device.
Generalized linear isotherm regularity equation of state applied to metals
Directory of Open Access Journals (Sweden)
H. Sun
2012-03-01
Full Text Available A three-parameter equation of state (EOS without physically incorrect oscillations is proposed based on the generalized Lennard-Jones (GLJ potential and the approach in developing linear isotherm regularity (LIR EOS of Parsafar and Mason [J. Phys. Chem., 1994, 49, 3049]. The proposed (GLIR EOS can include the LIR EOS therein as a special case. The three-parameter GLIR, Parsafar and Mason (PM [Phys. Rev. B, 1994, 49, 3049], Shanker, Singh and Kushwah (SSK [Physica B, 1997, 229, 419], Parsafar, Spohr and Patey (PSP [J. Phys. Chem. B, 2009, 113, 11980], and reformulated PM and SSK EOSs are applied to 30 metallic solids within wide pressure ranges. It is shown that the PM, PMR and PSP EOSs for most solids, and the SSK and SSKR EOSs for several solids, have physically incorrect turning points, and pressure becomes negative at high enough pressure. The GLIR EOS is capable not only of overcoming the problem existing in other five EOSs where the pressure becomes negative at high pressure, but also gives results superior to other EOSs
Generalized structural equations improve sexual-selection analyses.
Directory of Open Access Journals (Sweden)
Sonia Lombardi
Full Text Available Sexual selection is an intense evolutionary force, which operates through competition for the access to breeding resources. There are many cases where male copulatory success is highly asymmetric, and few males are able to sire most females. Two main hypotheses were proposed to explain this asymmetry: "female choice" and "male dominance". The literature reports contrasting results. This variability may reflect actual differences among studied populations, but it may also be generated by methodological differences and statistical shortcomings in data analysis. A review of the statistical methods used so far in lek studies, shows a prevalence of Linear Models (LM and Generalized Linear Models (GLM which may be affected by problems in inferring cause-effect relationships; multi-collinearity among explanatory variables and erroneous handling of non-normal and non-continuous distributions of the response variable. In lek breeding, selective pressure is maximal, because large numbers of males and females congregate in small arenas. We used a dataset on lekking fallow deer (Dama dama, to contrast the methods and procedures employed so far, and we propose a novel approach based on Generalized Structural Equations Models (GSEMs. GSEMs combine the power and flexibility of both SEM and GLM in a unified modeling framework. We showed that LMs fail to identify several important predictors of male copulatory success and yields very imprecise parameter estimates. Minor variations in data transformation yield wide changes in results and the method appears unreliable. GLMs improved the analysis, but GSEMs provided better results, because the use of latent variables decreases the impact of measurement errors. Using GSEMs, we were able to test contrasting hypotheses and calculate both direct and indirect effects, and we reached a high precision of the estimates, which implies a high predictive ability. In synthesis, we recommend the use of GSEMs in studies on
General off-shell phase equations for local interactions
International Nuclear Information System (INIS)
Dolinszky, T.
1977-11-01
First order linear differential equations are developed for the completely off-shell phase shift in terms of the cut-off radius of the local two-body interaction. The input to these equations involves on-shell as well as half-off-shell phase functions the latter of which in turn satisfy first order linear differential equations with on-shell phase functions as input. It is concluded that the solution of these new first-order linear differential equations developed within the framework of the standard phase approach is an appropriate means of calculating completely off-shell phase shifts. (D.P.)
Conservation Laws for a Generalized Coupled Korteweg-de Vries System
Directory of Open Access Journals (Sweden)
Daniel Mpho Nkwanazana
2013-01-01
Full Text Available We construct conservation laws for a generalized coupled KdV system, which is a third-order system of nonlinear partial differential equations. We employ Noether's approach to derive the conservation laws. Since the system does not have a Lagrangian, we make use of the transformation u=Ux, v=Vx and convert the system to a fourth-order system in U, V. This new system has a Lagrangian, and so the Noether approach can now be used to obtain conservation laws. Finally, the conservation laws are expressed in the u, v variables, and they constitute the conservation laws for the third-order generalized coupled KdV system. Some local and infinitely many nonlocal conserved quantities are found.
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
Updated generalized biomass equations for North American tree species
David C. Chojnacky; Linda S. Heath; Jennifer C. Jenkins
2014-01-01
Historically, tree biomass at large scales has been estimated by applying dimensional analysis techniques and field measurements such as diameter at breast height (dbh) in allometric regression equations. Equations often have been developed using differing methods and applied only to certain species or isolated areas. We previously had compiled and combined (in meta-...
Solution of a general pexiderized permanental functional equation
Indian Academy of Sciences (India)
49
f(ux + vy, uy − vx, zw) = g(x, y, z) h(u, v, w) is determined without any regularity assumptions. This equation arises from identities satisfied by the permanent of certain symmetric matrices. The solution so obtained are applied to deduce a number of existing related functional equations. Keywords. permanent; multiplicative ...
Affine Malcev Algebra and N = 8 Kdv
Toppan, F.
2002-03-01
In this talk I report the results of two recent papers concerning the realization of the N = 8 supersymmetry from the division algebra of the octonions. At first I discuss a Sugawara realization for the "Non-associative N = 8 SCA" in terms of a superaffinization of the algebra of octonions. Next, I discuss the fact that the N = 8 SCA provides a generalized Poisson brackets structure for an N = 8 super-KdV.
Directory of Open Access Journals (Sweden)
I. Capuzzo Dolcetta
2007-12-01
Full Text Available We analyze the validity of the Maximum Principle for viscosity solutions of fully nonlinear second order elliptic equations in general unbounded domains under suitable structure conditions on the equation allowing notably quadratic growth in the gradient terms.
Directory of Open Access Journals (Sweden)
Liu Yang
2014-01-01
Full Text Available We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.
A quantum gravity tensor equation formally integrating general relativity with quantum mechanics
Duan, Xu
2016-01-01
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger integral equation. When N becomes sufficiently large, it is equivalent to Einstein field equation. This illustrates formal unification and intrinsic compatibility of general relativity with quantum mechanics. The quantum gravity equation ma...
General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vectors
Fochi, Margherita
2012-01-01
Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...... of the nonintegrability parameter versus the integrability parameter. The heteroclinic map orbit is derived on the basis of a variational principle. Finally, we use homoclinic and heteroclinic orbits as initial conditions to excite designed stationary localized solutions of desired width in the dynamics of the discrete...
International Nuclear Information System (INIS)
Moussa, M.H.M.; El-Shiekh, Rehab M.
2010-01-01
In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov-Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases. (general)
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Dark and bright soliton; KdV equation; nonlinear Schrödinger equation; G(m, n) equation. PACS Nos 42.81.Dp; 42.65.Tg; 05.45.Yv. 1. Introduction. To find exact solutions of the nonlinear evolution equations (NLEEs) is one of the cen- tral themes in mathematics and physics. In recent years, many powerful methods have.
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 80; Issue 2. Soliton solutions of some nonlinear evolution equations with time-dependent coefficients ... In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable ...
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models.We establish the distinctdispersion relation for each equation. We use the simplified Hirota's method to obtain multiple soliton ...
Breaking soliton equations and negative-order breaking soliton ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... Abstract. We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models. We establish the distinct dispersion relation for each equation. We use the simplified Hirota's method to ...
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)
Effective Potential from the Generalized Time-Dependent Schrödinger Equation
Directory of Open Access Journals (Sweden)
Trifce Sandev
2016-09-01
Full Text Available We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potential. The general form of the effective potential that leads to a standard time-dependent Schrodinger equation with the same solution as the generalized one is derived explicitly. Further, effective potentials for several special cases, such as Dirac delta, power-law, Mittag-Leffler and truncated power-law memory kernels, are expressed in terms of the Mittag-Leffler functions. Such complex potentials have been used in the transport simulations in quantum dots, and in simulation of resonant tunneling diode.
A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order
Directory of Open Access Journals (Sweden)
Abdon Atangana
2013-01-01
Full Text Available The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented. Some theorems are generalized. The modified equation is approximately solved by using the variational iteration method and the Green function technique. The numerical simulation of solution of the modified equation gives a better prediction than the standard one.
Generalization of the Dirac’s Equation and Sea
DEFF Research Database (Denmark)
Javadi, Hossein; Forouzbakhsh, Farshid; Daei Kasmaei, Hamed
2016-01-01
Newton's second law is motion equation in classic mechanics that does not say anything about the nature of force. The equivalent formulations and their extensions such as Lagrangian and Hamiltonian do not explain about mechanism of converting Potential energy to Kinetic energy and Vice versa....... In quantum mechanics, Schrodinger equation is similar to Newton's second law in classic mechanics. Quantum mechanics is also extension of Newtonian mechanics to atomic and subatomic scales and relativistic mechanics is extension of Newtonian mechanics to high velocities near to velocity of light too...
Generalized Freud's equation and level densities with polynomial potential
Boobna, Akshat; Ghosh, Saugata
2013-08-01
We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.
Generalized uniqueness theorem for ordinary differential equations in Banach spaces.
Hassan, Ezzat R; Alhuthali, M Sh; Al-Ghanmi, M M
2014-01-01
We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...
A general polynomial solution to convection–dispersion equation ...
Indian Academy of Sciences (India)
Jiao Wang
A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute ...
Numerical Solutions of Generalized Burger's-Huxley Equation by ...
African Journals Online (AJOL)
... results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems. Keywords: Burger's-Huxley, modified variational iteration method, lagrange multiplier, Taylor's series, partial differential equation ...
Generalized Freud's equation and level densities with polynomial ...
Indian Academy of Sciences (India)
Here, we make a numerical analysis of orthogonal polynomials corresponding to d = 3,. 4 and 5. We derive the corresponding Freud's equation and calculate Rμ = hμ/hμ−1. We observe interesting patterns in the behaviour of Rμ. Once we have an understanding of Rμ, we use these results to obtain level densities.
Generalized Freud's equation and level densities with polynomial ...
Indian Academy of Sciences (India)
5 are derived and using this Rμ = hμ/hμ−1 is obtained, where hμ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of Rμ, are obtained using Freud's equation and using this, explicit results of level densities as N → ∞ are derived using the ...
On asymptotic expansion of general solution of Chew-Low equations
International Nuclear Information System (INIS)
Gerdt, V.P.; Zharkov, A.Yu.
1984-01-01
The connection between the global and local expansion of the general solution of the Chew-Low equations is considered. The reppesentations of the Chew-Low equation is used in the form of a system of nonlinear-finite difference equations. The investigation of the properties of the general solution is based on reducing the nonlinear equations to the infinite chain of inhomogeneous linear finite difference equations. It is achieved by global expansion of the general solution in series over powers of one of the arbitrary periodical function c(w), determining the structure of the general integral of the Chew-Low equations. It is shown that in each order in c(w) the asymptotic expansion of the global representation gives the well known local expansion of the general solution. It is confirmed by direct numerical investigation of the asymptotic behaviour of the physical interesting solutions possessing the Born pole
Directory of Open Access Journals (Sweden)
M. Arshad
Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method
Stabilization and asymptotic behavior of a generalized telegraph equation
Nicaise, Serge
2015-12-01
We analyze the stability of different models of the telegraph equation set in a real interval. They correspond to the coupling between a first-order hyperbolic system and a first-order differential equation of parabolic type. We show that some models have an exponential decay rate, while other ones are only polynomially stable. When the parameters are constant, we show that the obtained polynomial decay is optimal and in the case of an exponential decay that the decay rate is equal to the spectral abscissa. These optimality results are based on a careful spectral analysis of the operator. In particular, we characterize its full spectrum that is made of a discrete set of eigenvalues and an essential spectrum reduced to one point.
Solution of a general pexiderized permanental functional equation
Indian Academy of Sciences (India)
49
and the result follows by equating these last two relations. We return now to the proof of the lemma. Note from C9) that T is completely deter- mined if we know the values of T on the unit circle. Consider any two points on the unit circle (α, β) = (cos γ, sin γ), (x, y) = (cos θ, sin θ) with angles γ, θ oriented counterclock- wise.
A generalized biharmonic equation and its applications to ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
complex conjugate of w) and integrate each term of the resulting equation over the range of z by parts a ...... matrix C2(x) being Hermitian in a finite dimensional space, the spectral theorem gives that these form an orthonormal basis to Cn for each x in V i.e., u† i (x)uj (x) = δij . We thus have an expression χ(x) = n. ∑ i=1.
Estimates for a general fractional relaxation equation and application to an inverse source problem
Bazhlekova, Emilia
2018-01-01
A general fractional relaxation equation is considered with a convolutional derivative in time introduced by A. Kochubei (Integr. Equ. Oper. Theory 71 (2011), 583-600). This equation generalizes the single-term, multi-term and distributed-order fractional relaxation equations. The fundamental and the impulse-response solutions are studied in detail. Properties such as analyticity and subordination identities are established and employed in the proof of an upper and a lower bound. The obtained...
Solving the generalized Langevin equation with the algebraically correlated noise
International Nuclear Information System (INIS)
Srokowski, T.; Ploszajczak, M.
1997-01-01
The Langevin equation with the memory kernel is solved. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated at the assumption that the system is in the thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Levy walks with divergent moments of the velocity distribution. The motion of a Brownian particle is considered both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle. (author)
Persistence of travelling waves in a generalized Fisher equation
International Nuclear Information System (INIS)
Kyrychko, Yuliya N.; Blyuss, Konstantin B.
2009-01-01
Travelling waves of the Fisher equation with arbitrary power of nonlinearity are studied in the presence of long-range diffusion. Using analogy between travelling waves and heteroclinic solutions of corresponding ODEs, we employ the geometric singular perturbation theory to prove the persistence of these waves when the influence of long-range effects is small. When the long-range diffusion coefficient becomes larger, the behaviour of travelling waves can only be studied numerically. In this case we find that starting with some values, solutions of the model lose monotonicity and become oscillatory
International Nuclear Information System (INIS)
Calogero, F.
1976-01-01
A generalized Wronskian type relation is used to obtain a number of expressions for the scattering and bound state parameters (reflection and transmission coefficients, bound state energies and normalization constants) in the context of the one dimensional Schroedinger equation. These expressions are in the form of integrals over the wave functions multiplied by appropriate (generally nonlinear) combinations of the potentials and their derivatives. Some of them provide the basis for deriving classes of nonlinear partial differential equations that are solvable by the inverse scattering method. The main interest of this approach rests in its simplicity and in its delivery of nonlinear evolution equations that may involve more than one (space) variable and contain coefficients that are not constant
Spherical Kadomtsev–Petviashvili equation for dust acoustic waves ...
Indian Academy of Sciences (India)
the last term in the left-hand side of eq. (5) disappears and the SKP equation (5) reduces to the ordinary spherical KdV equation. We can find an exact solitary wave solution for the SKP equation (5) by using a suitable variable transformation. In eq. (5), the two terms with variable coefficient can be cancelled if we assume ζ ...
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation, Phase I
National Aeronautics and Space Administration — The overall objective of the proposed project is to develop a generalized lattice Boltzmann (GLB) approach as a potential computational aeroacoustics (CAA) tool for...
General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vectors
Directory of Open Access Journals (Sweden)
Margherita Fochi
2012-01-01
Full Text Available Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.
A generalized biharmonic equation and its applications to ...
Indian Academy of Sciences (India)
In this general survey we look back on and rewrite this work almost in exactly the way it evolved out of a few naive looking calculations in hydrodynamic instability. We show in the process the close relationship that exists between mathematical analysis and its applications with due credit to intuition as the main source of ...
On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation
International Nuclear Information System (INIS)
Figueiredo Camargo, Rubens; Capelas de Oliveira, Edmundo; Vaz, Jayme
2012-01-01
The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a function with three-parameter which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalized Mittag-Leffler function. As particular cases some recent results are recovered.
Linear relativistic gyrokinetic equation in general magnetically confined plasmas
International Nuclear Information System (INIS)
Tsai, S.T.; Van Dam, J.W.; Chen, L.
1983-08-01
The gyrokinetic formalism for linear electromagnetic waves of arbitrary frequency in general magnetic-field configurations is extended to include full relativistic effects. The derivation employs the small adiabaticity parameter rho/L 0 where rho is the Larmor radius and L 0 the equilibrium scale length. The effects of the plasma and magnetic field inhomogeneities and finite Larmor-radii effects are also contained
A generalized biharmonic equation and its applications to ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
such that 0 ≤ z ≤ 1,D stands for d/dz;α, σ, R and Rs are positive constants; p = pr +ipi is, in general, a complex constant such that pr and pr are real constants, ψ(z) = ψr (z)+iψi(z) and T (z) = Tr (z) + iTi(z) are independent variables which are complex valued functions of z in [0, 1] such that ψr (z), ψi(z), Tr (z) and Ti(z) are real ...
Group classification and conservation laws of the generalized Klein-Gordon-Fock equation
Muatjetjeja, B.
2016-08-01
In the present paper, we perform Lie and Noether symmetries of the generalized Klein-Gordon-Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.
Generally covariant Hamilton-Jacobi equation and rotated liquid sphere metrics
International Nuclear Information System (INIS)
Abdil'din, M.M.; Abdulgafarov, M.K.; Abishev, M.E.
2005-01-01
In the work Lense-Thirring problem on corrected Fock's first approximation metrics by Hamilton-Jacobi method considered. Generally covariant Hamilton-Jacobi equation had been sold by separation of variable method. Path equation of probe particle motion in rotated liquid sphere field is obtained. (author)
Riemann integral of a random function and the parabolic equation with a general stochastic measure
Radchenko, Vadym
2012-01-01
For stochastic parabolic equation driven by a general stochastic measure, the weak solution is obtained. The integral of a random function in the equation is considered as a limit in probability of Riemann integral sums. Basic properties of such integrals are studied in the paper.
Generalized Sturmian Solutions for Many-Particle Schrödinger Equations
DEFF Research Database (Denmark)
Avery, John; Avery, James Emil
2004-01-01
The generalized Sturmian method for obtaining solutions to the many-particle Schrodinger equation is reviewed. The method makes use of basis functions that are solutions of an approximate Schrodinger equation with a weighted zeroth-order potential. The weighting factors are especially chosen so...
Stability of Quartic Functional Equations in the Spaces of Generalized Functions
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces of tempered distributions and Fourier hyperfunctions.
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.
Directory of Open Access Journals (Sweden)
Maxim Olegovich Korpusov
2012-07-01
Full Text Available In this article the initial-boundary-value problem for generalized dissipative high-order equation of Klein-Gordon type is considered. We continue our study of nonlinear hyperbolic equations and systems with arbitrary positive energy. The modified concavity method by Levine is used for proving blow-up of solutions.
Solution of the General Helmholtz Equation Starting from Laplace’s Equation
2002-11-01
Salazar Palma Grupo de Microondas y Radar, Dpto. Senales, Sistemas y Radiocomunicaciones ETSI Telecomunicacion, Universidad Politecnica de Madrid Ciudad...updated at each step of the iteration. excitation. A new boundary integral method for Further, the BIM formulations are in most cases solving the...Hankel functions as it is commonly done in BIM element solutions of the same problem. Application of [10]. Besides its generality to solve Laplace’s
Propagators of Generalized Schrödinger Equations Related by First-order Supersymmetry
Directory of Open Access Journals (Sweden)
A. Schulze-Halberg
2011-01-01
Full Text Available We construct an explicit relation between propagators of generalized Schrödinger equations that are linked by a first-order supersymmetric transformation. Our findings extend and complement recent results on the conventional case [1].
New multi-soliton solutions for generalized Burgers-Huxley equation
Directory of Open Access Journals (Sweden)
Liu Jun
2013-01-01
Full Text Available The double exp-function method is used to obtain a two-soliton solution of the generalized Burgers-Huxley equation. The wave has two different velocities and two different frequencies.
General solution of the Universal equation in n-dimensional space
International Nuclear Information System (INIS)
Fairlie, D.B.; Leznov, A.N.
1994-01-01
Using the explicit form of solution of the system it is possible to construct the general solution of the Universal Equation which was found before with the help of the method of Legendre Transform. 6 refs
International Nuclear Information System (INIS)
Rawajfeh, M. K.; Al-Matar, A.
2000-01-01
A generalized equation relating equilibrium data, phase ratio and fractional recovery is developed. The use of this equation reduces the presentation of these data to a single dimensionless curve independent of the system and the operating conditions. The validity of this equation is tested using experimental data for different liquid - liquid systems at various condition. a reasonable agreement between experimental results and predicated ones was obtained. The use of this equation in investigating the effect of phase ratio on the fractional recovery is illustrated. (authors). 6 refs., 4 figs., 3 tabs
Mathieu's Equation and its Generalizations: Overview of Stability Charts and their Features
DEFF Research Database (Denmark)
Kovacic, Ivana; Rand, Richard H.; Sah, Si Mohamed
2018-01-01
This work is concerned with Mathieu's equation - a classical differential equation, which has the form of a linear second-order ordinary differential equation with Cosine-type periodic forcing of the stiffness coefficient, and its different generalizations/extensions. These extensions include......: the effects of linear viscous damping, geometric nonlinearity, damping nonlinearity, fractional derivative terms, delay terms, quasiperiodic excitation or elliptic-type excitation. The aim is to provide a systematic overview of the methods to determine the corresponding stability chart, its structure...... and features, and how it differs from that of the classical Mathieu's equation....
International Nuclear Information System (INIS)
Zhang Huiqun
2009-01-01
By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.
International Nuclear Information System (INIS)
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions
Geng, Xianguo; Guan, Liang; Xue, Bo
A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.
Directory of Open Access Journals (Sweden)
Haci Mehmet Baskonus
2016-07-01
Full Text Available In this paper, we apply the sine-Gordon expansion method which is one of the powerful methods to the generalized-Zakharov equation with complex structure. This algorithm yields new complex hyperbolic function solutions to the generalized-Zakharov equation with complex structure. Wolfram Mathematica 9 has been used throughout the paper for plotting two- and three-dimensional surface of travelling wave solutions obtained.
Akram, Ghazala; Sadaf, Maasoomah
2018-02-01
A modified algorithm for homotopy analysis method (MHAM) is presented for the solution of nonlinear damped generalized regularized long-wave equation. The modified algorithm has less computational cost than standard HAM and also overcomes the difficulty in calculating complicated integrals. The MHAM is applied on different cases of the damped generalized regularized long-wave equation subject to suitable initial conditions. The numerical results show that the approximate solutions are in good agreement with the exact solutions.
López Pouso, Rodrigo; Márquez Albés, Ignacio
2018-04-01
Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.
The General Traveling Wave Solutions of the Fisher Equation with Degree Three
Directory of Open Access Journals (Sweden)
Wenjun Yuan
2013-01-01
degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006, Guo and Chen (1991, and Ağırseven and Öziş (2010. Moreover, all wg,1(z are new general meromorphic solutions of the Fisher equations with degree three for c=±3/2. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.
A Note about the General Meromorphic Solutions of the Fisher Equation
Directory of Open Access Journals (Sweden)
Jian-ming Qi
2014-01-01
Full Text Available We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991, and wg,i(z are new general meromorphic solutions of the Fisher equation for c=±5i/6. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.
General form of the Euler-Poisson-Darboux equation and application of the transmutation method
Directory of Open Access Journals (Sweden)
Elina L. Shishkina
2017-07-01
Full Text Available In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations.
Shah, Jayna J; Gaitan, Michael; Geist, Jon
2009-10-01
Temperature mapping based on fluorescent signal intensity ratios is a widely used noncontact approach for investigating temperature distributions in various systems. This noninvasive method is especially useful for applications, such as microfluidics, where accurate temperature measurements are difficult with conventional physical probes. However, the application of a calibration equation to relate fluorescence intensity ratio to temperature is not straightforward when the reference temperature in a given application is different than the one used to derive the calibration equation. In this report, we develop and validate generalized calibration equations that can be applied for any value of reference temperature. Our analysis shows that a simple linear correction for a 40 degrees C reference temperature produces errors in measured temperatures between -3 to 8 degrees C for three previously published sets of cubic calibration equations. On the other hand, corrections based on an exact solution of these equations restrict the errors to those inherent in the calibration equations. The methods described here are demonstrated for cubic calibration equations derived by three different groups, but the general method can be applied to other dyes and calibration equations.
On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave
Directory of Open Access Journals (Sweden)
Arbab A. I.
2009-04-01
Full Text Available We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges.
International Nuclear Information System (INIS)
Liu Chengshi
2008-01-01
Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc, are reduced to an integrable ODE expressed by u + p(u)(u') 2 + q(u) = 0 whose general solution can be given. Furthermore, combining complete discrimination system for polynomial, the classifications of all single travelling wave solutions to these equations are obtained. The equation u + p(u)(u') 2 + q(u) = 0 includes the equation (u') 2 = f(u) as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
Soliton solutions of the generalized sinh-Gordon equation by the ...
Indian Academy of Sciences (India)
substituting αm,...,v and the general solutions of eq. (8) into (7) we have more travelling wave solutions of the nonlinear evolution eq. (1). 3. Application to the generalized sinh-Gordon equation. First, consider the following transformation: ξ = λ(x + ct), η = λ (x + a ct) , a = c2,. (9) where λ, c are two parameters to be determined.
Generalized linear differential equations in a Banach space : continuous dependence on a parameter
Czech Academy of Sciences Publication Activity Database
Monteiro, G.A.; Tvrdý, Milan
2013-01-01
Roč. 33, č. 1 (2013), s. 283-303 ISSN 1078-0947 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized differential equations * continuous dependence * Kurzweil-Stieltjes integral Subject RIV: BA - General Mathematics Impact factor: 0.923, year: 2013 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=7615
Generalized equations for estimating DXA percent fat of diverse young women and men: The Tiger Study
Popular generalized equations for estimating percent body fat (BF%) developed with cross-sectional data are biased when applied to racially/ethnically diverse populations. We developed accurate anthropometric models to estimate dual-energy x-ray absorptiometry BF% (DXA-BF%) that can be generalized t...
Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations
International Nuclear Information System (INIS)
Aboanber, A E
2006-01-01
A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback
Hsieh, Chang-Yu; Cao, Jianshu
2018-01-01
We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.
On the integrability of the generalized Fisher-type nonlinear diffusion equations
International Nuclear Information System (INIS)
Wang Dengshan; Zhang Zhifei
2009-01-01
In this paper, the geometric integrability and Lax integrability of the generalized Fisher-type nonlinear diffusion equations with modified diffusion in (1+1) and (2+1) dimensions are studied by the pseudo-spherical surface geometry method and prolongation technique. It is shown that the (1+1)-dimensional Fisher-type nonlinear diffusion equation is geometrically integrable in the sense of describing a pseudo-spherical surface of constant curvature -1 only for m = 2, and the generalized Fisher-type nonlinear diffusion equations in (1+1) and (2+1) dimensions are Lax integrable only for m = 2. This paper extends the results in Bindu et al 2001 (J. Phys. A: Math. Gen. 34 L689) and further provides the integrability information of (1+1)- and (2+1)-dimensional Fisher-type nonlinear diffusion equations for m = 2
New Exact Solutions for the (3+1-Dimensional Generalized BKP Equation
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Jun Su
2016-01-01
Full Text Available The Wronskian technique is used to investigate a (3+1-dimensional generalized BKP equation. Based on Hirota’s bilinear form, new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions are formally derived. Moreover we analyze the strangely mechanical behavior of the Wronskian determinant solutions. The study of these solutions will enrich the variety of the dynamics of the nonlinear evolution equations.
Analytical approximate solutions for a general class of nonlinear delay differential equations.
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.
Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation
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M. El-Kady
2013-01-01
Full Text Available Numerical treatments for the generalized Burger's—Huxley GBH equation are presented. The treatments are based on cardinal Chebyshev and Legendre basis functions with Galerkin method. Gauss quadrature formula and El-gendi method are used to convert the problem into a system of ordinary differential equations. The numerical results are compared with the literatures to show efficiency of the proposed methods.
Directory of Open Access Journals (Sweden)
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
International Nuclear Information System (INIS)
Senthilvelan, M; Torrisi, M; Valenti, A
2006-01-01
By using Lie's invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schroedinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra E χ o . We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schr?dinger equations which can be mapped, by means of an equivalence transformation of E χ o , to the well-known cubic Schroedinger equation. We also provide the explicit form of the transformation
Yu, Jie; Liu, Yikan; Yamamoto, Masahiro
2018-04-01
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.
New multidimensional partially integrable generalization of S-integrable N-wave equation
International Nuclear Information System (INIS)
Zenchuk, A. I.
2007-01-01
This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. The method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n. The associated solution space is not full, although it is parametrized by certain number of arbitrary functions of (n-1) variables. We consider four-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example
Sensitivity theory for general non-linear algebraic equations with constraints
International Nuclear Information System (INIS)
Oblow, E.M.
1977-04-01
Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems
He, Guitian; Tian, Yan; Luo, Maokang
2018-03-01
The resonance behavior in a generalized Langevin equation and fractional generalized Langevin equation with random trichotomous inherent frequency and a generalized Mittag-Leffler noise are extensively investigated. An expression for the noise spectral of the generalized Mittag-Leffler noise is studied. Using the Shapiro–Loginov formula and Laplace transformation technique, exact expressions for the spectral amplification of generalized Langevin equation and fractional generalized Langevin equation are obtained. The simulation results turn out to show that the spectral amplification is a non-monotonic function of the characteristics of noise parameters and system parameters. In particular, the influence of generalized Mittag-Leffler noise is able to induce the generalized stochastic resonance phenomenon. The influence of the driving frequency is able to induce bona fide stochastic resonance and stochastic multi-resonance phenomena. It is found that the resonance behavior of the fractional generalized Langevin equation has more material results than that of the (non-fractional) generalized Langevin equation.
Soliton evolution and radiation loss for the Korteweg--de Vries equation
International Nuclear Information System (INIS)
Kath, W.L.; Smyth, N.F.
1995-01-01
The time-dependent behavior of solutions of the Korteweg--de Vries (KdV) equation for nonsoliton initial conditions is considered. While the exact solution of the KdV equation can in principle be obtained using the inverse scattering transform, in practice it can be extremely difficult to obtain information about a solution's transient evolution by this method. As an alternative, we present here an approximate method for investigating this transient evolution which is based upon the conservation laws associated with the KdV equation. Initial conditions which form one or two solitons are considered, and the resulting approximate evolution is found to be in good agreement with the numerical solution of the KdV equation. Justification for the approximations employed is also given by way of the linearized inverse scattering solution of the KdV equation. In addition, the final soliton state determined from the approximate equations agrees very well with the final state determined from the exact inverse scattering transform solution
Exp-Function Method for a Generalized MKdV Equation
Directory of Open Access Journals (Sweden)
Yuzhen Chai
2014-01-01
Full Text Available Under investigation in this paper is a generalized MKdV equation, which describes the propagation of shallow water in fluid mechanics. In this paper, we have derived the exact solutions for the generalized MKdV equation including the bright soliton, dark soliton, two-peak bright soliton, two-peak dark soliton, shock soliton and periodic wave solution via Exp-function method. By figures and symbolic computations, we have discussed the propagation characteristics of those solitons under different values of those coefficients in the generalized MKdV equation. The method constructing soliton solutions in this paper may be useful for the investigations on the other nonlinear mathematical physics model and the conclusions of this paper can give theory support for the study of dynamic features of models in the shallow water.
On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation
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Chunyan Huang
2014-01-01
Full Text Available We study the analytic property of the (generalized quadratic derivative Ginzburg-Landau equation (1/2⩽α⩽1 in any spatial dimension n⩾1 with rough initial data. For 1/2<α⩽1, we prove the analyticity of local solutions to the (generalized quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spaces Mp,11-2α(1⩽p⩽∞. For α=1/2, we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data in B˙∞,10(ℝn∩M∞,10(ℝn. The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term.
Maxwell's equations in divergence form for general media with applications to MHD
International Nuclear Information System (INIS)
Van Putten, M.H.P.M.
1991-01-01
Maxwell's equations in media with general constitutive relations are reformulated in covariant form as a system of divergence equations without constraints. Our reformulation enables us to express general electro-magneto-fluid problems as hyperbolic systems in divergence form. We illustrate this method on the MHD problem. In the absence of constraints, a general representation is derived for the characteristic form for first-order systems of quasi-linear partial differential equations in vector fields and scalars. Using this covariant formulation of characteristics, we find that the principle of covariance imposes a very rigid structure on the infinitesimally small amplitude waves in MHD. To demonstrate the power of the reformulation, we study numerically ultra-relativistic wave breaking using the divergence formulation of MHD. (orig.)
New generalized phase shift approach to solve the Helmholtz acoustic wave equation
Abeykoon, Sameera K. (Nee Rajapakshe)
2008-10-01
We have developed and given some proof of concept applications of a new method of solving the Helmholtz wave equation in order to facilitate the exploration of oil and gas. The approach is based on a new way to generalize the "one-way" wave equation, and to impose correct boundary conditions. The full two-way nature of the Helmholtz equation is considered, but converted into a pseudo "one-way" form with a generalized phase shift structure for propagation in the depth z. Two coupled first order partial differential equations in the depth variable z are obtained from the Helmholtz wave equation. Our approach makes use of very simple, standard ideas from differential equations and early ideas on the non-iterative solution of the Lippmann-Schwinger equation in quantum scattering. In addition, a judicious choice of operator splitting is introduced to ensure that only explicit solution techniques are required. This avoids the need for numerical matrix inversions. The initial conditions are more challenging due to the need to ensure that the solution satisfies proper boundary conditions associated with the waves traveling in two directions. This difficulty is resolved by solving the Lippmann-Schwinger integral equation in an explicit, non-iterative fashion. It is solved by essentially "factoring out" the physical boundary conditions, thereby converting the inhomogeneous Lippmann-Schwinger integral equation of the second kind into a Volterra integral equation of the second kind. Due to the special structure of the kernel, which is a consequence of the causal nature of the Green's function in the Lippmann-Schwinger equation, this turns out to be extremely efficient. The coupled first order differential equations will be solved using the "modified Cayley method" developed in Kouri's group some years ago. The Feshbach projection operator technique is used for constructing a solution that is stable with respect to "evanescent" or "non-propagating" waves. This method is
Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces
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Toka Diagana
2012-03-01
Full Text Available In this article, first we introduce and study the concept of $mathbb{S}_{gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy, which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in $mathbb{S}_{gamma}^p$-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient.
Blow-up in nonlinear Schroedinger equations. I. A general review
DEFF Research Database (Denmark)
Juul Rasmussen, Jens; Rypdal, K.
1986-01-01
The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.......The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem....
Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger-Boussinesq Equations
Qiao, Li-Jing; Tang, Sheng-Qiang; Zhao, Hai-Xia
2015-06-01
In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schrödinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schrödinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth soliton and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Supported by National Natural Science Foundation of China under Grant Nos. 11361017, 11161013 and Natural Science Foundation of Guangxi under Grant Nos. 2012GXNSFAA053003, 2013GXNSFAA019010, and Program for Innovative Research Team of Guilin University of Electronic Technology
A generalized hydrodynamical Gurevich-Zybin equation of Riemann type and its Lax type integrability
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M.V. Pavlov
2010-01-01
Full Text Available This paper is devoted to the study of a hydrodynamical equation of Riemann type, generalizing the remarkable Gurevich-Zybin system. This multi-component non-homogenous hydrodynamic equation is characterized by the only characteristic flow velocity. The compatible bi-Hamiltonian structures and Lax type representations of the 3-and 4-component generalized Riemann type hydrodynamical system are analyzed. For the first time the obtained results augment the theory of integrability of hydrodynamic type systems, originally developed only for distinct characteristic velocities in homogenous case.
Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview
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Fernando D. Nobre
2017-01-01
Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.
Latella, Ivan; Pérez-Madrid, Agustín
2013-10-01
The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.
Comparison of stator-mounted permanent-magnet machines based on a general power equation
DEFF Research Database (Denmark)
Chen, Zhe; Hua, Wei; Cheng, Ming
2009-01-01
The stator-mounted permanent-magnet (SMPM) machines have some advantages compared with its counterparts, such as simple rotor, short winding terminals, and good thermal dissipation conditions for magnets. In this paper, a general power equation for three types of SMPM machine is introduced first......, and then, power equations considering the specific topologies are derived. Based on these power equations, theoretical comparisons are carried out between various types of the SMPM machines. In all, eight topologies have been presented and benchmarked. It reveals that the flux switching permanent......-magnet (PM) machine owns higher power density than the flux reversal PM machine and the doubly salient PM machine under same outer diameter. The comparison based on the power equation has established a foundation for optimizing the SMPM machines....
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Energy Technology Data Exchange (ETDEWEB)
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
Directory of Open Access Journals (Sweden)
T. D. Frank
2016-12-01
Full Text Available In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker–Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropriately-defined entropy measures, such as the Boltzmann–Gibbs–Shannon entropy and the Tsallis entropy. In general, the free energy Fokker–Planck equations associated with these generalized entropy measures correspond to nonlinear partial differential equations. Irrespective of the entropy-related nonlinearities occurring in these nonlinear partial differential equations, it is shown that semi-analytical solutions for the stationary probability densities of the active Nambu systems can be obtained provided that the pumping mechanisms of the active systems assume the so-called canonical-dissipative form and depend explicitly only on Nambu invariants. Applications are presented both for purely-dissipative and for active systems illustrating that the proposed framework includes as a special case stochastic equilibrium systems.
Unified Einstein-Virasoro master equation in the general non-linear $\\sigma$ model
De Boer, J
1997-01-01
The Virasoro master equation (VME) describes the general affine-Virasoro construction T=L^{ab}J_aJ_b+iD^a \\dif J_a in the operator algebra of the WZW model, where L^{ab} is the inverse inertia tensor and D^a is the improvement vector. In this paper, we generalize this construction to find the general (one-loop) Virasoro construction in the operator algebra of the general non-linear sigma model. The result is a unified Einstein-Virasoro master equation which couples the spacetime spin-two field L^{ab} to the background fields of the sigma model. For a particular solution L_G^{ab}, the unified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the general affine-Virasoro construction and the VME when the sigma model is taken to be the WZW action. More generally, the unified system describes a space of conformal field theories which is presumably much larger than the sum of the general affine-Virasoro construction and the sigma model w...
Directory of Open Access Journals (Sweden)
Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
Darwish, Mohamed Abdalla; Rzepka, Beata
2014-01-01
We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+). We show that this equation has at least one asymptotically stable solution.
Closure of the gauge algebra, generalized Lie equations and Feynman rules
International Nuclear Information System (INIS)
Batalin, I.A.
1984-01-01
A method is given by which an open gauge algebra can always be closed and even made abelian. As a preliminary the generalized Lie equations for the open group are obtained. The Feynman rules for gauge theories with open algebras are derived by reducing the gauge theory to a non-gauge one. (orig.)
Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation
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Xiaolian Ai
2014-01-01
Full Text Available Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions.
A generalized variational algebra and conserved densities for linear evolution equations
International Nuclear Information System (INIS)
Abellanas, L.; Galindo, A.
1978-01-01
The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach a rigorous characterization of the polynomial kernel of the variational derivative is given. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order. (Auth.)
Generalization of the Biot--Savart law to Maxwell's equations using special relativity
International Nuclear Information System (INIS)
Neuenschwander, D.E.; Turner, B.N.
1992-01-01
Maxwell's equations are obtained by generalizing the laws of magnetostatics, which follow from the Biot--Savart law and superposition, to be consistent with special relativity. The Lorentz force on a charged particle and its rate of energy change also follow by making Newton's second law for a particle in a magnetostatic field consistent with special relativity
Application of Extended Tanh Method to Generalized Burgers-type Equations
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Hamid Panahipour
2012-02-01
Full Text Available In this paper, we show that the extended tanh method can be applied readily to generate exact soliton solutions of generalized forms of Burgers-KdV, Burgers-EW, two-dimensional Burgers-KdV and two-dimensional Burgers-EW equations.
General solution of Poisson equation in three dimensions for disk-like galaxies
International Nuclear Information System (INIS)
Tong, Y.; Zheng, X.; Peng, O.
1982-01-01
The general solution of the Poisson equation is solved by means of integral transformations for Vertical BarkVertical Barr>>1 provided that the perturbed density of disk-like galaxies distributes along the radial direction according to the Hankel function. This solution can more accurately represent the outer spiral arms of disk-like galaxies
Painlevé integrability and a new exact solution of a generalized Hirota-Satsuma equation
Ye, Yujian; di, Yanmei; Song, Junquan
2017-12-01
In this paper, Painlevé integrability of a generalized Hirota-Satsuma (gHS) equation is confirmed by using the Weiss-Tabor-Carnevale (WTC) test. Then, a new exact solution with two arbitrary functions is constructed. Some new soliton structures are illustrated analytically by selecting appropriate functions.
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Maxim Ioan
2009-05-01
Full Text Available In our paper we build a reccurence from generalized Garman equation and discretization of 3-dimensional domain. From reccurence we build an algorithm for computing values of an option based on time, momentan volatility of support and value of support on a
Generalized Hyers-Ulam Stability of Quadratic Functional Equations: A Fixed Point Approach
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Choonkil Park
2008-03-01
Full Text Available Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(2x+y=4f(x+f(y+f(x+yÃ¢ÂˆÂ’f(xÃ¢ÂˆÂ’y in Banach spaces.
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...
Exact travelling wave solutions for the generalized shallow water wave equation
International Nuclear Information System (INIS)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A.; Sabry, R.
2003-01-01
Using homogeneous balance method an auto-Baecklund transformation for the generalized shallow water wave equation is obtained. Then solitary wave solutions are found. Also, modified extended tanh-function method is applied and new exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions
Exact travelling wave solutions for the generalized shallow water wave equation
Energy Technology Data Exchange (ETDEWEB)
Elwakil, S.A.; El-labany, S.K.; Zahran, M.A.; Sabry, R
2003-07-01
Using homogeneous balance method an auto-Baecklund transformation for the generalized shallow water wave equation is obtained. Then solitary wave solutions are found. Also, modified extended tanh-function method is applied and new exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions.
A multivariate family-based association test using generalized estimating equations : FBAT-GEE
Lange, C; Silverman, SK; Xu, [No Value; Weiss, ST; Laird, NM
In this paper we propose a multivariate extension of family-based association tests based on generalized estimating equations. The test can be applied to multiple phenotypes and to phenotypic data obtained in longitudinal studies without making any distributional assumptions for the phenotypic
Czech Academy of Sciences Publication Activity Database
Dilna, N.; Rontó, András
2008-01-01
Roč. 133, č. 4 (2008), s. 435-445 ISSN 0862-7959 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : functional differential equation * Cauchy problem * initial value problem * differential inequality Subject RIV: BA - General Mathematics
Interrelation of alternative sets of Lax-pairs for a generalized nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Iino, Kazuhiro; Ichikawa, Yoshihiko; Wadati, Miki.
1982-05-01
Examination of the inverse scattering transformation schemes for a generalized nonlinear Schroedinger equation reveals the fact that the algorithm of Chen-Lee-Liu gives rise to the Lax-pairs for the squared eigenfunctions of the Wadati-Konno-Ichikawa scheme, which has been formulated as superposition of the Ablowitz-Kaup-Newell-Segur scheme and the Kaup-Newell scheme. (author)
Tables of generalized Airy functions for the asymptotic solution of the differential equation
Nosova, L N
1965-01-01
Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.
A garden of orchids: a generalized Harper equation at quadratic irrational frequencies
Mestel, B. D.; Osbaldestin, A. H.
2004-10-01
We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.
A garden of orchids: a generalized Harper equation at quadratic irrational frequencies
Energy Technology Data Exchange (ETDEWEB)
Mestel, B D [Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA (United Kingdom); Osbaldestin, A H [Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HE (United Kingdom)
2004-10-01
We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.
The generalized hyers-ulam stability of sextic functional equation in ...
African Journals Online (AJOL)
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following generalized sextic functional equation. Df (x, y):= f (mx+ y) +f (mx− y) +f(x+ my) +f(x− my) − (m4+ m2) [f(x+ y+f(x− y)] −2(m6− m4− m2+ 1) [f(x) + f(y)]. in matrix fuzzy normed spaces. Furthermore, using the fixed point method, we also ...
Directory of Open Access Journals (Sweden)
Xin Liang
2018-01-01
Full Text Available In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous advection dispersion processes.
International Nuclear Information System (INIS)
Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.
1994-01-01
The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian structures for KP hierarchies leading to the linear and non-linear W ∞ algebras are derived. The realization of the corresponding generators in terms of two boson currents is presented and it is shown to be related to many integrable models which are bi-Hamiltonian. We can also realize those generators by adding extra currents, coupled in a particular way allowing for instance a description of multi-layered Benney equations or multi- component non-linear Schroedinger equation. In this case we can have a second Hamiltonian bracket structure which violates Jacobi identity. We consider the reduction to one-boson systems leading to KdV and mKdV hierarchies. A Miura transformation relating these two hierarchies is obtained by restricting gauge transformation between corresponding two-boson hierarchies. Connection to Drinfeld-Sokolov approach is also discussed in the SL (2, IR) gauge theory. (author)
International Nuclear Information System (INIS)
Rosenfeld, M.; Kwak, D.; Vinokur, M.
1988-01-01
A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references
Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot
2018-05-01
The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.
Kwon, Young-Sam; Li, Fucai
2018-03-01
In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
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
Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
Directory of Open Access Journals (Sweden)
Kanyuta Poochinapan
2014-01-01
Full Text Available Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.
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...
Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance
Directory of Open Access Journals (Sweden)
Tanki Motsepa
2014-01-01
Full Text Available We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
A general form of the cross energy parameter of equations of state
DEFF Research Database (Denmark)
Coutinho, Joao A. P.; Panayiotis, Vlamos; Kontogeorgis, Georgios
2000-01-01
Phase equilibrium calculations with cubic equations of state are sensitive to mixing and combining rules employed. In this work, we present a suitable general form of the combining rule for the cross-energy parameter, often considered to be the key property in phase equilibrium calculations...... parameter as the variable instead of the commonly employed kij offers useful insight into the behavior of cubic equations of state for a large number of asymmetric systems including gas/alkanes, polymer solutions and blends, and alcohol/alkane and gas/solid systems....
Stability with respect to initial time difference for generalized delay differential equations
Directory of Open Access Journals (Sweden)
Ravi Agarwal
2015-02-01
Full Text Available Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability with initial time difference are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations are employed. Several examples are given to illustrate the theory.
Jasim Mohammed, M; Ibrahim, Rabha W; Ahmad, M Z
2017-03-01
In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.
Stability and bifurcation analysis of a generalized scalar delay differential equation.
Bhalekar, Sachin
2016-08-01
This paper deals with the stability and bifurcation analysis of a general form of equation D(α)x(t)=g(x(t),x(t-τ)) involving the derivative of order α ∈ (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
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Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
A class of doubly periodic wave solutions for the generalized Nizhnik-Novikov-Veselov equation
International Nuclear Information System (INIS)
Peng Yanze
2005-01-01
A general solution including two arbitrary functions is first obtained for the generalized Nizhnik-Novikov-Veselov equation by means of WTC truncation method. A class of doubly periodic wave solutions, which are expressed as rational functions of the Jacobi elliptic functions with different moduli, result from the general solution. Limit cases are considered and some new solitary structures are revealed. The interaction properties of periodic waves are numerically studied and found to be nonelastic. Under long wave limit, a two-dromion solution with the new solution structure is obtained and interaction between the two dromions is completely elastic
A generalized constitutive equation for creep of polymers at multiaxial loading
Altenbach, H.; Altenbach, J.; Zolochevsky, A.
1996-11-01
This paper introduced a unified formulation for generalized deformation models including load dependent effects (2nd order effects). It is given in more detail for stationary creep of isotropic, orthotropic, and anisotropic material behavior. A further generalization of the introduced 6-parameter constitutive equation is possible by coupling creep and damage. These generalizations include the classical theory of creep damage [13]. The proof of the proposed theory is given in [20-22] for special cases with a reduced number of material parameters. The results of calculations show a good agreement with results from multiaxial tests.
Zedan, Hassan A.; El Adrous, Eman
2012-01-01
We introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. ...
The ICVSIE: A General Purpose Integral Equation Method for Bio-Electromagnetic Analysis.
Gomez, Luis J; Yucel, Abdulkadir C; Michielssen, Eric
2018-03-01
An internally combined volume surface integral equation (ICVSIE) for analyzing electromagnetic (EM) interactions with biological tissue and wide ranging diagnostic, therapeutic, and research applications, is proposed. The ICVSIE is a system of integral equations in terms of volume and surface equivalent currents in biological tissue subject to fields produced by externally or internally positioned devices. The system is created by using equivalence principles and solved numerically; the resulting current values are used to evaluate scattered and total electric fields, specific absorption rates, and related quantities. The validity, applicability, and efficiency of the ICVSIE are demonstrated by EM analysis of transcranial magnetic stimulation, magnetic resonance imaging, and neuromuscular electrical stimulation. Unlike previous integral equations, the ICVSIE is stable regardless of the electric permittivities of the tissue or frequency of operation, providing an application-agnostic computational framework for EM-biomedical analysis. Use of the general purpose and robust ICVSIE permits streamlining the development, deployment, and safety analysis of EM-biomedical technologies.
Zhao, L. W.; Du, J. G.; Yin, J. L.
2017-12-01
This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.
International Nuclear Information System (INIS)
Kenyon, A. J.; Wojdak, M.; Ahmad, I.; Loh, W. H.; Oton, C. J.
2008-01-01
We discuss the use of rate equations to analyze the sensitization of erbium luminescence by silicon nanoclusters. In applying the general form of second-order coupled rate-equations to the Si nanocluster-erbium system, we find that the photoluminescence dynamics cannot be described using a simple rate equation model. Both rise and fall times exhibit a stretched exponential behavior, which we propose arises from a combination of a strongly distance-dependent nanocluster-erbium interaction, along with the finite size distribution and indirect band gap of the silicon nanoclusters. Furthermore, the low fraction of erbium ions that can be excited nonresonantly is a result of the small number of ions coupled to nanoclusters
Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation
Hofstrand, A.; Moloney, J. V.
2018-03-01
In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.
Eslami, M.; Mirzazadeh, M.
2014-09-01
The KdV equation plays an important role in describing motions of long waves in shallow water under gravity, one-dimensional nonlinear lattice, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics and other areas. The KdV equation is a well-known model for the description of nonlinear long internal waves in a fluid stratified by both density and current. The aim of this paper is to present solitary wave solutions of the fifth-order KdV equations with time-dependent coefficients. The Kudryashov method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving high-order nonlinear partial differential equations with time-dependent coefficients in mathematical physics.
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.
Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions
Farassat, F.; Brentner, Kenneth S.; Dunn, mark H.
2007-01-01
The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.
Energy Technology Data Exchange (ETDEWEB)
Youn, Sam Son; Lee, Soon Bok [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Kim, Jong Bum; Lee, Hyung Yeon; Yoo, Bong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2000-05-01
The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicably of the present method.
Directory of Open Access Journals (Sweden)
Fariba Khayyati
2016-09-01
Full Text Available Background: To define underlying predictors of tobacco smoking among Iranian Teenagers in a generalized structural equation model. Materials and Methods: In this cross-sectional study, a Generalized Structural Equation Model based on planned behavioral theory was used to explain the relationship among different factors such as demographic factors, subjective norms, and the intention to tobacco and, in turn, intention with tobacco use. The sample consisted of 4,422 high school students, based on census, in East Azerbaijan province, Iran. The questioner was designed adapting to the objectives of study. It was used global youth tobacco survey to design the queries of tobacco use. Results: The model had a good fit on data. Adjusting for age and gender, there was a statistically significant relationship between the intention to consumption and the following factors: working while studying (P
Directory of Open Access Journals (Sweden)
Sukjung Hwang
2015-11-01
Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1
The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations
Roberts, D.
1985-01-01
The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.
Nodal soliton solutions for generalized quasilinear Schrödinger equations
Energy Technology Data Exchange (ETDEWEB)
Deng, Yinbin, E-mail: ybdeng@mail.ccnu.edu.cn; Peng, Shuangjie, E-mail: sjpeng@mail.ccnu.edu.cn [School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079 (China); Wang, Jixiu, E-mail: wangjixiu127@aliyun.com [School of Mathematics and Computer Science, Hubei University of Arts and Science, Xiangyang 441053 (China)
2014-05-15
This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in R{sup N} which arise from plasma physics, fluid mechanics, as well as high-power ultashort laser in matter. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem.
Inelastic collision of two solitons for generalized BBM equation with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Jingdong Wei
2015-06-01
Full Text Available We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H^1(R energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution.
N-Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation
Directory of Open Access Journals (Sweden)
Jian Zhou
2014-01-01
Full Text Available The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK equation. By using Hirota method, the analytic one-, two-, three-, and N-soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media.
Wang, Yu-Zhu; Wei, Changhua
2018-04-01
In this paper, we investigate the initial value problem for the generalized double dispersion equation in R^n. Weighted decay estimate and asymptotic profile of global solutions are established for n≥3 . The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233-254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.
A Generalized FDM for solving the Poisson's Equation on 3D Irregular Domains
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J. Izadian
2014-01-01
Full Text Available In this paper a new method for solving the Poisson's equation with Dirichlet conditions on irregular domains is presented. For this purpose a generalized finite differences method is applied for numerical differentiation on irregular meshes. Three examples on cylindrical and spherical domains are considered. The numerical results are compared with analytical solution. These results show the performance and efficiency of the proposed method.
Directory of Open Access Journals (Sweden)
Ayşe Betül Koç
2014-01-01
Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations
International Nuclear Information System (INIS)
Sczaniecki, L.
1981-02-01
A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)
A General Construction of Linear Differential Equations with Solutions of Prescribed Properties
Czech Academy of Sciences Publication Activity Database
Neuman, František
2004-01-01
Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...... an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making...
Nonlinear Fokker-Planck equations with and without bifurcations and generalized thermostatistics
International Nuclear Information System (INIS)
Shiino, Masatoshi
2002-01-01
Nonlinear Fokker-Planck equations exhibiting bifurcation phenomena are studied within the framework of generalized thermostatistics. Liapunov functions are constructed that take the form of free energy involving the generalized entropies of Tsallis, and H-theorems are shown to hold. The H-theorems ensure, instead of uniqueness of the equilibrium distribution, global stability of the systems. A local stability analysis is conducted, and the second-order variations of the Liapunov functions are computed to find their relevant part whose sign governs the stability of the equilibrium distributions of the systems
Directory of Open Access Journals (Sweden)
M. Eshaghi Gordji
2011-01-01
Full Text Available We prove the generalized Hyers-Ulam-Rassias stability of a general system of Euler-Lagrange-type quadratic functional equations in non-Archimedean 2-normed spaces and Menger probabilistic non-Archimedean-normed spaces.
Nonlinear self-adjointness of the Krichever-Novikov equation
Galiakberova, L. R.; Ibragimov, N. H.
2014-02-01
It is known that the classification of third-order evolutionary equations with the constant separant possessing a nontrivial Lie-Bäcklund algebra (in other words, integrable equations) results in the linear equation, the KdV equation and the Krichever-Novikov equation. The first two of these equations are nonlinearly self-adjoint. This property allows to associate conservation laws of the equations in question with their symmetries. The problem on nonlinear self-adjointness of the Krichever-Novikov equation has not been solved yet. In the present paper we solve this problem and find the explicit form of the differential substitution providing the nonlinear self-adjointness.
On the generalization of statistical thermodynamic functions by a Riccati differential equation.
Peña, J. J.; Rubio-Ponce, A.; Morales, J.
2016-08-01
In this work, we propose a non-linear differential equation of Riccati-type, where the standard partition function Z(T) is taken as its particular solution leading to their generalization Zg(T); from there, other related statistical thermodynamic functions are generalized. As an useful application of our proposal, other thermodynamic functions, namely, the internal energy, heat capacity, Helmholtz free energy and entropy, associated to the model of the ideal monatomic gas in D-dimensions are generalized. According to our results, thermodynamic properties derived from the standard partition functions by means of ordinary statistical mechanics are incomplete. In fact, although asymptotically with the increasing of temperature the generalized statistical thermodynamic functions reduce to the standard ones, these contain an extra term which is dominant at very low temperature indicating that standard findings should be corrected.
Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism
Smirnov, O. M.
2011-07-01
Context. The radio interferometer measurement equation (RIME), especially in its 2 × 2 form, has provided a comprehensive matrix-based formalism for describing classical radio interferometry and polarimetry, as shown in the previous three papers of this series. However, recent practical and theoretical developments, such as phased array feeds (PAFs), aperture arrays (AAs) and wide-field polarimetry, are exposing limitations of the formalism. Aims: This paper aims to develop a more general formalism that can be used to both clearly define the limitations of the matrix RIME, and to describe observational scenarios that lie outside these limitations. Methods: Some assumptions underlying the matrix RIME are explicated and analysed in detail. To this purpose, an array correlation matrix (ACM) formalism is explored. This proves of limited use; it is shown that matrix algebra is simply not a sufficiently flexible tool for the job. To overcome these limitations, a more general formalism based on tensors and the Einstein notation is proposed and explored both theoretically, and with a view to practical implementations. Results: The tensor formalism elegantly yields generalized RIMEs describing beamforming, mutual coupling, and wide-field polarimetry in one equation. It is shown that under the explicated assumptions, tensor equations reduce to the 2 × 2 RIME. From a practical point of view, some methods for implementing tensor equations in an optimal way are proposed and analysed. Conclusions: The tensor RIME is a powerful means of describing observational scenarios not amenable to the matrix RIME. Even in cases where the latter remains applicable, the tensor formalism can be a valuable tool for understanding the limits of such applicability.
International Nuclear Information System (INIS)
Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela
2014-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability. (orig.)
About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models
Directory of Open Access Journals (Sweden)
M. De La Sen
2008-01-01
Full Text Available This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability, the degree of sympathy of the species with the habitat (described by a so-called environment carrying capacity, a penalty term to deal with overpopulation levels, the harvesting (fishing or hunting regulatory quota, or related to use of pesticides when fighting damaging plagues, and the independent consumption which basically quantifies predation. The independent consumption is considered as a part of a more general additive disturbance which also potentially includes another extra additive disturbance term which might be attributed to net migration from or to the habitat or modeling measuring errors. Both potential contributions are included for generalization purposes in the proposed modified generalized Beverton-Holt equation. The properties of stability and boundedness of the solution sequences, equilibrium points of the stationary model, and the existence of oscillatory solution sequences are investigated. A numerical example for a population of aphids is investigated with the theoretical tools developed in the paper.
Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela
2014-05-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.
Bragg reflection in mosaic crystals. I. General solution of the Darwin equations
International Nuclear Information System (INIS)
Sears, V.F.
1996-01-01
The Darwin equations, which describe the multiple Bragg reflection of X-rays or neutrons in a mosaic crystal slab, have previously been solved only for special cases. Here, the complete and exact analytical solution of these equations is obtained for both the Bragg case (reflection geometry) and the Laue case (transmission geometry) with the help of a computer algebra program and it is shown that the resulting general expressions for both the reflectivity R and the transmissivity T can each be expressed in a compact form. It is found, for example, that for a mosaic crystal anomalous absorption occurs only in the Bragg case and not in the Laue case. This is in contrast to the dynamical theory of diffraction, which applies to an ideally perfect crystal, where anomalous absorption (due to the Borrmann effect) is found in both Laue and Bragg cases. With this new general expression for R, the Fankuchen gain is calculated for a crystal of finite thickness, taking correctly into account the effects of both absorption and secondary extinction. General expressions for the optimum crystal thickness are also obtained for both Bragg and Laue cases. In a companion paper, these general results are applied to a detailed numerical calculation of the reflecting properties of various neutron monochromator crystals. (author)
A family of wave equations with some remarkable properties.
da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos
2018-02-01
We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.
A family of wave equations with some remarkable properties
da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos
2018-02-01
We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.
International Nuclear Information System (INIS)
Athanasakis, I E; Papadopoulou, E P; Saridakis, Y G
2014-01-01
Fisher's equation has been widely used to model the biological invasion of single-species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods
Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow
Braun, M. J.; Wheeler, R. L., III; Hendricks, R. C.; Mullen, R. L.
An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.
An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)
International Nuclear Information System (INIS)
Shi Ting-Yu; Ge Hong-Xia; Cheng Rong-Jun
2013-01-01
A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The exact mathematical result of the GFE has been widely used in population dynamics and genetics, where it originated. Many researchers have studied the numerical solutions of the GFE, up to now. In this paper, we introduce an element-free Galerkin (EFG) method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics. Compared with other numerical methods, the EFG method for the GFE needs only scattered nodes instead of meshing the domain of the problem. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. In comparison with the traditional method, numerical solutions show that the new method has higher accuracy and better convergence. Several numerical examples are presented to demonstrate the effectiveness of the method
Generalized conditional symmetries and related solutions of the Grad-Shafranov equation
Energy Technology Data Exchange (ETDEWEB)
Cimpoiasu, Rodica, E-mail: rodicimp@yahoo.com [University of Craiova, 13 A.I.Cuza, 200585 Craiova (Romania)
2014-04-15
The generalized conditional symmetry (GCS) method is applied to a specific case of the Grad–Shafranov (GS) equation, in cylindrical geometry assuming the existence of an axial symmetry. We investigate the conditions that yield the GS equation admitting a special class of second-order GCSs. The determining system for the unknown arbitrary functions is solved in several special cases and new exact solutions, including solitary waves, different in form and structure from the ones obtained using other nonclassical symmetry methods, are pointed out. Several plots of the level sets or flux surfaces of the new solutions as well as surfaces with vanishing flow are displayed. The obtained solutions can be useful for studying plasma equilibrium, transport phenomena, and magnetohydrodynamic stability.
Directory of Open Access Journals (Sweden)
Luis Gavete
2018-01-01
Full Text Available We apply a 3D adaptive refinement procedure using meshless generalized finite difference method for solving elliptic partial differential equations. This adaptive refinement, based on an octree structure, allows adding nodes in a regular way in order to obtain smooth transitions with different nodal densities in the model. For this purpose, we define an error indicator as stop condition of the refinement, a criterion for choosing nodes with the highest errors, and a limit for the number of nodes to be added in each adaptive stage. This kind of equations often appears in engineering problems such as simulation of heat conduction, electrical potential, seepage through porous media, or irrotational flow of fluids. The numerical results show the high accuracy obtained.
On Generalized Self-Duality Equations Towards Supersymmetric Quantum Field Theories Of Forms
Baulieu, L; Baulieu, Laurent; Laroche, Celine
1998-01-01
We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T invariant under a sub-group H of SO(D). Second, the representation for the SO(D) curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the `self-duality' equations can be candidates as gauge functions for SO(D)-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for dimensions greater than 9, for various p-form gauge fields.
Development of Generalized Correlation Equation for the Local Wall Shear Stress
International Nuclear Information System (INIS)
Jeon, Yu Mi; Park, Ju Hwan
2010-06-01
The pressure drop characteristics for a fuel channel are essential for the design and reliable operation of a nuclear reactor. Over several decades, analytical methods have been developed to predict the friction factor in the fuel bundle flows. In order to enhance the accuracy of prediction for the pressure drop in a rod bundle, the influences of a channel wall and the local shear stress distribution should be considered. Therefore, the correlation equation for a local wall shear stress distribution should be developed in order to secure an analytical solution for the friction factor of a rod bundle. For a side subchannel, which has the influence of the channel wall, the local wall shear stress distribution is dependent on the ratio of wall to diameter (W/D) as well as the ratio of pitch to diameter (P/D). In the case that W/D has the same value with P/D, the local shear stress distribution can be simply correlated with the function of angular position for each value of P/D. While in the case where W/D has a different value than P/D, the correlation equation should be developed for each case of P/D and W/D. Therefore, in the present study, the generalized correlation equation of the local wall shear stress distribution was developed for a side subchannel in the case where W/D has a different value than P/D. Consequently, the generalized correlation equation of a local wall shear stress distribution can be represented by the equivalent pitch to diameter ratio, P'/D for the case that P/D and W/D had a different value
PyR@TE. Renormalization group equations for general gauge theories
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Kepner, Gordon R
2010-04-13
The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical
A nonstandard numerical method for the modified KdV equation
Indian Academy of Sciences (India)
Author Affiliations. AYHAN AYDIN1 CANAN KOROGLU2. Department of Mathematics, Atilim University, Ankara 06836, Turkey; Department of Mathematics, Hacettepe University, Beytepe, Ankara 06800, Turkey ...
The integrability of an extended fifth-order KdV equation with Riccati ...
Indian Academy of Sciences (India)
Science Foundation of China (No. 61021004), Shanghai Leading Academic Discipline. Project (No. B412), National High Technology Research and Development Program. (No. 2011AA010101) and Shanghai Knowledge Service Platform for Trustworthy. Internet of Things (No. ZF1213). References. [1] L Matsson, J. Theor.
Kraenkel, R. A.; Senthilvelan, M.; Zenchuk, A. I.
2000-08-01
In this Letter we investigate Lie symmetries of a (2+1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1+1)-dimensional systems of partial differential equations in which one of them turns out to be a (1+1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation.
International Nuclear Information System (INIS)
Batcho, P.F.; Karniadakis, G.E.
1994-01-01
The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures
Nikoloulopoulos, Aristidis K
2016-06-30
The method of generalized estimating equations (GEE) is popular in the biostatistics literature for analyzing longitudinal binary and count data. It assumes a generalized linear model for the outcome variable, and a working correlation among repeated measurements. In this paper, we introduce a viable competitor: the weighted scores method for generalized linear model margins. We weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model. Because the weighted scores method is a parametric method based on likelihood, we propose composite likelihood information criteria as an intermediate step for model selection. The same criteria can be used for both correlation structure and variable selection. Simulations studies and the application example show that our method outperforms other existing model selection methods in GEE. From the example, it can be seen that our methods not only improve on GEE in terms of interpretability and efficiency but also can change the inferential conclusions with respect to GEE. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Hai-Feng Zhang
2013-01-01
Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.
About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models
De La Sen, M.
2008-01-01
Es reproducción del documento publicado en http://dx.doi.org/10.1155/2008/592950 This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called ...
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
Limit cycles for a class of discontinuous generalized Liénard polynomial differential equations
Llibre, Jaume
2013-01-01
Agraïments/Ajudes: The second author is partially supported by a FAPESP-BRAZIL grant 2012/20884-8. Both authors are also supported by the joint project CAPES–MECD grant PHB-2009-0025-PC. We divide R2 in l sectors S1, ..., Sl, with l > 1 even. We define in R2 a discontinuous differential system such that in each sector Sk, for k = 1, ..., l, is defined a smooth generalized Lienard polynomial differential equation ¨x + fi(x) ˙x + gi(x) = 0, i = 1, 2 alternatively, where fi and gi are polynom...
An energy-stable generalized- α method for the Swift–Hohenberg equation
Sarmiento, Adel
2017-11-16
We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.
Are the general equations to predict BMR applicable to patients with anorexia nervosa?
Marra, M; Polito, A; De Filippo, E; Cuzzolaro, M; Ciarapica, D; Contaldo, F; Scalfi, L
2002-03-01
To determine whether the general equations to predict basal metabolic rate (BMR) can be reliably applied to female anorectics. Two hundred and thirty-seven female patients with anorexia nervosa (AN) were divided into an adolescent group [n=43, 13-17 yrs, 39.3+/-5.0 kg, body mass index (BMI) (weight/height) 15.5+/-1.8 kg/m2] and a young-adult group (n=194, 18-40 yrs, 40.5+/-6.1 kg, BMI 15.6+/-1.9 kg/m2). BMR values determined by indirect calorimetry were compared with those predicted according to either the WHO/FAO/UNU or the Harris-Benedict general equations, or using the Schebendach correction formula (proposed for adjusting the Harris-Benedict estimates in anorectics). Measured BMR was 3,658+/-665 kJ/day in the adolescent and 3,907+/-760 kJ/day in the young-adult patients. In the adolescent group, the differences between predicted and measured values were (mean+/-SD) 1,466 529 kJ/day (+44+/-21%) for WHO/FAO/UNU, 1,587+/-552 kJ/day (+47+/-23%) for the Harris-Benedict and -20+/-510 kJ/day for the Schebendach (+1+/-13%), while in the young-adult group the corresponding values were 696+/-570 kJ/day (+24+/-24%), 1,252+/-644 kJ/day (+37+/-27%) and -430+/-640 kJ/day (-9+/-16%). The bias was negatively associated with weight and BMI in both groups when using the WHO/FAO/UNU and Harris-Benedict equations, and with age in the young-adult group for the Harris-Benedict and Schebendach equations. The WHO/FAO/UNU and Harris-Benedict equations greatly overestimate BMR in AN. Accurate estimation is to some extent dependent on individual characteristics such as age, weight or BMI. The Schebendach correction formula accurately predicts BMR in female adolescents, but not in young adult women with AN.
Fawibe, Ademola Emmanuel; Odeigah, Louis O; Saka, Mohammed J
2017-03-06
The increasing importance of pulmonary function testing in diagnosing and managing lung diseases and assessing improvement has necessitated the need for locally derived reference equations from a sample of the general Nigerian population. It was a cross sectional study in which we used linear regression models to obtain equations for reference values and lower limits of normal for spirometric indices in adult Nigerians from a sample of the general population aged 18-65 years (males) and 18-63 years (females). Seven hundred and twenty participants made up of 358 males and 362 females who satisfactorily completed the spirometric measurements using the ATS/ERS reproducibility and acceptability criteria were included in the analysis. The most important predictive variables were height and age. The values of the spirometic indices increase with increasing stature but decrease with increasing age in both sexes. The sex difference in all the indices is also apparent as all the indices, except FEV 1 /FVC, are higher in men than in women. Our values are higher than values obtained from previous studies in Nigeria (except FEV 1 /FVC) but the differences were not statistically significant. This suggests that although the values are increasing, the increase is yet to be significantly different from values obtained using the past equations. The implication of this is that there is need for periodic study to derive new equations so as to recognise when there is significant difference. There was no significant difference between values from our equations and those obtained from study among Ethiopians. Compared to report from Iran, our FVC and FEV 1 values (in males and females) as well as PEFR (in females) are significantly lower. Our values are also lower than values from Poland. We also observed disparities between our values and those of Afro Americans from the GLI study. Our findings show that it is important to always interpret ventilatory function tests in any individual by
Towards a General Equation for the Survival of Microbes Transferred between Solar System Bodies
Fries, M.; Steele, A.
2014-01-01
It should be possible to construct a general equation describing the survival of microbes transferred between Solar System bodies. Such an equation will be useful for constraining the likelihood of transfer of viable organisms between bodies throughout the lifetime of the Solar System, and for refining Planetary Protection constraints placed on future missions. We will discuss the construction of such an equation, present a plan for definition of pertinent factors, and will describe what research will be necessary to quantify those factors. Description: We will examine the case of microbes transferred between Solar System bodies as residents in meteorite material ejected from one body (the "intial body") and deposited on another (the "target body"). Any microbes transferred in this fashion will experience four distinct phases between their initial state on the initial body, up to the point where they colonize the target body. Each of these phases features phenomena capable of reducing or exterminating the initial microbial population. They are: 1) Ejection: Material is ejected from the initial body, imparting shock followed by rapid desiccation and cooling. 2) Transport: Material travels through interplanetary space to the target body, exposing a hypothetical microbial population to extended desiccation, irradiation, and temperature extremes. 3) Infall: Material is deposited on the target body, diminishing the microbial population through shock, mass loss, and heating. 4) Adaptation: Any microbes which survive the previous three phases must then adapt to new chemophysical conditions of the target body. Differences in habitability between the initial and target bodies dominate this phase. A suitable general-form equation can be assembled from the above factors by defining the initial number of microbes in an ejected mass and applying multiplicitive factors based on the physical phenomena inherent to each phase. It should be possible to present the resulting equation
da Silva, Roberto; Drugowich de Felício, José Roberto; Martinez, Alexandre Souto
2012-06-01
The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature β. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q=1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q≠1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.
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Ali H. Bhrawy
2014-01-01
Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
International Nuclear Information System (INIS)
Nepomechie, Rafael I
2013-01-01
An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of this equation describes all the eigenvalues of the transfer matrix of this model. We also propose a generating function for the inhomogeneous T-Q equations of arbitrary spin. (fast track communication)
On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
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M. Eshaghi Gordji
2009-01-01
Full Text Available We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by+f(ax−by=(b(a+b/2f(x+y+(b(a+b/2f(x−y+(2a2−ab−b2f(x+(b2−abf(y where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by+f(ax−by=2a2f(x+2b2f(y for fixed integers a, b with a,b≠0 and a±b≠0.
A theory of solving TAP equations for Ising models with general invariant random matrices
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-03-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida-Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
Application of generalized estimating equations to a study in vitro of radiation sensitivity
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Cologne, J.B.; Carter, R.L.; Fujita, Shoichiro; Ban, Sadayuki.
1993-08-01
We describes an application of the generalized estimating equation (GEE) method (Liang K-Y, Zeger SL: Longitudinal data analysis using generalized linear models. Biometrika 73:13-22, 1986) for regression analyses of correlated Poisson data. As an alternative to the use of an arbitrarily chosen working correlation matrix, we demonstrate the use of GEE with a reasonable model for the true covariance structure among repeated observations within individuals. We show that, under such a split-plot design with large clusters, the asymptotic relative efficiency of GEE with simple (independence or exchangeable) working correlation matrices is rather low. We also illustrate the use of GEE with an empirically estimated model for overdispersion in a large study of radiation sensitivity where cluster size is small and a simple working correlation structure is sufficient. We conclude by summarizing issues and needs for further work concerning efficiency of the GEE parameter estimates in practice. (author)
The Quark-Gluon Plasma Equation of State and the Generalized Uncertainty Principle
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L. I. Abou-Salem
2015-01-01
Full Text Available The quark-gluon plasma (QGP equation of state within a minimal length scenario or Generalized Uncertainty Principle (GUP is studied. The Generalized Uncertainty Principle is implemented on deriving the thermodynamics of ideal QGP at a vanishing chemical potential. We find a significant effect for the GUP term. The main features of QCD lattice results were quantitatively achieved in case of nf=0, nf=2, and nf=2+1 flavors for the energy density, the pressure, and the interaction measure. The exciting point is the large value of bag pressure especially in case of nf=2+1 flavor which reflects the strong correlation between quarks in this bag which is already expected. One can notice that the asymptotic behavior which is characterized by Stephan-Boltzmann limit would be satisfied.
O'Connor, Daniel P; Bray, Molly S; McFarlin, Brian K; Sailors, Mary H; Ellis, Kenneth J; Jackson, Andrew S
2010-10-01
Popular generalized equations for estimating percent body fat (BF%) developed with cross-sectional data are biased when applied to racially/ethnically diverse populations. We developed accurate anthropometric models to estimate dual-energy x-ray absorptiometry BF% (DXA-BF%) that can be generalized to ethnically diverse young adults in both cross-sectional and longitudinal field settings. This longitudinal study enrolled 705 women and 428 men (aged 17-35 yr) for 30 wk of exercise training (3 d·wk(-1) for 30 min·d(-1) of 65%-85% predicted V˙O2max). The distribution of ethnicity was as follows: 37% non-Hispanic white, 29% Hispanic, and 34% African-American. DXA-BF%, skinfold thicknesses, and body mass index (BMI) were collected at baseline and after 15 and 30 wk. Skinfolds, BMI, and race/ethnicity were significant predictors of DXA-BF% in linear mixed model regression analysis. For comparable anthropometric measures (e.g., BMI), DXA-BF% was lower in African-American women and men but higher in Hispanic women compared with non-Hispanic white. Addition of BMI to the skinfold model improved the SEE for women (3.6% vs 4.0%), whereas BMI did not improve prediction accuracy of men (SEE = 3.1%). These equations provide accurate predictions of DXA-BF% for diverse young women and men in both cross-sectional and longitudinal settings. To our knowledge, these are the first published body composition equations with generalizability to multiple time points, and the SEE estimates are among the lowest published in the literature.
Li, DaLei; Lou, Yu-Qing; Esimbek, Jarken
2018-01-01
We study self-similar hydrodynamics of spherical symmetry using a general polytropic (GP) equation of state and derive the GP dynamic Lane-Emden equation (LEE) with a radial inertial force. In reference to Lou & Cao, we solve the GP dynamic LEE for both polytropic index γ = 1 + 1/n and the isothermal case n → +∞; our formalism is more general than the conventional polytropic model with n = 3 or γ = 4/3 of Goldreich & Weber. For proper boundary conditions, we obtain an exact constant solution for arbitrary n and analytic variable solutions for n = 0 and n = 1, respectively. Series expansion solutions are derived near the origin with the explicit recursion formulae for the series coefficients for both the GP and isothermal cases. By extensive numerical explorations, we find that there is no zero density at a finite radius for n ≥ 5. For 0 ≤ n 0 for monotonically decreasing density from the origin and vanishing at a finite radius for c being less than a critical value Ccr. As astrophysical applications, we invoke our solutions of the GP dynamic LEE with central finite boundary conditions to fit the molecular cloud core Barnard 68 in contrast to the static isothermal Bonnor-Ebert sphere by Alves et al. Our GP dynamic model fits appear to be sensibly consistent with several more observations and diagnostics for density, temperature and gas pressure profiles.
Stella, L.; Lorenz, C. D.; Kantorovich, L.
2014-04-01
The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e.g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Westgate, Philip M
2014-06-15
Generalized estimating equations are commonly used to analyze correlated data. Choosing an appropriate working correlation structure for the data is important, as the efficiency of generalized estimating equations depends on how closely this structure approximates the true structure. Therefore, most studies have proposed multiple criteria to select the working correlation structure, although some of these criteria have neither been compared nor extensively studied. To ease the correlation selection process, we propose a criterion that utilizes the trace of the empirical covariance matrix. Furthermore, use of the unstructured working correlation can potentially improve estimation precision and therefore should be considered when data arise from a balanced longitudinal study. However, most previous studies have not allowed the unstructured working correlation to be selected as it estimates more nuisance correlation parameters than other structures such as AR-1 or exchangeable. Therefore, we propose appropriate penalties for the selection criteria that can be imposed upon the unstructured working correlation. Via simulation in multiple scenarios and in application to a longitudinal study, we show that the trace of the empirical covariance matrix works very well relative to existing criteria. We further show that allowing criteria to select the unstructured working correlation when utilizing the penalties can substantially improve parameter estimation. Copyright © 2014 John Wiley & Sons, Ltd.
Cusping, transport and variance of solutions to generalized Fokker-Planck equations
Carnaffan, Sean; Kawai, Reiichiro
2017-06-01
We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.
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Nicola Koper
2012-03-01
Full Text Available Resource selection functions (RSF are often developed using satellite (ARGOS or Global Positioning System (GPS telemetry datasets, which provide a large amount of highly correlated data. We discuss and compare the use of generalized linear mixed-effects models (GLMM and generalized estimating equations (GEE for using this type of data to develop RSFs. GLMMs directly model differences among caribou, while GEEs depend on an adjustment of the standard error to compensate for correlation of data points within individuals. Empirical standard errors, rather than model-based standard errors, must be used with either GLMMs or GEEs when developing RSFs. There are several important differences between these approaches; in particular, GLMMs are best for producing parameter estimates that predict how management might influence individuals, while GEEs are best for predicting how management might influence populations. As the interpretation, value, and statistical significance of both types of parameter estimates differ, it is important that users select the appropriate analytical method. We also outline the use of k-fold cross validation to assess fit of these models. Both GLMMs and GEEs hold promise for developing RSFs as long as they are used appropriately.
Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models
Corrigan, E.; Parini, R.
2017-07-01
The main purpose of this paper is to extend results, which have been obtained previously to describe the classical scattering of solitons with integrable defects of type I, to include the much larger and intricate collection of finite-gap solutions defined in terms of generalised theta functions. In this context, it is generally not feasible to adopt a direct approach, via ansätze for the fields to either side of the defect tuned to satisfy the defect sewing conditions. Rather, essential use is made of the fact that the defect sewing conditions themselves are intimately related to Bäcklund transformations in order to set up a strategy to enable the calculation of the field on one side by suitably transforming the field on the other side. The method is implemented using Darboux transformations and illustrated in detail for the sine-Gordon and KdV models. An exception, treatable by both methods, indirect and direct, is provided by the genus 1 solutions. These can be expressed in terms of Jacobi elliptic functions, which satisfy a number of useful identities of relevance to this problem. There are new features to the solutions obtained in the finite-gap context but, in all cases, if a (multi)soliton limit is taken within the finite-gap solutions previously known results are recovered.
Bogan, Yu A.
2017-10-01
By means of a new approach, the general boundary value problem for a higher order elliptic equation with two independent variables, and a normal set of boundary conditions and simple complex characteristics is reduced to the Fredholm system of integral equations in a bounded region with a smooth boundary.
International Nuclear Information System (INIS)
Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.
1977-12-01
The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)
GENERAL: Symmetry Reductions of a Lax Pair for (2+1)-Dimensional Differential Sawada-Kotera Equation
Zhi, Hong-Yan
2009-05-01
Based on the symbolic computational system — Maple, the similarity reductions of a Lax pair for the (2+1)-dimensional differential Sawada-Kotera (SK) equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair's compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.
Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations
Zhi, Longxiao; Gu, Hanming
2018-03-01
The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.
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Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
Generalized time-dependent Schrödinger equation in two dimensions under constraints
Sandev, Trifce; Petreska, Irina; Lenzi, Ervin K.
2018-01-01
We investigate a generalized two-dimensional time-dependent Schrödinger equation on a comb with a memory kernel. A Dirac delta term is introduced in the Schrödinger equation so that the quantum motion along the x-direction is constrained at y = 0. The wave function is analyzed by using Green's function approach for several forms of the memory kernel, which are of particular interest. Closed form solutions for the cases of Dirac delta and power-law memory kernels in terms of Fox H-function, as well as for a distributed order memory kernel, are obtained. Further, a nonlocal term is also introduced and investigated analytically. It is shown that the solution for such a case can be represented in terms of infinite series in Fox H-functions. Green's functions for each of the considered cases are analyzed and plotted for the most representative ones. Anomalous diffusion signatures are evident from the presence of the power-law tails. The normalized Green's functions obtained in this work are of broader interest, as they are an important ingredient for further calculations and analyses of some interesting effects in the transport properties in low-dimensional heterogeneous media.
An extended step characteristic method for solving the transport equation in general geometries
International Nuclear Information System (INIS)
DeHart, M.D.; Pevey, R.E.; Parish, T.A.
1994-01-01
A method for applying the discrete ordinates method to solve the Boltzmann transport equation on arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the geometrical shape of a mesh element characteristic of a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. By using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. Results for a number of test problems have been compared with solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well as numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN-II computer programs
Lim, S. C.; Teo, L. P.
2009-08-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann-Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion.
Seadawy, Aly R.; Arshad, M.; Lu, Dianchen
2017-04-01
In this article, our aim is to further extend the applications of modified extended direct algebraic method on new coupled systems, which have many important applications in mathematical physics. many exact solutions out of which some are new in different forms such as soliton, solitary wave, periodic, elliptic function solutions of new coupled KdV and new coupled Zakharov-Kuznetsov (ZK) systems are constructed by employing this method. The constructed exact solutions are also presented graphically. The modulation instability is utilized to discuss the stability of obtained solutions. All solutions are stable and exact solutions. The obtained results show that the modified extended method is general and effective. Furthermore, many other new coupled systems arising in mathematical physics can also be solved by this powerful and effective method.
Lee, C. T.; Lee, C. C.
2015-04-01
This paper introduces a systematic approach to investigate a higher order nonlinear dispersive wave equation for modeling different wave modes. We present both the conventional KdV-type soliton and anomaly type solitons for the equation. We also show the conservation laws and Hamiltonian structures for the equation. Our results suggest that the underlying equation has more interacting soliton phenomena than one would have known for the classical KdV and Boussinesq equation.
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Pelinovsky, Dmitry E.; Yang Jianke
2005-01-01
We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons
O, Hyong-Chol; Jo, Jong-Jun; Kim, Ji-Sok
2016-02-01
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and study such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results can be used in pricing real defaultable bonds under consideration of existence of discrete coupons or taxes on coupons.
International Nuclear Information System (INIS)
Ozaki, Hideaki
2004-01-01
Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We employ the derivative expansion and take in up to the second-order term, i.e., one-order higher than the gradient approximation. After constructing self-energy resumed propagator, we formulated two kinds of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the 'bare' number density function, and the second one is formulated on the basis of 'physical' number density function. In the course of construction of the second framework, the generalized Boltzmann equations directly come out, which describe the evolution of the system. (author)
Accelerating the convergence of path integral dynamics with a generalized Langevin equation
Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele
2011-02-01
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Accelerating the convergence of path integral dynamics with a generalized Langevin equation.
Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele
2011-02-28
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Tamellini, L.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
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Akanda Md. Abdus Salam
2017-03-01
Full Text Available Individual heterogeneity in capture probabilities and time dependence are fundamentally important for estimating the closed animal population parameters in capture-recapture studies. A generalized estimating equations (GEE approach accounts for linear correlation among capture-recapture occasions, and individual heterogeneity in capture probabilities in a closed population capture-recapture individual heterogeneity and time variation model. The estimated capture probabilities are used to estimate animal population parameters. Two real data sets are used for illustrative purposes. A simulation study is carried out to assess the performance of the GEE estimator. A Quasi-Likelihood Information Criterion (QIC is applied for the selection of the best fitting model. This approach performs well when the estimated population parameters depend on the individual heterogeneity and the nature of linear correlation among capture-recapture occasions.
Vidal-Sallé, Emmanuelle; Chassagne, Pierre
2007-06-01
This paper presents a nonlinear viscoelastic orthotropic constitutive equation applied to wood material. The proposed model takes into account mechanical and mechanosorptive creep via a 3D stress ratio and moisture change rate for a cylindrical orthotropic material. Orthotropic frame is based on the grain direction (L), radial (R) and hoop (T) directions, which are natural wood directions. Particular attention is taken to ensure the model to fulfill the necessary dissipation conditions. It is based on a rheological generalized Maxwell model with two elements in parallel in addition with a single linear spring taking into account the long term response. The proposed model is implemented in the finite element code ABAQUS/Standard® via a user subroutine UMAT and simple example is shown to demonstrate the capability of the proposed model. Future works would deal with damage and fracture prediction for wooden structures submitted to climate variations and mechanical loading.
Dark soliton pair of ultracold Fermi gases for a generalized Gross-Pitaevskii equation model.
Wang, Ying; Zhou, Yu; Zhou, Shuyu; Zhang, Yongsheng
2016-07-01
We present the theoretical investigation of dark soliton pair solutions for one-dimensional as well as three-dimensional generalized Gross-Pitaevskii equation (GGPE) which models the ultracold Fermi gas during Bardeen-Cooper-Schrieffer-Bose-Einstein condensates crossover. Without introducing any integrability constraint and via the self-similar approach, the three-dimensional solution of GGPE is derived based on the one-dimensional dark soliton pair solution, which is obtained through a modified F-expansion method combined with a coupled modulus-phase transformation technique. We discovered the oscillatory behavior of the dark soliton pair from the theoretical results obtained for the three-dimensional case. The calculated period agrees very well with the corresponding reported experimental result [Weller et al., Phys. Rev. Lett. 101, 130401 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.130401], demonstrating the applicability of the theoretical treatment presented in this work.
General solution of the Dirac equation for quasi-two-dimensional electrons
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Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Generalized finite-difference time-domain schemes for solving nonlinear Schrodinger equations
Moxley, Frederick Ira, III
The nonlinear Schrodinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, higher-order accurate and stable schemes are often required to solve a large-scale linear system. Conversely, spectral methods via Fourier transforms for space discretization coupled with Runge-Kutta methods for time stepping become too complex when applied to multidimensional problems. One of the most prevalent challenges in developing these numerical schemes is that they satisfy the conservation laws. The objective of this dissertation was to develop a higher-order accurate and simple finite difference scheme for solving the NLSE. First, the wave function was split into real and imaginary components and then substituted into the NLSE to obtain coupled equations. These components were then approximated using higher-order Taylor series expansions in time, where the derivatives in time were replaced by the derivatives in space via the coupled equations. Finally, the derivatives in space were approximated using higher-order accurate finite difference approximations. As such, an explicit and higher order accurate finite difference scheme for solving the NLSE was obtained. This scheme is called the explicit generalized finite-difference time-domain (explicit G-FDTD). For purposes of completeness, an implicit G-FDTD scheme for solving the NLSE was also developed. In this
Validation of generalized anthropometric equations for body density estimate in military women
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José Fernandes Filho
2006-03-01
Full Text Available The validation of the equations for predicting body density allows verifying the accuracy of estimated body density on a population different from that used in the original equation. In this way, the purpose of this study was to verify the validity of six generalized prediction equations of body density in military women. The sample was composed by 107 military women, with ages varying from 18 to 45 years (30.48 ± 6.40 years, total body mass of 58.60 ± 6.99kg and stature of 164.78 ± 5.81cm. Six skinfolds and one circumference were measured according to the selected equations. To estimate body density, the indirect method of hydrostatic densitometry (validation criterion and the doubly indirect methods of prediction equations by Jackson et al. (1980, 3 skinfolds, and by Petroski (1995 were used. Mean body density measured by hydrostatic densitometry was 1.046058 ± 0.011001 g/ml. To validate the equations Pearson´s linear correlations were used and the results were considered acceptable (r = 0.71 to 0.76. When comparing predicted to measured density, it was found that only the quadratic equation using 5 skinfolds by Petroski (1995 did not show any statistical difference (t = 0.573 to p value = 0.568. The correlation coefficient for this equation was r = 0.74, which is also considered acceptable. Total error was ET =0.0075 g/ml and the standard error of the estimate was EPE = 0.0066 g/ml, both onsidered very good values for the validation process. These results permit the conclusion that the generalized quadratic equation by Petroski (1995, using 5 skinfolds (subscapular, triceps, suprailiac, abdominal and medial calf is concurrently valid for estimating body density among military women. RESUMO A validação de equações de predição da densidade corporal permite verificar se os resultados preditos podem estimar, de forma coerente, a densidade corporal de uma população diferente da que originou as equações. Diante desta afirmativa, o
Affine Malcev algebra and N=8 KdV
Energy Technology Data Exchange (ETDEWEB)
Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas]. E-mail: toppan@cbpf.br
2001-09-01
In this talk I report the results of two recent papers concerning the realization of the N = 8 supersymmetry from the division algebra of the octonions. At first I discuss a Sugawara realization for the 'Non-associative N = 8 SCA' in terms of a superaffinization of the algebra of octonions. Next, I discuss the fact that the N = 8 SCA provides a generalized Poisson brackets structure for an N = 8 super-KdV. (author)
Stumpf, H.
2003-01-01
Generalized de Broglie-Bargmann-Wigner (BBW) equations are relativistically invariant quantum mechanical many body equations with nontrivial interaction, selfregularization and probability interpretation. Owing to these properties these equations are a suitable means for describing relativistic bound states of fermions. In accordance with de Broglie's fusion theory and modern assumptions about the partonic substructure of elementary fermions, i.e., leptons and quarks, the three-body generalized BBW-equations are investigated. The transformation properties and quantum numbers of the three-parton equations under the relevant group actions are elaborated in detail. Section 3 deals with the action of the isospin group SU(2), a U(1) global gauge group for the fermion number, the hypercharge and charge generators. The resulting quantum numbers of the composite partonic systems can be adapted to those of the phenomenological particles to be described. The space-time transformations and in particular rotations generated by angular momentum operators are considered in Section 4. Based on the compatibility of the BBW-equations and the group theoretical constraints, in Sect. 5 integral equations are formulated in a representation with diagonal energy and total angular momentum variables. The paper provides new insight into the solution space and quantum labels of resulting integral equations for three parton states and prepares the ground for representing leptons and quarks as composite systems.
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Md. Nur Alam
2014-03-01
Full Text Available The new approach of generalized (G′/G-expansion method is significant, powerful and straightforward mathematical tool for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs arise in the field of engineering, applied mathematics and physics. Dispersive effects due to microstructure of materials combined with nonlinearities give rise to solitary waves. In this article, the new approach of generalized (G′/G-expansion method has been applied to construct general traveling wave solutions of the strain wave equation in microstructured solids. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering fields.
Ren, Jiagang; Wu, Jing; Zhang, Hua
2015-01-01
In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.
International Nuclear Information System (INIS)
Edgar, S.B.
1990-01-01
The structures of the N.P. and G.H.P formalisms are reviewed in order to understand and demonstrate the important role played by the commutator equations in the associated integration procedures. Particular attention is focused on how the commutator equations are to be satisfied, or checked for consistency. It is shown that Held's integration method will only guarantee genuine solutions of Einstein's equations when all the commutator equations are correctly and completely satisfied. (authors)
Euler-Lagrange equations for holomorphic structures on twistorial generalized Kähler manifolds
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Zeki Kasap
2016-02-01
showing motion modeling partial di¤erential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the Maple software. Additionally, of the implicit solution of the equations to be drawn the graph.
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
International Nuclear Information System (INIS)
Zawaideh, E.S.
1985-01-01
A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime
Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.
2018-03-01
We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.
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Thomson Peter C
2003-05-01
Full Text Available Abstract To date, most statistical developments in QTL detection methodology have been directed at continuous traits with an underlying normal distribution. This paper presents a method for QTL analysis of non-normal traits using a generalized linear mixed model approach. Development of this method has been motivated by a backcross experiment involving two inbred lines of mice that was conducted in order to locate a QTL for litter size. A Poisson regression form is used to model litter size, with allowances made for under- as well as over-dispersion, as suggested by the experimental data. In addition to fixed parity effects, random animal effects have also been included in the model. However, the method is not fully parametric as the model is specified only in terms of means, variances and covariances, and not as a full probability model. Consequently, a generalized estimating equations (GEE approach is used to fit the model. For statistical inferences, permutation tests and bootstrap procedures are used. This method is illustrated with simulated as well as experimental mouse data. Overall, the method is found to be quite reliable, and with modification, can be used for QTL detection for a range of other non-normally distributed traits.
Baczewski, Andrew D.; Bond, Stephen D.
2013-07-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Generalized method of moments: A novel discretization technique for integral equations
Nair, Naveen V.
Integral equation formulations to solve electromagnetic scattering and radiation problems have existed for over a century. The method of moments (MoM) technique to solve these integral equations has been in active use for over 40 years and has become one of the cornerstones of electromagnetic analysis. It has been successfully employed in a wide variety of problems ranging from scattering and antenna analysis to electromagnetic compatibility analysis to photonics. In MoM, the unknown quantity (currents or fields) is represented using a set of basis functions. This representation, together with Galerkin testing, results in a set of equations that may then be solved to obtain the coefficients of expansion. The basis functions are typically constructed on a tessellation of the geometry and its choice is critical to the accuracy of the final solution. As a result, considerable energy has been expended in the design and construction of optimal basis functions. The most common of these functions in use today are the Rao-Wilton-Glisson (RWG) functions that have become the de-facto standard and have also spawned a set of higher order complete and singular variants. However, their near-ubiquitous popularity and success notwithstanding, they come with certain important limitations. The chief among these is the intimate marriage between the underlying triangulation of the geometry and the basis function. While this coupling maintains continuity of the normal component of these functions across triangle boundaries and makes them very easy to implement, this also implies an inherent restriction on the kind of basis function spaces that can be employed. This thesis aims to address this issue and provides a novel framework for the discretization of integral equations that demonstrates several significant advantages. In this work, we will describe a new umbrella framework for the discretization of integral equations called the Generalized Method of Moments (GMM). We will show that
Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations
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Laurent Delisle
2012-08-01
Full Text Available We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
International Nuclear Information System (INIS)
Xu Tianzhou; Rassias, John Michael; Xu Wanxin
2010-01-01
We establish some stability results concerning the general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces. In addition, we establish some results of approximately general mixed additive-cubic mappings in non-Archimedean fuzzy normed spaces. The results improve and extend some recent results.
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DeHart, Mark David [Texas A & M Univ., College Station, TX (United States)
1992-12-01
A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.
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Soloviev Igor A.
2016-01-01
Full Text Available Stochastic differential equations are proposed on the basis of generalized Fokker-Planck-Kolmogorov equation. From the statements of boundary and initial value problems for probabilistic density, dispersion and differential entropy the conditions for stability of solutions and changes in scenarios of development of random phenomena of heat and nuclear particle transfer are obtained. [Projekat Ministartsva nauke Republike Srbije, br. 174005 i br. 174024
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Chih-Chun Hsieh
2012-01-01
Full Text Available This study performs a precipitation examination of the phase using the general diffusion equation with comparison to the Vitek model in dissimilar stainless steels during multipass welding. Experimental results demonstrate that the diffusivities (, , and of Cr, Ni, and Si are higher in -ferrite than (, , and in the phase, and that they facilitate the precipitation of the σ phase in the third pass fusion zone. The Vitek diffusion equation can be modified as follows: .
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Haotao Cai
2017-01-01
Full Text Available We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.
New Similarity Reduction Solutions for the (2+1)-Dimensional Nizhnik—Novikov—Veselov Equation
Zhi, Hong-Yan
2013-03-01
In this paper, some new formal similarity reduction solutions for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. Firstly, we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced equation, three types of similarity solutions are derived, such as multi-soliton like solutions, variable separations solutions, and KdV type solutions.
International Nuclear Information System (INIS)
Gelinas, R.J.; Doss, S.K.; Miller, K.
1981-01-01
The moving finite element (MFE) method has been reduced to practice in the automatic solution program DYLA for general systems of transient partial differential equations (PDEs) in 1-D. Several test examples are presented which illustrate the unique node movement and systematic control features which are intrinsic in the MFE method. Computational dilemmas of numerical diffusion, Gibbs overshooting and undershooting, zone tangling, and grid remap (or re-connection) aliasing, which occur frequently in conventional PDE methods, are essentially eliminated in the MFE mehtod. Arbitrarily large gradients (or shocks) can be solved with extremely high resolution and accuracy for non-coincident, or even counterdirected, propagating wavefronts. Boundary layers of arbitrarily small dimensions are solved with high accuracy simultaneously with the large-scale structures in reactive and non-reactive fluid calculations. The MFE method requires a small fraction of the grid nodes which are used in conventional PDE solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate PDE solutions on entire problem domains. Courant--Friedrichs--Lewy time-step limits are exceeded by wide margins (by factors of two to several thousand). Finally, the extension of the MFE method to 2-D is briefly discussed
Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly
Dong, J. M.; Zhang, Y. H.; Zuo, W.; Gu, J. Z.; Wang, L. J.; Sun, Y.
2018-02-01
The Wigner isobaric multiplet mass equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question of the origin of the Nolen-Schiffer anomaly (NSA) found in the Coulomb displacement energy of mirror nuclei. We find that the naturally emerged CSB term in GIMME is largely responsible for explaining the NSA.
A Kronecker product variant of the FACR method for solving the generalized Poisson equation
Hendrickx, Jef; van Barel, Marc
2002-03-01
We present a fast direct method for the solution of a linear system , where M is a block tridiagonal Toeplitzmatrix with A on the diagonal and T on the two subdiagonals (A and T commute). Such matrices are obtained from a finite difference approximation to Poisson's equation with nonconstant coefficients in one direction (among others). The new method is called KPCR(l)-method and begins with l steps of cyclic reduction after which the remaining system is solved by a Kronecker product method. For an appropriate choice of l the asymptotic operation count for an n×n grid is O(n2 log2 log2 n), which is faster than either cyclic reduction or the Kronecker product method itself. The algorithm is similar to and has the same complexity as the FACR(l)-algorithm, which is a combination of cyclic reduction and Fourier analysis (or matrix decomposition). However, the FACR(l)-algorithm only reaches this complexity if A (and T) can be diagonalized by a fast transformation, where the new method is fast for every banded A and T. Moreover, the KPCR(l)-method can be easily generalized to the case where A and T do not commute.
Energy Technology Data Exchange (ETDEWEB)
Tinsley, B.M.
1981-11-15
Three main points are made in this paper: (1) It is shown that, contrary to common belief, extrapolation of standard data suggests that ''stars'' below 0.1 M/sub sun/ are most unlikely to add significantly to the local surface density. (2) The general equations of chemical evolution are revised to separate living stars explicitly from dead remnants; it is then easier to incorporate constraints based on star counts, etc., consistently into models. (3) A schematic, analytic model is proposed for the solar neighborhood: there is an initial burst of (halo) star formation, followed by a lull with no star formation, and then by evolution of the disk itself with constant rates of star formation and infall. This model crudely represents the outer regions of some dynamical models for disk formation, and it is related to two-era models by many authors, and to a recent disk model by Twarog. A new specific model is proposed, with empirical constraints based on point (1) and on Twarog's stellar ages and metallicities. Predictions of the model agree with nucleochronological ages of the elements and with the stellar age-metallicity relation.
Soliton stability criterion for generalized nonlinear Schrödinger equations.
Quintero, Niurka R; Mertens, Franz G; Bishop, A R
2015-01-01
A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p'(v)0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed.
McDonagh, J L; van Mourik, T; Mitchell, J B O
2015-11-01
In this work we make predictions of several important molecular properties of academic and industrial importance to seek answers to two questions: 1) Can we apply efficient machine learning techniques, using inexpensive descriptors, to predict melting points to a reasonable level of accuracy? 2) Can values of this level of accuracy be usefully applied to predicting aqueous solubility? We present predictions of melting points made by several novel machine learning models, previously applied to solubility prediction. Additionally, we make predictions of solubility via the General Solubility Equation (GSE) and monitor the impact of varying the logP prediction model (AlogP and XlogP) on the GSE. We note that the machine learning models presented, using a modest number of 2D descriptors, can make melting point predictions in line with the current state of the art prediction methods (RMSE≥40 °C). We also find that predicted melting points, with an RMSE of tens of degrees Celsius, can be usefully applied to the GSE to yield accurate solubility predictions (log10 S RMSE<1) over a small dataset of drug-like molecules. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation
Rossi, Mariana; Kapil, Venkat; Ceriotti, Michele
2018-03-01
Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. We develop quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, and show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modeling of vibrational dynamics of molecules, liquids, and solids.
Generalized estimating equations to evaluate the dependence of lifetime in confined Africanized bees
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Carla Guimarães Brighenti
2016-01-01
Full Text Available Research with honeybee needs experimentation in cages. In laboratory bioassays to assess the lifetime of Apis mellifera, each sampling unit contained a group of bees confined in a cage. Since current is a longitudinal analysis to assess the effect of time dependence on the survival of bees fed on different diets, generalized estimating equations applied to the logit model were used to assess the viability of incorporating correlation structures that related the survival of bees observed in each cage over time, so that the mortality of a given number of bees might influence the mortality of the others. Results showed that there was time dependence between the observations of bees inside the cages, and the working correlation matrix adjusted by longitudinal analysis was ‘Non-stationary-M-dependent’ in which the number of periods of dependence must be specified. Correlations are not the same for all observations of all periods. The solution with granulated sugar and the solution with granulated sugar enriched with lemon juice proved to have the lowest level of mortality during the assessed periods. Assay showed that bees tended to die during daytime.
Comparison of generalized Reynolds and Navier Stokes equations for flow of a power law fluid
Mullen, R. L.; Prekwas, A.; Braun, M. J.; Hendricks, R. C.
1987-01-01
This paper compares a finite element solution of a modified Reynolds equation with a finite difference solution of the Navier-Stokes equation for a power law fluid. Both the finite element and finite difference formulation are reviewed. Solutions to spiral flow in parallel and conical geometries are compared. Comparison with experimental results are also given. The effects of the assumptions used in the Reynolds equation are discussed.
Non-linear partial differential equations an algebraic view of generalized solutions
Rosinger, Elemer E
1990-01-01
A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen
International Nuclear Information System (INIS)
Sieniutycz, S.; Berry, R.S.
1993-01-01
A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ''To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy
Zhang, Yiwei; Xu, Zhiyuan; Shen, Xiaotong; Pan, Wei
2014-08-01
There is an increasing need to develop and apply powerful statistical tests to detect multiple traits-single locus associations, as arising from neuroimaging genetics and other studies. For example, in the Alzheimer's Disease Neuroimaging Initiative (ADNI), in addition to genome-wide single nucleotide polymorphisms (SNPs), thousands of neuroimaging and neuropsychological phenotypes as intermediate phenotypes for Alzheimer's disease, have been collected. Although some classic methods like MANOVA and newly proposed methods may be applied, they have their own limitations. For example, MANOVA cannot be applied to binary and other discrete traits. In addition, the relationships among these methods are not well understood. Importantly, since these tests are not data adaptive, depending on the unknown association patterns among multiple traits and between multiple traits and a locus, these tests may or may not be powerful. In this paper we propose a class of data-adaptive weights and the corresponding weighted tests in the general framework of generalized estimation equations (GEE). A highly adaptive test is proposed to select the most powerful one from this class of the weighted tests so that it can maintain high power across a wide range of situations. Our proposed tests are applicable to various types of traits with or without covariates. Importantly, we also analytically show relationships among some existing and our proposed tests, indicating that many existing tests are special cases of our proposed tests. Extensive simulation studies were conducted to compare and contrast the power properties of various existing and our new methods. Finally, we applied the methods to an ADNI dataset to illustrate the performance of the methods. We conclude with the recommendation for the use of the GEE-based Score test and our proposed adaptive test for their high and complementary performance. Copyright © 2014 Elsevier Inc. All rights reserved.
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
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Mehta, M; Dancer, K A; Gould, M D; Links, J [Centre for Mathematical Physics, School of Physical Sciences, University of Queensland, Brisbane 4072 (Australia)
2006-01-06
The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U{sub q}[gl(m vertical bar n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U{sub q}[osp(m vertical bar n)]. In this manner, we obtain generalizations of the Perk-Schultz model. (letter to the editor)
International Nuclear Information System (INIS)
García-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.
2012-01-01
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schrödinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
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Huanhe Dong
2014-01-01
Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
International Nuclear Information System (INIS)
Zawaideh, E.; Najmabadi, F.; Conn, R.W.
1986-01-01
A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)
The generalized cosmic equation of state. A revised study with cosmological standard rulers
Energy Technology Data Exchange (ETDEWEB)
Ma, Yubo [Shanxi Datong University, School of Physics, Datong (China); Zhang, Jia [Weinan Normal University, Department of Physics, School of Mathematics and Physics, Weinan, Shanxi (China); Cao, Shuo; Zheng, Xiaogang; Xu, Tengpeng; Qi, Jingzhao [Beijing Normal University, Department of Astronomy, Beijing (China)
2017-12-15
In this paper, the generalized equation of state (GEoS) for dark energy (w{sub β} = w{sub 0} - w{sub β}[(1+z){sup -β} - 1]/β) is investigated with the combined standard ruler data from the observations of intermediate-luminosity radio quasars, galaxy clusters, BAO and CMB. The constraint results show that the best-fit EoS parameters are w{sub 0} = -0.94{sup +0.57}{sub -0.41}, w{sub β} = -0.17{sup +2.45}{sub -4.81} and β = -1.42 (with a lower limit of β > -2.70 at 68.3% C.L.), which implies that at early times the dark energy vanishes. In the framework of nine truncated GEoS models with different β parameters, our findings present very clear evidence disfavoring the case that dark energy always dominates over the other material components in the early universe. Moreover, stringent constraints can be obtained in combination with the latest measurements of Hubble parameter at different redshifts: w{sub 0} = -1.01{sup +0.56}{sub -0.31}, w{sub β} = 0.01{sup +2.33}{sub -4.52} and β = -0.42 (with a lower limit of β > -2.40 at 68.3% C.L.). Finally, the results obtained from the transition redshift (z{sub t}) and Om(z) diagnostic indicate that: (1) The above constraints on the GEoS model agree very well with the transition redshift interval 0.49 ≤ z{sub t} ≤ 0.88 within 1σ error region. (2) At the current observational level, the GEoS model is practically indistinguishable from ΛCDM, although a small deviation from ΛCDM cosmology is present in the combined standard ruler data. (orig.)
Exact solutions of (3â¯+â¯1-dimensional generalized KP equation arising in physics
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Syed Tauseef Mohyud-Din
Full Text Available In this work, we have obtained some exact solutions to (3â¯+â¯1-dimensional generalized KP Equation. The improved tanÏ(Î¾2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanÏ(Î¾2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3â¯+â¯1-dimensional generalized KP equation
International Nuclear Information System (INIS)
Jakubov, T.S.; Mainwaring, D.E.
2006-01-01
In the present work a generalized Kelvin equation for a fluid confined in thick-walled cylindrical capillary is developed. This has been accomplished by including the potential energy function for interaction between a solid wall of a capillary and a confined fluid into the Kelvin equation. Using the Lennard-Jones 12-6 potential, an explicit form of the potential energy functions as expressed by hypergeometrical functions have been derived-firstly, for the interaction between a solid wall and a test atom placed at an arbitrary point in a long open-end capillary, and thereafter for the body-body interaction between the solid wall and a confined Lennard-Jones fluid. Further, this generalized Kelvin equation has been applied to detailed description hysteresis phenomena in such capillaries. All numerical calculations have been carried out for the model argon-graphite system at 90 K
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Milena Netka
2009-01-01
Full Text Available The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.
Kaufman, Allan N.
1987-01-01
The covariant coupled equations for plasma dynamics and the Maxwell field are expressed as a phase-space-Lagrangian action principle. The linear interaction is transformed to the bilinear beat Hamiltonian by a gauge-invariant Lagrangian Lie transform. The result yields the generalized linear susceptibility directly.
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Tian Zhou Xu
2012-01-01
Full Text Available The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation in n-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.
International Nuclear Information System (INIS)
Prykarpatsky, Anatoliy K; Artemovych, Orest D; Popowicz, Ziemowit; Pavlov, Maxim V
2010-01-01
A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic equations at N = 3, 4 is devised. The approach is also applied to studying the Lax-type integrability of the well-known Korteweg-de Vries dynamical system.
Czech Academy of Sciences Publication Activity Database
Pekár, S.; Brabec, Marek
2018-01-01
Roč. 124, č. 2 (2018), s. 86-93 ISSN 0179-1613 Institutional support: RVO:67985807 Keywords : correlated data * generalized estimating equations * marginal model * regression models * statistical analysis Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.398, year: 2016
On large-time energy concentration in solutions to the Navier-Stokes equations in general domains
Czech Academy of Sciences Publication Activity Database
Skalák, Zdeněk
2011-01-01
Roč. 91, č. 9 (2011), s. 724-732 ISSN 0044-2267 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.863, year: 2011
International Nuclear Information System (INIS)
Dobrev, V. K.; Stoimenov, S.
2010-01-01
The singular vectors in Verma modules over the Schroedinger algebra s(n) in (n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schroedinger algebras are constructed.
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Leonid Berezansky
2003-02-01
Full Text Available We study a scalar delay differential equation with a bounded distributed delay, $$ dot{x}(t+ int_{h(t}^t x(s,d_s R(t,s - int_{g(t}^t x(s,d_s T(t,s=0, $$ where $R(t,s$, $T(t,s$ are nonnegative nondecreasing in $s$ for any $t$, $$ R(t,h(t=T(t,g(t=0, quad R(t,s geq T(t,s. $$ We establish a connection between non-oscillation of this differential equation and the corresponding differential inequalities, and between positiveness of the fundamental function and the existence of a nonnegative solution for a nonlinear integral inequality that constructed explicitly. We also present comparison theorems, and explicit non-oscillation and oscillation results. In a separate publication (part II, we will consider applications of this theory to differential equations with several concentrated delays, integrodifferential, and mixed equations.
Esposito, Elena
2012-01-01
2010 - 2011 The aim of this research is the construction and the analysis of new families of numerical methods for the integration of special second order Ordinary Differential Equations (ODEs). The modeling of continuous time dynamical systems using second order ODEs is widely used in many elds of applications, as celestial mechanics, seismology, molecular dynamics, or in the semidiscretisation of partial differential equations (which leads to high dimensional systems and ...
Singh, Pawan P; Maier, Dirk E; Cushman, John H; Haghighi, Kamyar; Corvalan, Carlos
2004-07-01
Within the framework of continuum mechanics, Singh et al. developed an integro-differential equation, which applies to both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport in swelling biological systems. A dimensionless form of the equation was obtained and transformed from moving Eulerian to the stationary Lagrangian coordinates. Here a solution scheme for the transport equation is developed to predict moisture transport and viscoelastic stresses in spheroidal biopolymeric materials. The equation was solved numerically and results used for predicting drying and sorption curves, moisture profiles, and viscoelastic stresses in soybeans. The Lagrangian solution was obtained by assembling together several schemes: the finite element method was used to discretize the equation in space; non-linearity was addressed using the Newton-Raphson method; the Volterra term was handled via a time integration scheme of Patlashenko et al. and the Galerkin rule was used to solve the time-differential term. The solution obtained in Lagrangian coordinates was transformed back to the Eulerian coordinates. In part II of this sequence we present the numerical results.
Infinite sets of conservation laws for linear and non-linear field equations
International Nuclear Information System (INIS)
Niederle, J.
1984-01-01
The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation
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Guo Chun Wen
2009-05-01
Full Text Available This article concerns the oblique derivative problems for second-order quasilinear degenerate equations of mixed type with several characteristic boundaries, which include the Tricomi problem as a special case. First we formulate the problem and obtain estimates of its solutions, then we show the existence of solutions by the successive iterations and the Leray-Schauder theorem. We use a complex analytic method: elliptic complex functions are used in the elliptic domain, and hyperbolic complex functions in the hyperbolic domain, such that second-order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients. An application of the complex analytic method, solves (1.1 below with $m=n=1$, $a=b=0$, which was posed as an open problem by Rassias.
Transport methods: general. 8. Formulation of Transport Equation in a Split Form
International Nuclear Information System (INIS)
Stancic, V.
2001-01-01
The singular eigenfunction expansion method has enabled the application of functional analysis methods in transport theory. However, when applying it, the users were discouraged, since in most problems, including slab problems, an extra problem has occurred. It appears necessary to solve the Fredholm integral equation in order to determine the expansion coefficients. There are several reasons for this difficulty. One reason might be the use of the full-range expansion techniques even in the regions where the function is singular. Such an example is the free boundary condition that requires the distribution to be equal to zero. Moreover, at μ = 0, the transport equation becomes an integral one. Both reasons motivated us to redefine the transport equation in a more natural way. Similar to scattering theory, here we define the flux distribution as a direct sum of forward- and backward-directed neutrons, e.g., μ ≥ 0 and μ < 0, respectively. As a result, the plane geometry transport equation is being split into coupled-pair equations. Further, using an appropriate transformation, this pair of equations reduces to a self-adjoint one having the same form as the known full-range single flux. It is interesting that all the methods of full-range theory are applicable here provided the flux as well as the transformed transport operator are two-dimensional matrices. Applying this to the slab problem, we find explicit expressions for reflected and transmitted particles caused by an arbitrary plane source. That is the news in this paper. Because of space constraints, only fundamentals of this approach will be presented here. We assume that the reader is familiar with this field; therefore, the applications are noted only at the end. (author)
Khader, M M
2013-10-01
In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.
DEFF Research Database (Denmark)
Milovanov, A.V.; Juul Rasmussen, J.
2005-01-01
Equations built on fractional derivatives prove to be a powerful tool in the description of complex systems when the effects of singularity, fractal supports, and long-range dependence play a role. In this Letter, we advocate an application of the fractional derivative formalism to a fairly general...... class of critical phenomena when the organization of the system near the phase transition point is influenced by a competing nonlocal ordering. Fractional modifications of the free energy functional at criticality and of the widely known Ginzburg-Landau equation central to the classical Landau theory...... of second-type phase transitions are discussed in some detail. An implication of the fractional Ginzburg-Landau equation is a renormalization of the transition temperature owing to the nonlocality present. (c) 2005 Elsevier B.V. All rights reserved....
Energy Technology Data Exchange (ETDEWEB)
Atmaja, A.N. [Quantum Science Centre, Department of Physics, Faculty of Science, University of Malaya,50603 Kuala Lumpur (Malaysia); Research Center for Physics, Indonesian Institute of Sciences (LIPI),Kompleks PUSPIPTEK Serpong, Tangerang 15310 (Indonesia); Ramadhan, H.S. [Departemen Fisika, FMIPA, Universitas Indonesia,Depok 16424 (Indonesia); Hora, E. da [Coordenadoria Interdisciplinar de Ciência e Tecnologia & Departemento de Física,Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil)
2016-02-18
We use a recent on-shell method, developed in http://dx.doi.org/10.1103/PhysRevD.90.105009, to construct Bogomol’nyi equations of the three-dimensional generalized Maxwell-Higgs model http://dx.doi.org/10.1140/epjc/s10052-011-1833-9. The resulting Bogomol’nyi equations are parametrized by a constant C{sub 0} and they can be classified into two types determined by the value of C{sub 0}=0 and C{sub 0}≠0. We identify that the Bogomol’nyi equations obtained by Bazeia et al. http://dx.doi.org/10.1140/epjc/s10052-011-1833-9 are of the (C{sub 0}=0)-type Bogomol’nyi equations. We show that the Bogomol’nyi equations of this type do not admit the Prasad-Sommerfield limit in its spectrum. As a resolution, the vacuum energy must be lifted up by adding some constant to the potential. Some possible solutions whose energy equal to the vacuum are discussed briefly. The on-shell method also reveals a new (C{sub 0}≠0)-type Bogomol’nyi equations. This non-zero C{sub 0} is related to a non-trivial function f{sub C{sub 0}} defined as a difference between energy density of the scalar potential term and of the gauge kinetic term. It turns out that these Bogomol’nyi equations correspond to vortices with locally non-zero pressures, while their average pressureP remain zero globally by the finite energy constraint.
Stability of finite difference schemes for generalized von Foerster equations with renewal
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Henryk Leszczyński
2014-01-01
Full Text Available We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to \\(l^1\\ and \\(l^\\infty\\ norms.
Generalized Design Equations for Class-E Power Amplifiers with Finite DC Feed Inductance
Acar, M.; Annema, Anne J.; Nauta, Bram
2006-01-01
Abstract—In literature, it is widely accepted that the design of Class-E Power Amplifier (PA) with finite dc feed inductance requires a long iterative solution procedure. To avoid such iterative solution methods, analytical design equations should be known. The problem associated with the finite dc