Quantifying risks with exact analytical solutions of derivative pricing distribution
Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin
2017-04-01
Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Kuru, S [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J; Nieto, L M, E-mail: sengul.kuru@science.ankara.edu.t, E-mail: jnegro@fta.uva.e, E-mail: luismi@metodos.fam.cie.uva.e [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47071 Valladolid (Spain)
2009-11-11
Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields.
Kuru, S; Negro, J; Nieto, L M
2009-11-11
Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
Directory of Open Access Journals (Sweden)
Takibayev N.Zh.
2010-04-01
Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two ﬁxed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two ﬁxed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei ﬁxed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
Exact analytic solution of position-dependent mass Schrödinger equation
Rajbongshi, Hangshadhar
2017-10-01
Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.
Berrada, K.; Eleuch, H.
2017-09-01
Various schemes have been proposed to improve the parameter-estimation precision. In the present work, we suggest an alternative method to preserve the estimation precision by considering a model that closely describes a realistic experimental scenario. We explore this active way to control and enhance the measurements precision for a two-level quantum system interacting with classical electromagnetic field using ultra-short strong pulses with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we investigate the variation of the precision with a few cycles pulse and a smooth phase jump over a finite time interval. We show that by acting on the shape of the phase transient and other parameters of the considered system, the amount of information may be increased and has smaller decay rate in the long time. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.
Saengow, C.; Giacomin, A. J.
2017-12-01
The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.
Liu, Jiangen; Zhang, Yufeng
2018-01-01
This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.
Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law
Torres-Cordoba, Rafael; Martinez-Garcia, Edgar
2017-10-01
This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.
Fring, Andreas; Frith, Thomas
2017-01-01
We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.
Meleshko, Sergey V
2005-01-01
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Exact Solutions to Maccari's System
Pan, Jun-Ting; Gong, Lun-Xun
2007-07-01
Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.
Directory of Open Access Journals (Sweden)
Ivan D. Lobanov
2016-06-01
Full Text Available In this article, the problem of the number of spikes (level crossings of the stationary narrowband Gaussian process has been considered. The process was specified by an exponentially-cosine autocorrelation function. The problem had been solved earlier by Rice in terms of the joint probabilities’ density of the process and its derivative with respect to time, but in our article we obtained the solution using the functional of probabilities’ density (the functional was obtained by Amiantov, as well as an expansion of the canonical stochastic process. In this article, the optimal canonical expansion of a narrowband stochastic process based on the work of Filimonov and Denisov was also considered to solve the problem. The application of all these resources allowed obtaining an exact analytical solution of the problem on spikes of stationary narrowband Gaussian process. The obtained formulae could be used to solve, for example, some problems about the residual resource of some radiotechnical products, about the breaking sea waves and others.
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.
2014-01-01
Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium
Directory of Open Access Journals (Sweden)
M. A. Castro
2013-01-01
conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.
Exact cosmological solutions for MOG
Energy Technology Data Exchange (ETDEWEB)
Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2015-09-15
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Exact solution for generalized pairing
Pan, Feng; Draayer, J. P.
1997-01-01
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.
Exact solution to fractional logistic equation
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2017-03-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Curilef, S.; Plastino, A. R.; Plastino, A.
2013-06-01
Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q-generalized thermostatistical formalism, is characterized by a parameter q and in the limit q→1 reduces to the standard, linear Schrödinger equation. The q-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1 limit the q-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.
Exact Solutions in Modified Gravity Models
Directory of Open Access Journals (Sweden)
Valery V. Obukhov
2012-06-01
Full Text Available We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.
Sahu, Basudeb; Bhoi, Swagatika
2017-10-01
The decay of α particle from a nucleus is viewed as a quantum resonance state of a two-body scattering process of the α +daughter nucleus pair governed by a novel nucleus-nucleus potential in squared Woods-Saxon form. By the application of the rigorous optical model (OM) potential scattering (S -matrix) theory the genuineness of the potential for the system is established by giving a good explanation of the elastic scattering and reaction cross sections data of the α +nucleus pair. From the pole position in the complex momentum (k ) plane of the S matrix of the real part of the OM potential defined above, the energy and width of the resonance state akin to the decaying state of emission of α particle are extracted and from this width, the result of the α -decay half-life is derived to account for the experimental result of the half-life in the cases of a large number of α emitters including heavy and superheavy nuclei. The S matrix of the real OM potential is replaced by an analytical function expressed in terms of exact Schrödinger solutions of a global potential that closely represents the real Coulomb-nuclear interaction in the interior and the pure Coulomb wave functions outside, and the resonant poles of this S matrix in the complex momentum plane are used to give satisfactory results of decay half-lives of α coming out from varieties of nuclei.
Exact solution of the neutron transport equation in spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters
2017-03-15
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
... integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.
On exact solutions of the Bogoyavlenskii equation
Indian Academy of Sciences (India)
Abstract. Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a ...
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Exact solutions, energy, and charge of stable Q-balls
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2016-05-15
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)
Exact solutions for the biadjoint scalar field
Energy Technology Data Exchange (ETDEWEB)
White, C.D., E-mail: Christopher.White@glasgow.ac.uk [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland (United Kingdom); Centre for Research in String Theory, Queen Mary University of London, London E1 4NS (United Kingdom)
2016-12-10
Biadjoint scalar theories are novel field theories that arise in the study of non-abelian gauge and gravity amplitudes. In this short paper, we present exact nonperturbative solutions of the field equations, and compare their properties with monopole-like solutions in non-abelian gauge theory. Our results may pave the way for nonperturbative studies of the double copy.
Directory of Open Access Journals (Sweden)
Abdelhalim Ebaid
2013-01-01
Full Text Available In the cancer treatment, magnetic nanoparticles are injected into the blood vessel nearest to the cancer’s tissues. The dynamic of these nanoparticles occurs under the action of the peristaltic waves generated on the flexible walls of the blood vessel. Studying such nanofluid flow under this action is therefore useful in treating tissues of the cancer. In this paper, the mathematical model describing the slip peristaltic flow of nanofluid was analytically investigated. Exact expressions were deduced for the temperature distribution and nano-particle concentration. In addition, the effects of the slip, thermophoresis, and Brownian motion parameters on the temperature and nano-particle concentration profiles were discussed and further compared with other approximate results in the literatures. In particular, these results have been obtained at the same values of the physical examined parameters that was considered in Akbar et al., “Peristaltic flow of a nanofluid with slip effects,” 2012. The results reveal that remarkable differences are detected between the exact current results and those approximately obtained in the literatures for behaviour of the temperature profile and nano-particles concentration. Accordingly, the current analysis and results are considered as optimal and therefore may be taken as a base for any future comparisons.
Vaidya-like exact solutions with torsion
Blagojević, M
2015-01-01
Starting from the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Townsend massive gravity, a new class of the Vaidya-like exact solutions with torsion is constructed in the three-dimensional Poincar\\'e gauge theory. A particular subclass of these solutions is shown to possess the asymptotic conformal symmetry. The related canonical energy contains a contribution stemming from torsion.
Electromagnetic shock wave in nonlinear vacuum: exact solution.
Kovachev, Lubomir M; Georgieva, Daniela A; Kovachev, Kamen L
2012-10-01
An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
Nonlinear partial differential equations (NPDEs) of mathematical physics are major sub- jects in physical science. With the development of soliton theory, many useful methods for obtaining exact solutions of NPDEs have been presented. Some of them are: the (G /G)- expansion method [1–4], the simplest equation method ...
Exact solutions for helical magnetohydrodynamic equilibria
Energy Technology Data Exchange (ETDEWEB)
Villata, M. (Istituto di Fisica Generale, Universita di Torino, Via Pietro Giuria 1, I-10125 Torino (Italy)); Tsinganos, K. (Department of Physics, University of Crete and Research Center of Crete, GR-71409, Heraklion, Crete (Greece))
1993-07-01
Three novel classes of exact solutions of the generalized Grad--Shafranov equation for helically symmetric magnetohydrodynamic (MHD) equilibria are presented. The first two classes may be applied to helical MHD equilibria for plasma confined between two coaxial cylinders, while the third one to the modeling of helicoidal magnetic fields and flows in several recently observed astrophysical jets. The same solutions can be also used for the testing of sophisticated numerical codes. It is also shown that all helically symmetric MHD equilibria can be treated by the same general method which is employed to generate exact MHD solutions for systems possessing an ignorable coordinate in a system of three orthogonal basis vectors, although in the case of helical symmetry an [ital orthogonal] ignorable coordinate does not exist, contrary to what happens in the well-known cases of axial and translational symmetries.
Exact Solution for a Gravitational Wave Detector
Rabounski, Dmitri; Borissova, Larissa
2008-04-01
The experimental statement on gravitational waves proceeds from the equation for deviating geodesic lines and the equation for deviating non-geodesics. Weber's result was not based upon an exact solution to the equations, but on an approximate analysis of what could be expected: he expected that a plane weak wave of the space metric may displace two resting particles with respect to each other. In this work, exact solutions are presented for the deviation equation of both free and spring-connected particles. The solutions show that a gravitational wave may displace particles in a two-particle system only if they are in motion with respect to each other or the local space (there is no effect if they are at rest). Thus, gravitational waves produce a parametric effect on a two-particle system. According to the solutions, an altered detector construction can be proposed such that it might interact with gravitational waves: 1) a horizontally suspended cylindrical pig, whose butt-ends have basic relative oscillations induced by a laboratory source; 2) a free-mass detector where suspended mirrors have laboratory induced basic oscillations relative to each other.
Exact analytical density profiles and surface tension
Indian Academy of Sciences (India)
to nonideality, which distinguish electrolyte from nonelectrolyte solutions. An example is provided by the excess surface tension for an air–water interface, which is determined by the excess particle density, and which was first calculated by Onsager and Samaras. Because of the discrepancy between the dielectric constants ...
Exact solutions for the spin tune for model storage rings
Mane, S R
2002-01-01
We present exact analytical expressions for the spin tune for arbitrary values of the orbital action for several storage ring models. The models we treat contain Siberian Snakes, the use of which is essential to preserve the polarization of beams in high-energy proton storage rings. Our solutions contain some novel features. We also prove a previously conjectured claim about the behavior of spin tuneshifts in rings with multiple Snakes. The conjecture is based on numerical simulations, but our proof is analytical, and also nonperturbative.
Exact and approximate solutions for transient squeezing flow
Lang, Ji; Santhanam, Sridhar; Wu, Qianhong
2017-10-01
In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.
Some exact BPS solutions for exotic vortices and monopoles
Directory of Open Access Journals (Sweden)
Handhika S. Ramadhan
2016-07-01
Full Text Available We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell–Higgs and Yang–Mills–Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in [1,2]. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, f(|ϕ| and w(|ϕ|. For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad–Sommerfield limit. Our results generalize the exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that w(|ϕ| has negative value at some finite range of r, but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.
New exact travelling wave solutions of some complex nonlinear equations
Bekir, Ahmet
2009-04-01
In this paper, we establish exact solutions for complex nonlinear equations. The tanh-coth and the sine-cosine methods are used to construct exact periodic and soliton solutions of these equations. Many new families of exact travelling wave solutions of the coupled Higgs and Maccari equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems.
Energy Technology Data Exchange (ETDEWEB)
Villata, M. (Istituto di Fisica Generale dell' Universita, Via Pietro Giuria 1, I-10125 Torino (Italy)); Ferrari, A. (Osservatorio Astronomico di Torino, I-10025 Pino Torinese (Italy))
1994-07-01
In the framework of the analytical study of magnetohydrodynamic (MHD) equilibria with flow and nonuniform density, a general family of well-behaved exact solutions of the generalized Grad--Shafranov equation and of the whole set of time-independent MHD equations completed by the nonbarotropic ideal gas equation of state is obtained, both in helical and axial symmetry. The helical equilibrium solutions are suggested to be relevant to describe the helical morphology of some astrophysical jets.
Exact Analytical Solutions for Elastodynamic Impact
2015-11-30
z2v1ðl; tÞ ¼ 0; see also Nonaka et al. (1996, Eq. (17)). 176 G.A. Gazonas et al. / International Journal of Solids and Structures 75–76 (2015) 172–187...1–63. Nonaka , T., Clifton, R.J., Taichirookazaki, T., 1996. Longitudinal elastic waves in columns due to earthquake motion. Int. J. Impact Eng. 18
Exact solutions of some nonlinear partial differential equations using ...
Indian Academy of Sciences (India)
Research Articles Volume 81 Issue 2 August 2013 pp 225-236 ... Abstract. The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper ... By using this useful method, we found some exact solutions of the above-mentioned equations.
Exact solution for spin precession in the radiationless relativistic Kepler problem
Energy Technology Data Exchange (ETDEWEB)
Mane, S.R., E-mail: srmane001@gmail.com
2014-11-11
There is interest in circulating beams of polarized particles in all-electric storage rings to search for nonzero permanent electric dipole moments of subatomic particles. To this end, it is helpful to derive exact analytical solutions of the spin precession in idealized models, both for pedagogical reasons and to serve as benchmark tests for analysis and design of experiments. This paper derives exact solutions for the spin precession in the relativistic Kepler problem. Some counterintuitive properties of the solutions are pointed out.
Exact solution for spin precession in the radiationless relativistic Kepler problem
Mane, S. R.
2014-11-01
There is interest in circulating beams of polarized particles in all-electric storage rings to search for nonzero permanent electric dipole moments of subatomic particles. To this end, it is helpful to derive exact analytical solutions of the spin precession in idealized models, both for pedagogical reasons and to serve as benchmark tests for analysis and design of experiments. This paper derives exact solutions for the spin precession in the relativistic Kepler problem. Some counterintuitive properties of the solutions are pointed out.
Exact solutions and spacetime singularities in nonlocal gravity
National Research Council Canada - National Science Library
Li, Yao-Dong; Modesto, Leonardo; Rachwał, Lesław
2015-01-01
.... We prove that maximally symmetric spacetimes are exact solutions in both classes, while in dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant...
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In §2, an extended trial equation method is described for finding exact travelling wave solutions of nonlinear evolution equations with higher-order nonlinearity. In §3, as an application, some exact solutions to nonlinear partial differential equation such as the generalized Zakharov–Kuznetsov modified equal-width equation ...
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
where , , and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modiﬁed tanh–coth function method with computerized symbolic ...
Exact Solutions for Some Fractional Differential Equations
Sonmezoglu, Abdullah
2015-01-01
The extended Jacobi elliptic function expansion method is used for solving fractional differential equations in the sense of Jumarie’s modified Riemann-Liouville derivative. By means of this approach, a few fractional differential equations are successfully solved. As a result, some new Jacobi elliptic function solutions including solitary wave solutions and trigonometric function solutions are established. The proposed method can also be applied to other fractional differential e...
Analytic solutions of a class of nonlinearly dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, M-C [System Engineering Institute of Tianjin University, Tianjin, 300072 (China); Zhao, X-S; Liu, X [Tianjin University of Technology and Education, Tianjin, 300222 (China)], E-mail: mchwang123@163.com.cn, E-mail: xszhao@mail.nwpu.edu.cn, E-mail: liuxinhubei@163.com.cn
2008-02-15
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Fuzzy Weighted Average: Analytical Solution
van den Broek, P.M.; Noppen, J.A.R.
2009-01-01
An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact
Exact solutions in a model of vertical gas migration
Energy Technology Data Exchange (ETDEWEB)
Silin, Dmitriy B.; Patzek, Tad W.; Benson, Sally M.
2006-06-27
This work is motivated by the growing interest in injectingcarbon dioxide into deep geological formations as a means of avoidingatmospheric emissions of carbon dioxide and consequent global warming.One of the key questions regarding the feasibility of this technology isthe potential rate of leakage out of the primary storage formation. Weseek exact solutions in a model of gas flow driven by a combination ofbuoyancy, viscous and capillary forces. Different combinations of theseforces and characteristic length scales of the processes lead todifferent time scaling and different types of solutions. In the case of athin, tight seal, where the impact of gravity is negligible relative tocapillary and viscous forces, a Ryzhik-type solution implies square-rootof time scaling of plume propagation velocity. In the general case, a gasplume has two stable zones, which can be described by travelling-wavesolutions. The theoretical maximum of the velocity of plume migrationprovides a conservative estimate for the time of vertical migration.Although the top of the plume has low gas saturation, it propagates witha velocity close to the theoretical maximum. The bottom of the plumeflows significantly more slowly at a higher gas saturation. Due to localheterogeneities, the plume can break into parts. Individual plumes alsocan coalesce and from larger plumes. The analytical results are appliedto studying carbon dioxide flow caused by leaks from deep geologicalformations used for CO2 storage. The results are also applicable formodeling flow of natural gas leaking from seasonal gas storage, or formodeling of secondary hydrocarbon migration.
Exact solutions for dynamic response of a periodic spring and mass structure
Gao, Q.; Wu, F.; Zhang, H. W.; Zhong, W. X.; Howson, W. P.; Williams, F. W.
2012-02-01
This paper derives exact analytical solutions for the dynamic response of a periodic structure for which the unit cell consists of one mass and one spring. The solutions cover arbitrary initial conditions and both polynomial and harmonic external forces. They involve Bessel, Lommel, Weber and hypergeometric functions.
Analytical solution methods for geodesic motion
Hackmann, Eva
2015-01-01
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Pleba\\'nski--Demia\\'nski type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.
Exact solutions for the differential equations in fractal heat transfer
Directory of Open Access Journals (Sweden)
Yang Chun-Yu
2016-01-01
Full Text Available In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method.
The exact solutions of differential equation with delay
Hasebe, K; Sugiyama, Y
1998-01-01
The exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi's elliptic function. We also obtain the family of solutions of such type of equations.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
How hairpin vortices emerge from exact invariant solutions
Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania
2017-11-01
Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.
New approach to the exact solution of viscous flow due to stretching (shrinking and porous sheet
Directory of Open Access Journals (Sweden)
Azhar Ali
Full Text Available Exact analytical solutions for the generalized stretching (shrinking of a porous surface, for the variable suction (injection velocity, is presented in this paper. The solution is generalized in the sense that the existing solutions that correspond to various stretching velocities are recovered as a special case of this study. A suitable similarity transformation is introduced to find self-similar solution of the non-linear governing equations. The flow is characterized by a few non-dimensional parameters signifying the problem completely. These parameters are such that the whole range of stretching (shrinking problems discussed earlier can be recovered by assigning appropriate values to these parameters. A key point of the whole narrative is that a number of earlier works can be abridged into one generalized problem through the introduction of a new similarity transformation and finding its exact solution encompassing all the earlier solutions. Keywords: Exact solutions, New similarities, Permeable and moving sheet
The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM
Directory of Open Access Journals (Sweden)
Hafiz Abdul Wahab
2016-06-01
Full Text Available The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy Analysis method gives the same series solution as in Adomian Decomposition Method as well as homotopy Perturbation Method (Wahab et al, 2015 and we get the exact solution using the initial guess in Homotopy Analysis Method using the results obtained by Adomian Decomposition Method.
The exact solution of the Schrödinger equation with a polynomially spatially varying mass
Bednarik, Michal; Cervenka, Milan
2017-07-01
The Schrödinger equation with a position-dependent mass (SEPDM) is employed in many areas of quantum physics. Exact solutions for the SEPDM lie at the center of interest of the professional public because it helps us to understand the behavior of quantum particles in the cases in which their mass varies spatially. For this purpose, we used the mass function represented by a quartic polynomial and a quadratic potential function, which extends the current class of exact solutions of the SEPDM. The exact analytical solution of the problem is expressed as a linear combination of local Heun functions. Heun's equation contains many parameters, resulting in its general nature. We studied how limit changes in some of these parameters will affect the solution of the SEPDM. The obtained solutions are particularly suitable for the transfer matrix method and solutions of scattering problems; this is demonstrated by the calculation of bound states.
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Exact solution for a one-dimensional model for reptation.
Drzewiński, Andrzej; van Leeuwen, J M J
2006-05-01
We discuss the exact solution for the properties of the recently introduced "necklace" model for reptation. The solution gives the drift velocity, diffusion constant, and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n ...
Indian Academy of Sciences (India)
Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (, ) equation using functional variable method. M Mirzazadeh M Eslami. Volume 81 Issue ... The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for ...
Exact angular momentum projection based on cranked HFB solution
Energy Technology Data Exchange (ETDEWEB)
Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics
1998-03-01
Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)
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...
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...
Exact solution of unsteady flow generated by sinusoidal pressure gradient in a capillary tube
Directory of Open Access Journals (Sweden)
M. Abdulhameed
2015-12-01
Full Text Available In this paper, the mathematical modeling of unsteady second grade fluid in a capillary tube with sinusoidal pressure gradient is developed with non-homogenous boundary conditions. Exact analytical solutions for the velocity profiles have been obtained in explicit forms. These solutions are written as the sum of the steady and transient solutions for small and large times. For growing times, the starting solution reduces to the well-known periodic solution that coincides with the corresponding solution of a Newtonian fluid. Graphs representing the solutions are discussed.
Analytical Solution Of Complete Schwarzschild\\'s Planetary Equation
African Journals Online (AJOL)
It is well known how to solve the Einstein\\'s planetary equation of motion by the method of successive approximation for the corresponding orbit solution. In this paper, we solve the complete schwarzschild\\'s planetary equation of motion by an exact analytical method. The result reveals that there are actually eight exact ...
Exact solution of the two-axis countertwisting Hamiltonian
Pan, Feng; Zhang, Yao-Zhong; Draayer, Jerry P.
2017-01-01
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly 2 J + 1 for a given integer angular momentum quantum number J, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the J → ∞ limit for integer J case except a unique non-degenerate level with zero excitation energy.
The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations
Directory of Open Access Journals (Sweden)
Yadong Shang
2012-01-01
Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.
Exact solutions to three-dimensional time-dependent Schrödinger ...
Indian Academy of Sciences (India)
With a view to obtain exact analytic solutions to the time-dependent Schrödinger equation for a few potentials of physical interest in three dimensions, transformation-group method is used. Interestingly, the integrals of motion in the new coordinates turn out to be the desired invariants of the systems.
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte
2015-07-01
This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)
Exact traveling wave solutions of some nonlinear evolution equations
Kumar, Hitender; Chand, Fakir
2014-02-01
Using a traveling wave reduction technique, we have shown that Maccari equation, (2+1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation, (2+1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equations. Then using extended F-expansion and projective Riccati equation methods, many types of exact traveling wave solutions are obtained. With the aid of solutions of the elliptic-like equation, more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provide a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. A variety of structures of the exact solutions of the elliptic-like equation are illustrated.
The functional variable method for finding exact solutions of some ...
Indian Academy of Sciences (India)
and KEWANG CHEN. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, ... Introduction. The effort in finding exact solutions of nonlinear equations is very important for understanding most nonlinear physical phenomena. For instance, the nonlinear wave phenomena observed ...
More exact tunneling solutions in scalar field theory
Energy Technology Data Exchange (ETDEWEB)
Dutta, Koushik; Hector, Cecelie; Vaudrevange, Pascal M.; Westphal, Alexander
2011-11-15
We present exact bounce solutions and amplitudes for tunneling in (i) a piecewise linear-quartic potential and (ii) a piecewise quartic-quartic potential. We cross check their correctness by comparing with results obtained through the thin-wall approximation and with a piecewise linear-linear potential. We briefly comment on applications in cosmology. (orig.)
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
problems. More precisely, there is no unified method that can be used to handle all types of nonlinear problems. A powerful and effective method for finding exact ... Explicit solutions to nonlinear problems are of fundamental importance. ... fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on [7].
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach is based ...
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
Abstract. A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach ...
A procedure to construct exact solutions of nonlinear evolution ...
Indian Academy of Sciences (India)
physics pp. 337–344. A procedure to construct exact solutions of nonlinear evolution equations. ADEM CENGIZ ÇEVIKEL1,∗, AHMET BEKIR2, MUTLU AKAR3 and. SAIT SAN2. 1Yildiz Technical University, Faculty of Education, Department of Mathematics Education,. Davutpasa Campus, 34210, Esenler, Istanbul, Turkey.
Directory of Open Access Journals (Sweden)
Abdelhalim Ebaid
2014-01-01
Full Text Available The exact solution for any physical model is of great importance in the applied science. Such exact solution leads to the correct physical interpretation and it is also useful in validating the approximate analytical or numerical methods. The exact solution for the peristaltic transport of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel has been achieved. The main advantage of such exact solution is the avoidance of any kind of restrictions on the viscosity parameter α, unlike the previous study in which the restriction α ≪ 1 has been put to achieve the requirements of the regular perturbation method. Hence, various plots have been introduced for the exact effects of the viscosity parameter, Daray’s number, porosity, amplitude ratio, Jeffrey fluid parameter, and the amplitudes of the waves on the pressure rise and the axial velocity. These exact effects have been discussed and further compared with those approximately obtained in the literature by using the regular perturbation method. The comparisons reveal that remarkable differences have been detected between the current exact results and those approximately obtained in the literature for the axial velocity profile and the pressure rise.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems-e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system......The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... of finite sampling rate and sampling time for these models as well....
Exact solution of large asymmetric traveling salesman problems.
Miller, D L; Pekny, J F
1991-02-15
The traveling salesman problem is one of a class of difficult problems in combinatorial optimization that is representative of a large number of important scientific and engineering problems. A survey is given of recent applications and methods for solving large problems. In addition, an algorithm for the exact solution of the asymmetric traveling salesman problem is presented along with computational results for several classes of problems. The results show that the algorithm performs remarkably well for some classes of problems, determining an optimal solution even for problems with large numbers of cities, yet for other classes, even small problems thwart determination of a provably optimal solution.
A static axisymmetric exact solution of f(R)-gravity
Energy Technology Data Exchange (ETDEWEB)
Gutierrez-Pineres, Antonio C., E-mail: acgutierrez@correo.nucleares.unam.mx [Facultad de Ciencias Basicas, Universidad Tecnologica de Bolivar, CO 131001 Cartagena de Indias (Colombia); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Mexico D.F. (Mexico); Lopez-Monsalvo, Cesar S., E-mail: cesar.slm@correo.nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Mexico D.F. (Mexico)
2013-01-29
We present an exact, axially symmetric, static, vacuum solution for f(R)-gravity in Weyl's canonical coordinates. We obtain a general explicit expression for the dependence of df(R)/dR upon the r and z coordinates and then the corresponding explicit form of f(R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f(R){ne}R, this solution corresponds to a naked singularity.
On field redefinitions and exact solutions in string theory
Tseytlin, Arkady A
1993-01-01
String backgrounds associated with gauged $G/H$ WZNW models in general depend non-trivially on $\\alpha'$. We note, however, that there exists a local covariant $\\a'$-dependent field redefinition that relates the exact metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its leading-order form ($D=2$ black hole). As a consequence, there exists a `scheme' in which the string effective equations have the latter as an exact solution. However, the corresponding equation for the tachyon (which, like other Weyl anomaly coefficients, has scheme-dependent form) still contains corrections of all orders in $\\alpha'$. As a result, the `probes' (the tachyons) still feel the $\\alpha'$-corrected background. The field redefinitions we discuss contain the dilaton terms in the metric transformation law. We comment on exact forms of the duality transformation in different `schemes'.
Agent-based model for the h-index - Exact solution
Żogała-Siudem, Barbara; Cena, Anna; Gagolewski, Marek
2015-01-01
The Hirsch's $h$-index is perhaps the most popular citation-based measure of the scientific excellence. In 2013 G. Ionescu and B. Chopard proposed an agent-based model for this index to describe a publications and citations generation process in an abstract scientific community. With such an approach one can simulate a single scientist's activity, and by extension investigate the whole community of researchers. Even though this approach predicts quite well the $h$-index from bibliometric data, only a solution based on simulations was given. In this paper, we complete their results with exact, analytic formulas. What is more, due to our exact solution we are able to simplify the Ionescu-Chopard model which allows us to obtain a compact formula for $h$-index. Moreover, a simulation study designed to compare both, approximated and exact, solutions is included. The last part of this paper presents evaluation of the obtained results on a real-word data set.
Analyticity of solutions of singular fractional differential equations
Kangro, Urve
2016-06-01
We study singular fractional differential equations in spaces of analytic functions. We reformulate the equation as a cordial Volterra integral equation of the second kind and use results from the theory of cordial Volterra integral equations. This enables us to obtain conditions under which the equation has a unique analytic solution. Note that the smooth solution in this case is unique without any initial conditions; in fact, giving initial conditions usually results in nonsmooth solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.
On the Exact Solution of Wave Equations on Cantor Sets
Directory of Open Access Journals (Sweden)
Dumitru Baleanu
2015-09-01
Full Text Available The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM. We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs. The efficiency of the scheme is examined by two illustrative examples.
Conformal invariance and new exact solutions of the elastostatics equations
Chirkunov, Yu. A.
2017-03-01
We fulfilled a group foliation of the system of n-dimensional (n ≥ 2) Lame equations of the classical static theory of elasticity with respect to the infinite subgroup contained in normal subgroup of main group of this system. It permitted us to move from the Lame equations to the equivalent unification of two first-order systems: automorphic and resolving. We obtained a general solution of the automorphic system. This solution is an n-dimensional analogue of the Kolosov-Muskhelishvili formula. We found the main Lie group of transformations of the resolving system of this group foliation. It turned out that in the two-dimensional and three-dimensional cases, which have a physical meaning, this system is conformally invariant, while the Lame equations admit only a group of similarities of the Euclidean space. This is a big success, since in the method of group foliation, resolving equations usually inherit Lie symmetries subgroup of the full symmetry group that was not used for the foliation. In the three-dimensional case for the solutions of the resolving system, we found the general form of the transformations similar to the Kelvin transformation. These transformations are the consequence of the conformal invariance of the resolving system. In the three-dimensional case with a help of the complex dependent and independent variables, the resolving system is written as a simple complex system. This allowed us to find non-trivial exact solutions of the Lame equations, which direct for the Lame equations practically impossible to obtain. For this complex system, all the essentially distinct invariant solutions of the maximal rank we have found in explicit form, or we reduced the finding of those solutions to the solving of the classical one-dimensional equations of the mathematical physics: the heat equation, the telegraph equation, the Tricomi equation, the generalized Darboux equation, and other equations. For the resolving system, we obtained double wave of a
Saha Ray, S.; Sahoo, S.
2017-01-01
In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely time fractional modified Kawahara equations by using the ( G^'/G)-expansion method via fractional complex transform. As a result, new types of exact analytical solutions are obtained.
Exact supersymmetric string solutions in curved gravitational backgrounds
Antoniadis, Ignatios; Kounnas, Costas
1994-01-01
We construct a new class of exact and stable superstring solutions based on $N=4$ superconformal world-sheet symmetry. In a subclass of these, the full spectrum of string excitations is derived in a modular-invariant way. In the weak curvature limit, our solutions describe a target space with non-trivial metric and topology, and generalize the previously known (semi) wormhole. The effective field theory limit is identified in certain cases, with solutions of the $N=4$ and $N=8$ extended gauged supergravities, in which the number of space-time supersymmetries is reduced by a factor of 2 because of the presence of non-trivial dilaton, gravitational and/or gauge backgrounds. In the context of string theory, our solutions correspond to stable non-critical superstrings in the strong coupling region; the super-Liouville field couples to a unitary matter system with central charge $5\\le{\\hat c}_M\\le 9$.
A class of exact classical solutions to string theory.
Coley, A A
2002-12-31
We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.
Exact solutions to relativistic singular fractional power potentials
Agboola, Davids; Zhang, Yao-Zhong
2013-12-01
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non-relativistic limit is also discussed and using the Hellmann-Feynmann theorem, some useful expectation values are obtained.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Tariq, Hira; Akram, Ghazala
2017-05-01
In this article, new exact analytical solutions of some nonlinear evolution equations (NLEEs) arising in science, engineering and mathematical physics, namely time fractional Cahn-Allen equation and time fractional Phi-4 equation are developed using tanh method by means of fractional complex transform. The obtained results are demonstrated by graphs for the new solutions.
Exact analytical thermodynamic expressions for a Brownian heat engine.
Taye, Mesfin Asfaw
2015-09-01
The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.
Analytical solution for the convectively-mixed atmospheric boundary layer
Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.
2013-01-01
Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation
An exact solution for ideal dam-break floods on steep slopes
Ancey, C.; Iverson, R.M.; Rentschler, M.; Denlinger, R.P.
2008-01-01
The shallow-water equations are used to model the flow resulting from the sudden release of a finite volume of frictionless, incompressible fluid down a uniform slope of arbitrary inclination. The hodograph transformation and Riemann's method make it possible to transform the governing equations into a linear system and then deduce an exact analytical solution expressed in terms of readily evaluated integrals. Although the solution treats an idealized case never strictly realized in nature, it is uniquely well-suited for testing the robustness and accuracy of numerical models used to model shallow-water flows on steep slopes. Copyright 2008 by the American Geophysical Union.
Fifty Years of the Exact Solution of the Two-Dimensional Ising Model by Onsager
Bhattacharjee, Somendra M.; Khare, Avinash
1995-01-01
The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the landmarks in theoretical physics. On the occassion of the fifty years of the exact solution, we give a historical review of this model. After briefly discussing the exact solution by Onsager, we point out some of the recent developments in this field. The exact solution by Onsager has inspired several developments in various other fields. Some of these are also briefly mentioned.
Exact Solutions of a Generalized Weighted Scale Free Network
Directory of Open Access Journals (Sweden)
Li Tan
2013-01-01
Full Text Available We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.
Energy Technology Data Exchange (ETDEWEB)
Lode, Axel U.J.
2013-06-03
This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one- and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.
Analytical Solutions for Beams Passing Apertures with Sharp Boundaries
Luz, Eitam; Malomed, Boris A
2016-01-01
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.
Analytical solutions for systems of partial differential-algebraic equations.
Benhammouda, Brahim; Vazquez-Leal, Hector
2014-01-01
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
Strong interactions and exact solutions in nonlinear massive gravity
Koyama, Kazuya; Niz, Gustavo; Tasinato, Gianmassimo
2011-09-01
We investigate strong coupling effects in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of Fierz-Pauli. We analyze the conditions to recover general relativity via the Vainshtein mechanism in the weak field limit, and find three main cases depending on the choice of parameters. In the first case, the potential is such that all nonlinearities disappear and the vDVZ discontinuity cannot be avoided. In the second case, the Vainshtein mechanism allows to recover general relativity within a macroscopic radius from a source. In the last case, the strong coupling of the scalar graviton completely shields the massless graviton, and weakens gravity when approaching the source. In the second part of the paper, we explore new exact vacuum solutions, that asymptote to de Sitter or anti de Sitter space depending on the choice of parameters. The curvature of the space is proportional to the mass of the graviton, thus providing a cosmological background which may explain the present-day acceleration in terms of the graviton mass. Moreover, by expressing the potential for nonlinear massive gravity in a convenient form, we also suggest possible connections with a higher-dimensional framework.
Symmetry reductions and exact solutions of Shallow water wave equations
Clarkson, P A
1994-01-01
In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation u_{xxxt} + \\alpha u_x u_{xt} + \\beta u_t u_{xx} - u_{xt} - u_{xx} = 0,\\eqno(1) where \\alpha and \\beta are arbitrary, nonzero, constants, which is derivable using the so-called Boussinesq approximation. Two special cases of this equation, or the equivalent nonlocal equation obtained by setting u_x=U, have been discussed in the literature. The case \\alpha=2\\beta was discussed by Ablowitz, Kaup, Newell and Segur [{\\it Stud.\\ Appl.\\ Math.}, {\\bf53} (1974) 249], who showed that this case was solvable by inverse scattering through a second order linear problem. This case and the case \\alpha=\\beta were studied by Hirota and Satsuma [{\\it J.\\ Phys.\\ Soc.\\ Japan}, {\\bf40} (1976) 611] using Hirota's bi-linear technique. Further the case \\alpha=\\beta is solvable by inverse scattering through a third order linear problem. In this paper a catalogue of symmetry reductions is obtained using the classical Lie method and th...
Thermal impedance of multi-finger microelectronic structures: exact analytical model
Energy Technology Data Exchange (ETDEWEB)
Vintrou, Sebastien; Laraqi, Najib; Bairi, Abderrahmane, E-mail: nlaraqi@u-paris10.f, E-mail: nlaraqi@gmail.co [Universite Paris Ouest, Laboratoire Thermique Interfaces Environnement (TIE), EA 4415 PST Ville d' Avray, Departement GTE, 50 Rue de Sevres, F92410 Ville d' Avray (France)
2009-12-21
An exact analytical expression for the complex thermal impedance Z of multi-finger microelectronic components is presented in this paper. The integral transform technique has been used to obtain this expression and solve the three dimensional heat conduction equation directly in the frequency domain. Calculations were first performed for a single-finger on a single-layer structure in order to compare the results with those available in the literature and hence validate the solution. Generally, the comparison shows good agreement between our results and those given in most publications. When the structures are composed of several layers, the thermal impedance changes with the thermal conductivities and the thicknesses of the different layers. It is also affected by the thermal contact resistance between the layers. Some results illustrate the influence of these parameters. The case of a multi-finger component is then treated and the influence of distances between fingers is investigated. For all cases, the Nyquist diagram (i.e. Im(Z) versus Re(Z) for different pulsation values {omega}) is plotted. Mainly two zones are observed: one for the high frequencies and the other for the lower ones. The substrate dimensions are found to largely influence the scale of the low frequency zone whereas the distance between the fingers influences the higher one. Finally, the solution is applied to a multi-finger device in contact with a heat sink.
Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation
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Hossam A. Ghany
2014-01-01
Full Text Available F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.
Exact solutions of the time-fractional Fisher equation by using modified trial equation method
Tandogan, Yusuf Ali; Bildik, Necdet
2016-06-01
In this study, modified trial equation method has been proposed to obtain precise solutions of nonlinear fractional differential equation. Using the modified test equation method, we obtained some new exact solutions of the time fractional nonlinear Fisher equation. The obtained results are classified as a soliton solution, singular solutions, rational function solutions and periodic solutions.
Exact solution for the interior of a black hole
Nieuwenhuizen, T.M.
2008-01-01
Within the Relativistic Theory of Gravitation it is shown that the equation of state p = rho holds near the center of a black hole. For the stiff equation of state p = rho - rho(c) the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range
Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging
Bueno-Orovio, Alfonso; Burrage, Kevin
2017-11-01
The quantification of anomalous diffusion is increasingly being recognised as an advanced modality of analysis for the evaluation of tissue microstructure in magnetic resonance imaging (MRI). One powerful framework to account for anomalous diffusion in biological and structurally heterogeneous tissues is the use of diffusion operators based on fractional calculus theory, which generalises the physical principles of standard diffusion in homogeneous media. However, their non-locality makes analytical solutions often unavailable, limiting the applicability of these modelling and analysis techniques. In this paper, we derive compact analytical signal decays for practical MRI sequences in the anisotropic fractional Bloch-Torrey setting, as described by the space fractional Laplacian and importantly the time Caputo derivative. The attained solutions convey relevant characteristics of MRI in biological tissues not replicated by standard diffusion, including super-diffusive and sub-diffusive regimes in signal decay and the diffusion-driven incomplete refocusing of spins at the end of the sequence. These results may therefore have significant implications for advancing the current interpretation of MRI, and for the estimation of tissue properties based on exact solutions to underlying diffusive processes.
Exact unsteady solutions to the Navier-Stokes and viscous MHD equations
Energy Technology Data Exchange (ETDEWEB)
Bogoyavlenskij, Oleg I
2003-02-10
Infinite-dimensional families of exact solutions that depend on all four variables t,x,y,z are derived for the Navier-Stokes equations and for viscous magnetohydrodynamics equations. Soliton-like solutions--viscons--are introduced.
Analytic solution for tachyon condensation in open string field theory
Schnabl, M
2006-01-01
We propose a new basis in Witten's open string field theory, in which the star product simplifies considerably. For a convenient choice of gauge the classical string field equation of motion yields straightforwardly an exact analytic solution that represents the nonperturbative tachyon vacuum. The solution is given in terms of Bernoulli numbers and the equation of motion can be viewed as novel Euler--Ramanujan-type identity. It turns out that the solution is the Euler--Maclaurin asymptotic expansion of a sum over wedge states with certain insertions. This new form is fully regular from the point of view of level truncation. By computing the energy difference between the perturbative and nonperturbative vacua, we prove analytically Sen's first conjecture.
Conservation laws and exact solutions for nonlinear diffusion in anisotropic media
Avdonina, Elena D.; Ibragimov, Nail H.
2013-10-01
Conservation laws and exact solutions of nonlinear differential equations describing diffusion phenomena in anisotropic media with external sources are constructed. The construction is based on the method of nonlinear self-adjointness. Numerous exact solutions are obtained by using the recent method of conservation laws. These solutions are different from group invariant solutions and can be useful for investigating diffusion phenomena in complex media, e.g. in oil industry.
Analytical solution of one dimensional temporally dependent ...
African Journals Online (AJOL)
... chemically non-reactive. The first order decay term which is inversely proportional to the dispersion coefficient is also considered. Initially the porous domain is considered solute free. Analytical solutions are obtained by using Laplace transform technique for continuous uniform and increasing input source concentration.
Analytic solutions of nonlinear Cournot duopoly game
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2005-01-01
Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.
Analytic solutions in nonlinear massive gravity.
Koyama, Kazuya; Niz, Gustavo; Tasinato, Gianmassimo
2011-09-23
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r(g)m(2))(1/3), where m is the graviton mass and r(g) is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.
Statistical Physics Methods Provide the Exact Solution to a Long-Standing Problem of Genetics
Samal, Areejit; Martin, Olivier C.
2015-06-01
Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this Letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [Genetics 16, 357 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering two and three genes but the case of four or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.
Bifurcations and new exact travelling wave solutions for the ...
Indian Academy of Sciences (India)
2016-10-17
Oct 17, 2016 ... Abstract. By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, ...
Exact Travelling Wave Solutions of two Important Nonlinear Partial Differential Equations
Kim, Hyunsoo; Bae, Jae-Hyeong; Sakthivel, Rathinasamy
2014-04-01
Coupled nonlinear partial differential equations describing the spatio-temporal dynamics of predator-prey systems and nonlinear telegraph equations have been widely applied in many real world problems. So, finding exact solutions of such equations is very helpful in the theories and numerical studies. In this paper, the Kudryashov method is implemented to obtain exact travelling wave solutions of such physical models. Further, graphic illustrations in two and three dimensional plots of some of the obtained solutions are also given to predict their behaviour. The results reveal that the Kudryashov method is very simple, reliable, and effective, and can be used for finding exact solution of many other nonlinear evolution equations.
Kaltsas, Dimitrios A
2016-01-01
We derive exact solutions of the general linear form of the Grad-Shafranov (GS) equation, including incompressible equilbrium flow, using similarity reduction ansatzes motivated by the ansatz-based methods of group foliation and direct reduction. The linearity of the equilibrium equation allows linear combinations of solutions in order to obtain axisymmetric MHD equilibria with closed and nested magnetic surfaces which are favorable for the effective confinenment of laboratory plasmas. Employing the afforementioned ansatzes we also obtain analytical solutions for several non-linear forms of the GS equation.
Shebalin, John V.
1988-01-01
An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
Exact solution of corner-modified banded block-Toeplitz eigensystems
Cobanera, Emilio; Alase, Abhijeet; Ortiz, Gerardo; Viola, Lorenza
2017-05-01
Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.
An exact solution for a rotating black hole in modified gravity
Filippini, Francesco; Tasinato, Gianmassimo
2018-01-01
Exact solutions describing rotating black holes can offer important tests for alternative theories of gravity, motivated by the dark energy and dark matter problems. We present an analytic rotating black hole solution for a class of vector-tensor theories of modified gravity, valid for arbitrary values of the rotation parameter. The new configuration is characterised by parametrically large deviations from the Kerr-Newman geometry, controlled by non-minimal couplings between vectors and gravity. It has an oblate horizon in Boyer-Lindquist coordinates, and it can rotate more rapidly and have a larger ergosphere than black holes in General Relativity (GR) with the same asymptotic properties. We analytically investigate the features of the innermost stable circular orbits for massive objects on the equatorial plane, and show that stable orbits lie further away from the black hole horizon with respect to rotating black holes in GR. We also comment on possible applications of our findings for the extraction of rotational energy from the black hole.
Mixed Poisson distributions in exact solutions of stochastic autoregulation models.
Iyer-Biswas, Srividya; Jayaprakash, C
2014-11-01
In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.
Kunst, Flore K.; Trescher, Maximilian; Bergholtz, Emil J.
2017-08-01
The hallmark of topological phases is their robust boundary signature whose intriguing properties—such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals—are impossible to realize on the surface alone. Yet, despite the glaring simplicity of noninteracting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties including correlation functions, surface dispersion, Berry curvature, and the system size dependent gap closing, which necessarily occurs when the spatial localization switches surface. This further provides a deepened understanding of the bulk-boundary correspondence. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin-orbit-coupled kagome lattice, and Fermi arcs relevant for recently synthesized slabs of pyrochlore-based Eu2Ir2O7 and Nd2Ir2O7 , which realize an all-in-all-out spin configuration, as well as for spin-ice-like two-in-two-out and one-in-three-out configurations, which are both relevant for Pr2Ir2O7 . Remarkably, each of the pyrochlore examples exhibit clearly resolved Fermi arcs although only the one
Symmetries and exact solutions of fractional filtration equations
Gazizov, Rafail K.; Kasatkin, Alexey A.; Lukashchuk, Stanislav Yu.
2017-11-01
Few fractional differential models of fluid flow through porous medium are considered. We use several modifications of Darcy's law that contain time-and space-fractional derivatives corresponding to memory or non-local effects in filtration. Symmetry properties of the resulting nonlinear anomalous diffusion-type equations are analyzed and new group-invariant solutions are constructed. In particular, we obtain fractional analogues of so-called blow-up solutions.
Directory of Open Access Journals (Sweden)
Asterios Pantokratoras
2008-01-01
Full Text Available Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of 0∘C≤≤8∘C, where water density is nearly parabolic. Except for their use as benchmarking means for testing the numerical solution of the Navier-Stokes equations, the presented exact solutions with EMHD forces have use in flow separation control in aeronautics and hydronautics, whereas the MHD results have applications in process metallurgy and fusion technology. These analytical solutions are valid for flows with strong suction.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
Mushy-zone model with an exact solution
Energy Technology Data Exchange (ETDEWEB)
Solomon, A. D.; Wilson, D. G.; Alexiades, V.
1982-04-01
In this paper we propose a very simple model of a mushy zone which admits of an explicit solution. To our knowledge, it is the only instance where an actual observation of the mushy zone width and structure is used as a partial basis for the model definition. The model rests upon two unknown parameters. The first determines the relation between the equilibrium temperature gradient and the mushy zone width. The second depends upon the dendritic structure in the mushy zone, and is related to the solid fraction. Both can be estimated from experiments. We will limit ourselves to defining the model, presenting its closed form solution, and giving tables from which the solution can be found explicitly. It is shown that in most cases the predicted mushy zone is of very negligible importance.
Exact helicoidal and catenoidal solutions in five- and higher-dimensional Einstein-Maxwell theory
Ghezelbash, A. M.; Kumar, V.
2017-06-01
We present several new exact solutions in five- and higher-dimensional Einstein-Maxwell theory by embedding the Nutku instanton. The metric functions for the five-dimensional solutions depend only on a radial coordinate and on two spatial coordinates for the six- and higher-dimensional solutions. The six- and higher-dimensional metric functions are convolutedlike integrals of two special functions. We find that the solutions are regular almost everywhere and some spatial sections of the solution describe wormhole handles. We also find a class of exact and nonstationary convolutedlike solutions to the Einstein-Maxwell theory with a cosmological constant.
Exact half-BPS type IIB interface solutions I: local solution and supersymmetric Janus
Energy Technology Data Exchange (ETDEWEB)
D' Hoker, Eric; Estes, John; Gutperle, Michael [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States)
2007-06-15
The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS{sub 4} x S{sup 2} x S{sup 2} x {sigma} with SO(2, 3) x SO(3) x SO(3) symmetry in terms of two holomorphic functions on a Riemann surface {sigma}, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted AdS{sub 5} x S{sup 5} and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.
Exact half-BPS type IIB interface solutions II: flux solutions and multi-Janus
Energy Technology Data Exchange (ETDEWEB)
D' Hoker, Eric; Estes, John; Gutperle, Michael [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States)
2007-06-15
Regularity and topology conditions are imposed on the exact Type IIB solutions on AdS{sub 4} x S{sup 2} x S{sup 2} x {sigma} with 16 supersymmetries, which were derived in a companion paper [1]. We construct an infinite class of regular solutions with varying dilaton, and non-zero 3-form fluxes. Our solutions may be viewed as the fully back-reacted geometries of AdS{sub 5} x S{sup 5} (or more generally, Janus) doped with D5 and/or NS5 branes. The solutions are parametrized by the choice of an arbitrary genus g hyper-elliptic Riemann surface {sigma} with boundary, all of whose branch points are restricted to lie on a line. For genus 0, the Janus solution with 16 supersymmetries and 6 real parameters is recovered; its topology coincides with that of AdS{sub 5} x S{sup 5}. The genus g {>=} 1 solutions are parametrized by a total of 4g + 6 real numbers, 2g-1 of which are the real moduli of {sigma}. The solutions have 2g + 2 asymptotic AdS{sub 5} x S{sup 5} regions, g three-spheres with RR 3-form charge, and another g with NSNS 3-form charge. Collapse of consecutive branch points of {sigma} yields singularities which correspond to D5 and NS5 branes in the probe limit. It is argued that the AdS/CFT dual gauge theory to each of our solutions consists of a 2+1-dimensional planar interface on which terminate 2g + 2 half-Minkowski 3+1-dimensional space-time N = 4 super-Yang-Mills theories. Generally, the N = 4 theory in each Minkowski half-space-time may have an independent value of the gauge coupling, and the interface may support various operators, whose interface couplings are further free parameters of the dual gauge theory.
Energy Technology Data Exchange (ETDEWEB)
Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)
2013-03-15
New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.
Exact solutions of certain nonlinear chemotaxis diffusion reaction ...
Indian Academy of Sciences (India)
constructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc. Keywords. Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. PACS Nos 05.45.
Page 1 166 FG Tcheremissine - exact solution, fine mesh ----- crude ...
Indian Academy of Sciences (India)
the great advantage of these methods consists in their high reliability, which makes it possible to obtain solutions of rather low accuracy (but sufficient for practical purposes). This considerably ... other competitive method. On the other hand, some one- or two-dimensional problems which are not too complicated in geometry ...
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
Nonlinear diffusion equation; auxiliary equation method; solitary wave solution. PACS Nos 05.45.Yv; 02.30. ... tions not only of nonlinear partial differential equations but also of their coupled versions. These methods .... Case 1d: If A = 1, C = 2 − m2 and D = 1 − m2, then [18] z(ξ) = cn(ξ)/sn(ξ), and, from (7), we have u(ξ) = D1.
Differential invariants and exact solutions of the Einstein equations
Lychagin, Valentin; Yumaguzhin, Valeriy
2017-06-01
In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.
Some comments on developments in exact solutions in statistical mechanics since 1944
Baxter, R. J.
2010-11-01
Onsager and Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation ... The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the ...
ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC ...
African Journals Online (AJOL)
ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC RECTANGULAR PLATE ON WINKLERâ€™S FOUNDATION USING CHARACTERISTIC ... The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).
Analytic Solutions of the Space-Time Fractional Combined KdV-mKdV Equation
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2015-01-01
Full Text Available The fractional mapping method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional combined KdV-mKdV equation. Many types of exact analytical solutions are obtained. The solutions include generalized trigonometric and hyperbolic functions solutions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.
Exact and Approximate Stability of Solutions to Traveling Salesman Problems.
Niendorf, Moritz; Girard, Anouck R
2017-01-17
This paper presents the stability analysis of an optimal tour for the symmetric traveling salesman problem (TSP) by obtaining stability regions. The stability region of an optimal tour is the set of all cost changes for which that solution remains optimal and can be understood as the margin of optimality for a solution with respect to perturbations in the problem data. It is known that it is not possible to test in polynomial time whether an optimal tour remains optimal after the cost of an arbitrary set of edges changes. Therefore, this paper develops tractable methods to obtain under and over approximations of stability regions based on neighborhoods and relaxations. The application of the results to the two-neighborhood and the minimum 1 tree (M1T) relaxation are discussed in detail. For Euclidean TSPs, stability regions with respect to vertex location perturbations and the notion of safe radii and location criticalities are introduced. Benefits of this paper include insight into robustness properties of tours, minimum spanning trees, M1Ts, and fast methods to evaluate optimality after perturbations occur. Numerical examples are given to demonstrate the methods and achievable approximation quality.
On a revisit to the Painlevé test for integrability and exact solutions ...
Indian Academy of Sciences (India)
-dual equations for (2) gauge fields. Susanto Chakraborty Pranab Krishna Chanda. Research Articles Volume 66 ... Keywords. Painlevé analysis; integrability; auto-Backlund transformation; exact solutions; (2) gauge field; self-duality ...
Exact Solutions for Some Fractional Partial Differential Equations by the Method
Directory of Open Access Journals (Sweden)
Bin Zheng
2013-01-01
derivative. Based on a certain variable transformation, these fractional partial differential equations are transformed into ordinary differential equations of integer order. With the aid of mathematical software, a variety of exact solutions for them are obtained.
Energy Technology Data Exchange (ETDEWEB)
Barut, A.O. (Colorado Univ., Boulder (USA). Dept. of Physics); Oezaltin, O.; Uenal, N. (Dicle Univ., Diyarbakir (Turkey). Dept. of Physics)
1985-01-01
The Heisenberg equations for the Dirac electron in an external electromagnetic plane wave have been solved exactly in terms of incomplete ..gamma..-functions. As a special case the solution for a crossed constant electric and magnetic field is given.
Three classes of exact solutions to Klein-Gordon-Schrodinger equation
National Research Council Canada - National Science Library
Xia, Hongming; He, Wansheng; Hu, Linxia; Gao, Zhongshe
2013-01-01
Basing on the priori assumption principle, the main goal of this paper is to propose the rational expansion method that can be used to handle the exact solution of the nonlinear partial differential equation...
A new exact anisotropic solution of embedding class one
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K.; Smitha, T.T. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad (India); Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)
2016-07-15
We have presented a new anisotropic solution of Einstein's field equations for compact-star models. Einstein's field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor (Δ) by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor (Δ). The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2). (orig.)
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...... that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero....
An analytic solution to a driven interface problem
Energy Technology Data Exchange (ETDEWEB)
Hammerberg, J.E.; Pepin, J. [Los Alamos National Lab., NM (United States). Applied Theoretical and Computational Physics Div.
1997-10-01
The frictional properties of sliding metal interfaces at high velocities are not well known from either an experimental or theoretical point of view. The constitutive properties and macroscopic laws of frictional dynamics at high velocities necessary for materials continuum codes have only a qualitative validity and it is of interest to have analytic problems for sliding interfaces to enable separation of model from numerical effects. The authors present an exact solution for the space and time dependence of the plastic strain near a sliding interface in a planar semi-finite geometry. This solution is based on a particular form for the strain rate dependence of the flow stress and results in a hyperbolic telegrapher equation for the plastic strain. The form of the solutions and wave structure will be discussed.
An analytic solution to a driven interface problem
Energy Technology Data Exchange (ETDEWEB)
Hammerberg, J.E.; Pepin, J. [Applied Theoretical and Computational Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
1998-07-01
The frictional properties of sliding metal interfaces at high velocities are not well known either from an experimental or theoretical point of view. The constitutive properties and macroscopic laws of frictional dynamics at high velocities necessary for materials continuum codes have only a qualitative validity and it is of interest to have analytic problems for sliding interfaces to enable separation of model from numerical effects. We present an exact solution for the space and time dependence of the plastic strain near a sliding interface in a planar semi-infinite geometry. This solution is based on a particular form for the strain rate dependence of the flow stress and results in a hyperbolic telegrapher equation for the plastic strain. The form of the solutions and wave structure are discussed. {copyright} {ital 1998 American Institute of Physics.}
New methods to provide exact solutions for some unidirectional motions of rate type fluids
Directory of Open Access Journals (Sweden)
Fetecau Corina
2016-01-01
Full Text Available Based on three immediate consequences of the governing equations corresponding to some unidirectional motions of rate type fluids, new motion problems are tackled for exact solutions. For generality purposes, exact solutions are developed for shear stress boundary value problems of generalized Burgers fluids. Such solutions, for which the shear stress instead of its differential expressions is given on the boundary, are lack in the literature for such fluids. Consequently, the first exact solutions for motions of rate type fluids induced by an infinite plate or a circular cylinder that applies a constant shear f or an oscillating shear f sin(ωt to the fluid are here presented. In addition, all steady-state solutions can easily be reduced to known solutions for second grade and Newtonian fluids.
Analytic Solutions of Special Functional Equations
Directory of Open Access Journals (Sweden)
Octav Olteanu
2013-07-01
Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.
Exact solution of gyration radius of individual's trajectory for a simplified human mobility model
Yan, Xiao-Yong; Zhou, Tao; Wang, Bing-Hong
2010-01-01
Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and may eventually arrive to a steady value. However, up to now, the underlying mechanism leading to such a possibly steady value has not been well understood. In this Letter, we propose a simplified human mobility model to simulate individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that individual has constant travel speed and inferior limit of time at home and work, we prove that the daily moving area of an individual is an ellipse, and finally get an exact solution of the gyration radius. The analytical solution well captures the empirical observation reported in [M. C. Gonz`alez et al., Nature, 453 (2008) 779]. We also find that, in spite of the heterogeneous displacement ...
An Exact Method to Determine the Conductivity of Aqueous Solutions in Acid-Base Titrations
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Norma Rodríguez-Laguna
2015-01-01
Full Text Available Several works in the literature show that it is possible to establish the analytic equations to estimate the volume V of a strong base or a strong acid (Vb and Va, resp. being added to a solution of a substance or a mix of substances during an acid-base titration, as well as the equations to estimate the first derivative of the titration plot dpH/dV, and algebraic expressions to determine the buffer β capacity with dilution βdil. This treatment allows establishing the conditions of thermodynamic equilibria for all species within a system containing a mix of species from one or from various polyacid systems. The present work shows that it is possible to determine exactly the electric conductivity of aqueous solutions for these Brønsted acid-base titrations, because the functional relation between this property and the composition of the system in equilibrium is well known; this is achieved using the equivalent conductivity λi values of each of the ions present in a given system. The model employed for the present work confirms the experimental outcomes with the H2SO4, B(OH3, CH3COOH, and H3PO4 aqueous solutions’ titration.
Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution
Ghadiri, Majid; Jafari, Ali
2016-12-01
Present disquisition proposes an analytical solution method for exploring the vibration characteristics of a cantilever functionally graded nanobeam with a concentrated mass exposed to thermal loading for the first time. Thermo-mechanical properties of FGM nanobeam are supposed to change through the thickness direction of beam based on the rule of power-law (P-FGM). The small-scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Linear temperature rise (LTR) through thickness direction is studied. Existence of centralized mass in the free end of nanobeam influences the mechanical and physical properties. Timoshenko beam theory is employed to derive the nonlocal governing equations and boundary conditions of FGM beam attached with a tip mass under temperature field via Hamilton's principle. An exact solution procedure is exploited to achieve the non-dimensional frequency of FG nanobeam exposed to temperature field with a tip mass. A parametric study is led to assess the efficacy of temperature changes, tip mass, small scale, beam thickness, power-law exponent, slenderness and thermal loading on the natural frequencies of FG cantilever nanobeam with a point mass at the free end. It is concluded that these parameters play remarkable roles on the dynamic behavior of FG nanobeam subjected to LTR with a tip mass. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future thermo-mechanical analyses of FG nanobeam with tip mass.
Hemker, K.; Bakker, M.
2006-01-01
Analytical solutions are derived for steady state groundwater flow in a heterogeneous, anisotropic, semiconfined aquifer. The aquifer consists of a number of horizontal layers, while each layer consists of a number of homogeneous cells with different hydraulic conductivity tensors. An exact solution
New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation
Directory of Open Access Journals (Sweden)
Seyma Tuluce Demiray
2015-08-01
Full Text Available In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM and generalized Kudryashov method (GKM are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods.
Exact and heuristic solutions to the Double TSP with Multiple Stacks
DEFF Research Database (Denmark)
Petersen, Hanne Løhmann; Archetti, Claudia; Madsen, Oli B.G.
-pallet, which can be loaded in 3 stacks in a standard 40 foot container. Different exact and heuristic solution approaches to the DTSPMS have been implemented and tested. The exact approaches are based on different mathematical formulations of the problem which are solved using branch-and-cut. One formulation...... instances. The implemented heuristics include tabu search, simulated annealing and large neighbourhood search. Particularly the LNS approach shows promising results. It finds the known optimal solution of smaller instances (15 orders) within 10 seconds in most cases, and in 3 minutes it finds solutions...
Exact periodic wave solutions to the coupled schrِodinger-KdV ...
Indian Academy of Sciences (India)
Abstract. The exact solutions for the coupled non-linear partial differential equations are studied by means of the mapping method proposed recently by the author. Taking the coupled Schriodinger-KdV equation and DS equations as examples, abundant per- iodic wave solutions in terms of Jacobi elliptic functions are ...
Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation
Directory of Open Access Journals (Sweden)
Hongwei Yang
2012-01-01
Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.
Time-dependent exact solutions for Rosenau-Hyman equations with variable coefficients
Souza, Wescley Luiz de; Silva, Érica de Mello
2015-03-01
In this work we study Rosenau-Hyman-like equations that were obtained by imposing the Lie point symmetry algebra of standard KdV to a general K (m, n) equation with variable coefficients. We present time-dependent exact solutions for suited choices of parameters m and n, including the similarity solution related to rarefaction shock wave phenomena.
Exact solutions of the Fokker-Planck equation for the Malthus-Verhulst model
Brey, J. J.; Aizpuru, C.; Morillo, M.
1987-04-01
A class of particular solutions of the Fokker-Planck equation associated with the Malthus-Verhulst model is obtained. These time-dependent solutions are exact and allow us to study the evolution of both the distribution function and the moments. A careful analysis is carried out for the two simplest cases, showing the different possible types of relaxation.
Directory of Open Access Journals (Sweden)
Manoj Gaur
2016-01-01
Full Text Available We investigate the symmetry properties of a variable coefficient space-time fractional potential Burgers’ equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators, some group invariant solutions are deduced. Further, some exact solutions of fractional potential Burgers’ equation are generated by the invariant subspace method.
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…
Exact solutions of the Drinfel'd–Sokolov–Wilson equation using ...
Indian Academy of Sciences (India)
El Shorouk, Egypt. 2Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran ... mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. ... and physical scientists to obtain exact solutions of such nonlinear evolution equations and a num-.
Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length
Saakian, David B.
2017-08-01
We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.
An Exact Hot-Tube Solution For Thin Tape Helix Traveling-Wave Tube
Wong, Patrick; Lau, Y. Y.; Gilgenbach, Ronald; Chernin, David; Hoff, Brad
2017-10-01
The exact hot-tube dispersion relation for a thin tape helix traveling-wave tube (TWT) is derived for the first time, based on its exact cold-tube solution. This is an attempt to provide a reliable determination of the Pierce parameters, in particular the ``AC space-charge'' parameter QC, for a realistic TWT. The determination of QC remains an outstanding issue. The numerical results from the exact formulation will be compared with other approximate models of TWT that were commonly used in the literature for QC. This work was supported by AFOSR Grant No. FA9550-15-1-0097.
Zhang, Jinliang; Hu, Wuqiang; Ma, Yu
2016-12-01
In this paper, the famous Klein-Gordon-Zakharov equations are firstly generalized, the new special types of Klein-Gordon-Zakharov equations with the positive fractional power terms (gKGZE) are presented. In order to derive the exact solutions of new special gKGZE, the subsidiary higher order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aids of the Sub-ODE, the exact solutions of three special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.
Exact analytical representations for broadband transmission properties of quarter-wave multilayers.
Grigoriev, Victor; Biancalana, Fabio
2011-10-01
The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact analytical formula for the transmission spectrum, which is valid for the full spectral range and which contains only a limited number of parameters for structures satisfying the quarter-wave condition. These parameters are related to the poles of the scattering matrix, and we present an efficient algorithm to find them, which is based on considering the ray propagation inside the structure and subsequent application of the harmonic inversion technique. These results are significant for analyzing the reshaping of ultrashort pulses in multilayered structures. © 2011 Optical Society of America
Exact solutions for reconnective annihilation in magnetic configurations with three sources
Tassi, E.; Titov, V. S.; Hornig, G.
2002-01-01
Exact solutions of the steady resistive three dimensional (3D) magnetohydrodynamics (MHD) equations in cylindrical coordinates for an incompressible plasma are presented. The solutions are translationally invariant along one direction and in general they describe a process of reconnective annihilation in a curved current layer with non vanishing magnetic field. In the derivation of the solutions the ideal case with vanishing resistivity and electric field is considered first and then generali...
Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation
Aksoy, Esin; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2016-06-01
Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation are studied by the generalized Kudryashov method, the exp-function method and the (G'/G)-expansion method. The solutions obtained include the form of hyperbolic functions, trigonometric and rational functions. These methods are effective, simple, and many types of solutions can be obtained at the same time.
New exact solutions of the non-homogeneous Burgers equation in (1+1) dimensions
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel [Department of Science, University of Colima, Bernal Diaz del Castillo 340, Colima Villas San Sebastian, C P 28045, Colima (Mexico)
2007-04-15
We construct an invertible transformation between the non-homogeneous Burgers equation (NBE) and the stationary Schroedinger equation in (1+1) dimensions. By means of this transformation, each solution of the stationary Schroedinger equation generates a fully time-dependent solution of the NBE. As applications we derive exact solutions of the NBE for general power-law nonhomogeneities, generalizing former results on the linear case.
New exact solutions of sixth-order thin-film equation
Directory of Open Access Journals (Sweden)
Wafaa M. Taha
2014-01-01
Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.
Directory of Open Access Journals (Sweden)
Ilmārs Grants
2016-06-01
Full Text Available Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Rotating NS5-brane solution and its exact string theoretical description
Sfetsos, K.
1999-01-01
We construct the most general solution in type-II string theory that represents N coincident non-extremal rotating NS5-branes and determine the relevant thermodynamic quantities. We show that in the field theory limit, it has an exact description. In particular, it can be obtained by an O(3,3) duality transformation on the exact string background for the coset model SL(2,R)_{-N}/U(1) \\times SU(2)_N. In the extreme supersymmetric limit we recover the multicenter solution, with a ring singulari...
Regarding on the exact solutions for the nonlinear fractional differential equations
Directory of Open Access Journals (Sweden)
Kaplan Melike
2016-01-01
Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.
Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Baleanu, Dumitru
The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.
Directory of Open Access Journals (Sweden)
Özkan Güner
2014-01-01
Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.
Exact solutions to a schematic nuclear quark model and colorless superconductivity
DEFF Research Database (Denmark)
Bohr, Henrik; da Providencia, Joao
2008-01-01
Exact solutions are found to the equations of a standard nuclear quark model exemplified by the Bonn model which is defined in terms of an effective pairing force. We show, by symmetry arguments, that, in general, the ground state of this model is not color neutral. In particular, color-neutral s......Exact solutions are found to the equations of a standard nuclear quark model exemplified by the Bonn model which is defined in terms of an effective pairing force. We show, by symmetry arguments, that, in general, the ground state of this model is not color neutral. In particular, color...
A Coupling Technique for Analytical Solution of Time Fractional Biological Population Model
Mohan, R; Prajapati
2013-01-01
In this study, homotopy perturbation transform method (HPTM) is used to obtain the approximate analytical solutions of time fractional biological population model. The solution procedure obtained by proposed method indicate that the approach is easy to implement and accurate. Some numerical examples are given in the support of the validity of the method. These results reveal that the proposed method is very effective and easy to use. The comparisons between exact solution and approximate solu...
Analytical solutions of time–space fractional, advection–dispersion ...
Indian Academy of Sciences (India)
The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional ... Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Lahore Cantt 54792, Pakistan; Department of ...
Es'kin, V A; Kudrin, A V; Petrov, E Yu
2011-06-01
The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.
Directory of Open Access Journals (Sweden)
Alexander Shapovalov
2005-10-01
Full Text Available The complex WKB-Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross-Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors. Although the WKB-Maslov method is approximate in essence, it leads to exact solution of the Gross-Pitaevskii equation with an external and a nonlocal quadratic potential. For this equation, an exact solution of the Cauchy problem is constructed in the class of trajectory concentrated functions. A nonlinear evolution operator is found in explicit form and symmetry operators (mapping a solution of the equation into another solution are obtained for the equation under consideration. General constructions are illustrated by examples.
Exact solutions to the KDV-Burgers equation with forcing term using Tanh-Coth method
Chukkol, Yusuf Buba; Mohamad, Mohd Nor; Muminov, Mukhiddin I.
2017-08-01
In this paper, tanh-coth method was applied to derive the exact travelling wave solutions to the Korteweg-de-Vries and Burgers equation with forcing term(fKDVB). Solutions that are linear combination of solitary and shock wave solutions, and periodic wave solutions are obtained, by reducing the equation to the homogeneous type using a wave transformation. The method with the help of symbolic computation tool box provides a systematic way of solving many physical models involving nonlinear partial differential equations in mathematical physics.
Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel
Vasconcelos, Giovani L
2014-01-01
Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.
The Exact Solutions for a Point Mass Moving along a Stretched String on a Winkler Foundation
Directory of Open Access Journals (Sweden)
Q. Gao
2014-01-01
Full Text Available This paper derives the exact solutions for a point mass moving along a stretched infinite string on a Winkler foundation at a constant velocity. The solutions for the contact force between the string and the mass are derived and then the displacement responses of the string can be obtained easily. The solutions cover infinite string subjected to a moving mass at subsonic, sonic, or supersonic velocities. When time tends to infinity, the asymptotical solutions for the contact force between the mass and the string and for the displacement of the contact point are derived. The formulas derived are shown to be correct by comparison with the semianalytical method.
On some exact solutions of slightly variant forms of Yang's equations ...
Indian Academy of Sciences (India)
... Lecture Workshops · Refresher Courses · Symposia. Home; Journals; Pramana – Journal of Physics; Volume 70; Issue 5. On some exact solutions of slightly variant forms of Yang's equations and their graphical representations. Rupesh Kumar Sha Pranab Krishna Chanda. Research Articles Volume 70 Issue 5 May 2008 ...
Exact solutions to a class of nonlinear Schrödinger-type equations
Indian Academy of Sciences (India)
A class of nonlinear Schrödinger-type equations, including the Rangwala–Rao equation, the Gerdjikov–Ivanov equation, the Chen–Lee–Lin equation and the Ablowitz–Ramani–Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary ...
New exact solutions of fractional Hirota-Satsuma coupled Korteweg-de Vries equations
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Cui Lian-Xiang
2015-01-01
Full Text Available An improved extended tg-function method, which combines the fractional complex transform and the extended tanh-function method, is applied to find exact solutions of non-linear fractional partial differential equations. Generalized Hirota-Satsuma coupled Korteweg-de Vries equations are used as an example to elucidate the effectiveness and simplicity of the method.
Exact Solutions to the Fractional Differential Equations with Mixed Partial Derivatives
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Jun Jiang
2018-02-01
Full Text Available In this paper, the solvability of nonlinear fractional partial differential equations (FPDEs with mixed partial derivatives is considered. The invariant subspace method is generalized and is then used to derive exact solutions to the nonlinear FPDEs. Some examples are solved to illustrate the effectiveness and applicability of the method.
Lie group classifications and exact solutions for time-fractional Burgers equation
Wu, Guo-cheng
2010-01-01
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.
Exact solutions of some fractional differential equations by various expansion methods
Topsakal, Muammer; Guner, Ozkan; Bekir, Ahmet; Unsal, Omer
2016-10-01
In this paper, we construct the exact solutions of some nonlinear spacetime fractional differential equations involving modified Riemann-Liouville derivative in mathematical physics and applied mathematics; namely the fractional modified Benjamin-Bona- Mahony (mBBM) and Kawahara equations by using G'/G and (G'/G, 1/G)-expansion methods.
Exact solutions to a class of nonlinear Schrödinger-type equations
Indian Academy of Sciences (India)
Abstract. A class of nonlinear Schrödinger-type equations, including the Rangwala–Rao equation, the Gerdjikov–Ivanov equation, the Chen–Lee–Lin equation and the Ablowitz–. Ramani–Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of ...
New exact solutions to the generalized KdV equation with ...
Indian Academy of Sciences (India)
Abstract. In this paper, by using a transformation and an application of Fan subequation, we study a class of generalized Korteweg–de Vries (KdV) equation with generalized evolution. As a result, more types of exact solutions to the generalized KdV equation with generalized evolution are obtained, which include more ...
Directory of Open Access Journals (Sweden)
Ma Hong-Cai
2015-01-01
Full Text Available By using the improved hyperbolic function method, we investigate the variable coefficient Benjamin-Bona-Mahony-Burgers equation which is very important in fluid mechanics. Some exact solutions are obtained. Under some conditions, the periodic wave leads to the kink-like wave.
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring Motion
Cieśliński, J.; Gragert, P.K.H.; Sym, A.
1986-01-01
We present and discuss a three-parameter class of exact solutions to the localized-induction-approximation equations. These are one-soliton excitations (Bäcklund transforms) of the circular vortex motion. The corresponding generic vortex filament (of infinite or finite length) remains in the
New exact solutions for a charged fluid sphere in general relativity
Energy Technology Data Exchange (ETDEWEB)
Hajj-Boutros, J.; Sfeila, J.
1986-04-01
A new generation technique is elaborated in the case of static spherically symmetric distribution of a charged fluid. This technique deals only with a charged perfect fluid verifying a barytropic equation of state. Many new exact solutions are then generated from those of Pant and Sah, Banerjee and Santos, and Humi and Mansour. Their physical properties are then studied in some detail.
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
Analytical solutions for the recovery tests after constant-discharge ...
African Journals Online (AJOL)
A new analytical solution for residual drawdown during the recovery period after a constant rate pumping test is described. A comparison between the proposed solution, existing solutions and experimental data from field observation are presented. The proposed analytical solution is in perfect agreement with the ...
Exact solutions in modified massive gravity and off-diagonal wormhole deformations
Energy Technology Data Exchange (ETDEWEB)
Vacaru, Sergiu I. [Alexandru Ioan Cuza University, Rector' s Office, Iasi (Romania); CERN, Theory Division, Geneva 23 (Switzerland)
2014-03-15
We explore off-diagonal deformations of 'prime' metrics in Einstein gravity (for instance, for wormhole configurations) into 'target' exact solutions in f(R,T)-modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid--de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions. (orig.)
Exact solution of the space-time fractional coupled EW and coupled MEW equations
Raslan, K. R.; S. EL-Danaf, Talaat; K. Ali, Khalid
2017-07-01
In this paper, we obtained a traveling wave solution by using the Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations, such as the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEWE), which are the important soliton equations. Both equations are reduced to ordinary differential equations by use of the fractional complex transform and of the properties of the modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
Fully developed MHD natural convection flow in a vertical annular microchannel: An exact solution
Directory of Open Access Journals (Sweden)
Basant K. Jha
2015-07-01
Full Text Available An exact solution of steady fully developed natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical annular micro-channel with the effect of transverse magnetic field in the presence of velocity slip and temperature jump at the annular micro-channel surfaces is obtained. Exact solution is expressed in terms of modified Bessel function of the first and second kind. The solution obtained is graphically represented and the effects of radius ratio (η, Hartmann number (M, rarefaction parameter (βvKn, and fluid–wall interaction parameter (F on the flow are investigated. During the course of numerical computations, it is found that an increase in Hartmann number leads to a decrease in the fluid velocity, volume flow rate and skin friction. Furthermore, it is found that an increase in curvature radius ratio leads to an increase in the volume flow rate.
Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations
Vacaru, Sergiu I
2014-01-01
There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of solutions may posses, or not, Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormholes like objects matching external black ellipsoid - de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/ massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.
Exact solutions to sourceless charged massive scalar field equation on Kerr-Newman background
Wu, S. Q.; Cai, X.
1999-09-01
The covariant Klein-Gordon equation in the Kerr-Newman black hole geometry is separated into a radial part and an angular part. It is discovered that in the nonextreme case, these two equations belong to a generalized spin-weighted spheroidal wave equation. Then general exact solutions in integral forms and several special solutions with physical interest are given. While in the extreme case, the radial equation can be transformed into a generalized Whittaker-Hill equation. In both cases, five-term recurrence relations between coefficients in power series expansion of general solutions are presented. Finally, the connection between the radial equations in both cases is discussed.
Le Vine, D. M.; Meneghini, R.
1978-01-01
A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.
Analytical Solution for Reactive Solute Transport Considering Incomplete Mixing
Bellin, A.; Chiogna, G.
2013-12-01
The laboratory experiments of Gramling et al. (2002) showed that incomplete mixing at the pore scale exerts a significant impact on transport of reactive solutes and that assuming complete mixing leads to overestimation of product concentration in bimolecular reactions. We consider here the family of equilibrium reactions for which the concentration of the reactants and the product can be expressed as a function of the mixing ratio, the concentration of a fictitious non reactive solute. For this type of reactions we propose, in agreement with previous studies, to model the effect of incomplete mixing at scales smaller than the Darcy scale assuming that the mixing ratio is distributed within an REV according to a Beta distribution. We compute the parameters of the Beta model by imposing that the mean concentration is equal to the value that the concentration assumes at the continuum Darcy scale, while the variance decays with time as a power law. We show that our model reproduces the concentration profiles of the reaction product measured in the Gramling et al. (2002) experiments using the transport parameters obtained from conservative experiments and an instantaneous reaction kinetic. The results are obtained applying analytical solutions both for conservative and for reactive solute transport, thereby providing a method to handle the effect of incomplete mixing on multispecies reactive solute transport, which is simpler than other previously developed methods. Gramling, C. M., C. F. Harvey, and L. C. Meigs (2002), Reactive transport in porous media: A comparison of model prediction with laboratory visualization, Environ. Sci. Technol., 36(11), 2508-2514.
Directory of Open Access Journals (Sweden)
Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
Exact cosmological solutions of f(R theories via Hojman symmetry
Directory of Open Access Journals (Sweden)
Hao Wei
2016-02-01
Full Text Available Nowadays, f(R theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of f(R theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in f(R theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of f(R theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in f(R theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.
Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
Bleher, P M
2005-01-01
The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...
Manufactured analytical solutions for isothermal full-Stokes ice sheet models
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A. Sargent
2010-08-01
Full Text Available We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed.
The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
Liu, Albert Tianxiang; Zaveri, Rahul A.; Seinfeld, John H.
2014-06-01
We present the exact analytical solution of the transient equation of gas-phase diffusion of a condensing vapor to, and diffusion and reaction in, an aqueous droplet. Droplet-phase reaction is represented by first-order chemistry. The solution facilitates study of the dynamic nature of the vapor uptake process as a function of droplet size, Henry's law coefficient, and first-order reaction rate constant for conversion in the droplet phase.
Exact Solution of the Three-Body Santilli-Shillady Model of the Hydrogen Molecule
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Pérez-Enríquez R.
2007-04-01
Full Text Available The conventional representation of the H 2 molecule characterizes a 4-body system due to the independence of the orbitals of the two valence electrons as requested by quantum chemistry, under which conditions no exact solution is possible. To overcome this problem, Santilli and Shillady introduced in 1999 a new model of the H 2 -molecu- le in which the two valence electrons are deeply bounded-correlated into a single quasi-particle they called isoelectronium that is permitted by the covering hadronic chemistry. They pointed out that their new H 2 -model is a restricted 3-body system that, as such, is expected to admit an exact solution and suggested independent studies for its identification due to its relevance, e.g., for other molecules. In 2000, Aringazin and Kucherenko did study the Santilli-Shillady restricted 3-body model of the H 2 molecules, but they presented a variational solution that, as such, is not exact. In any case, the latter approach produced significant deviations from experimental data, such as a 19.6% inter-nuclear distance greater than the experimental value. In this paper we present, apparently for the first time, an exact solution of the Santilli-Shillady restricted 3-body model of the Hydrogen molecule along the lines of its originators and show that it does indeed represent correctly all basic data. Intriguingly, our solution confirms that the orbital of the isoelectronium (referred to as its charge distribution around the nuclei must be concentrated in a limited region of space given by the Santilli-Shillady oo-shaped orbits. Our exact solution is constructed by following the Ley-Koo solution to the Schr ̈ odinger equation for a confined hydrogen molecular ion, H + 2 . We show that a confined model to the 3-body molecule reproduces the ground state curve as calculated by Kolos, Szalewics and Monkhorst with a precision up to the 4-th digit and a precision in the representation of the binding energy up to the 5-th digit.
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Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields
Asenjo, Felipe A.; Hojman, Sergio A.
2017-07-01
A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.
Exact solutions to the supply chain equations for arbitrary, time-dependent demands
DEFF Research Database (Denmark)
Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn
2014-01-01
, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...
Exact solution of the two-level system and the Einstein solid in the microcanonical formalism
Energy Technology Data Exchange (ETDEWEB)
Bertoldi, Dalia S; Bringa, Eduardo M; Miranda, E N, E-mail: emiranda@mendoza-conicet.gov.ar [Instituto de Ciencias Basicas, UNCuyo 5500, Mendoza (Argentina)
2011-11-15
The two-level system and the Einstein model of a crystalline solid are taught in every course of statistical mechanics and they are solved in the microcanonical formalism because the number of accessible microstates can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials. In this paper, those two models are solved without any approximation, using the gamma function and its derivatives. Exact values are calculated for the entropy, temperature and specific heat, and the relative error between our exact solution and the approximate one using the Stirling approximation. This error is significant for small systems, with a number of particles N {approx} 100, as in studies of atomic clusters or nanoscale structures.
Energy Technology Data Exchange (ETDEWEB)
Tajahmad, Behzad [University of Tabriz, Faculty of Physics, Tabriz (Iran, Islamic Republic of)
2017-04-15
In this paper, we present the Noether symmetries of flat FRW spacetime in the context of a new action in teleparallel gravity which we construct based on the f(R) version. This modified action contains a coupling between the scalar field potential and magnetism. Also, we introduce an innovative approach, the beyond Noether symmetry (B.N.S.) approach, for exact solutions which carry more conserved currents than the Noether approach. By data analysis of the exact solutions, obtained from the Noether approach, late-time acceleration and phase crossing are realized, and some deep connections with observational data such as the age of the universe, the present value of the scale factor as well as the state and deceleration parameters are observed. In the B.N.S. approach, we consider the dark energy dominated era. (orig.)
Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model
Mazaré, Pierre Emmanuel
2011-12-01
In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.
Directory of Open Access Journals (Sweden)
Nelly S. Khapilova
2015-10-01
Full Text Available We present the analytical solution of the axisymmetric mixed problem for the isotropic half-space with the surface fixed elastically outside the circular area of the application of a distributed load. In the solution of the problem, the transition procedure from a distributed load to the concentrated force has been justified. A compact form of the exact analytical solution of the problem on the concentrated force applied to the half-space with the surface fixed elastically was obtained. In the specific case when the proportionality factor of normal stresses and displacements vanishing under the condition of the elastic fixing of the boundary, the constructed analytical solution was shown to coincide with the well-known Boussinesq formulae.
A new approach to the exact solutions of the effective mass Schrodinger equation
Tezcan, Cevdet; Sever, Ramazan; Yesiltas, Ozlem
2007-01-01
Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrodinger equation is also solved for the Morse potential transforming to the constant mass Schr\\"{o}dinger equation for a potential. One can also get solution of the effective mass Schrodinger equation starting from the constant m...
Exact solutions for MHD flow of couple stress fluid with heat transfer
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Najeeb Alam Khan
2016-01-01
Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.
Exact solution of a generalized two-sites Bose-Hubbard model
Filho, Gilberto N Santos
2016-01-01
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.
Symmetry properties, similarity reduction and exact solutions of fractional Boussinesq equation
Rashidi, Saeede; Hejazi, S. Reza
In this paper, some properties of the time fractional Boussinesq equation are presented. Group analysis of the time fractional Boussinesq equation with Riemann-Liouville derivative is performed and the corresponding optimal system of subgroups are determined. Next, we apply the obtained optimal systems for constructing reduced fractional ordinary differential equations (FODEs). Finally, we show how to derive exact solutions to time fractional Boussinesq equation via invariant subspace method.
Exact Solutions to Some Conformable Time Fractional Equations in Benjamin-Bona-Mahony Family
Korkmaz, Alper
2016-01-01
The conformable time fractional forms of some partial differential equations are solved in the study. The existence of chain rule and the derivative of composite function enable the equations to be reduced to some ordinary differential equations by using some particular wave transformations. The modified Kudryashov method implemented to derive the exact solutions for the Benjamin-Bona Mahony (BBM), the symmetric BBM and the equal width (EW) equations in the conformable fractional time derivat...
A procedure to construct exact solutions of nonlinear fractional differential equations.
Güner, Özkan; Cevikel, Adem C
2014-01-01
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Exact Solutions for Some Fractional Partial Differential Equations by the Method
Zheng, Bin
2013-01-01
We apply the method to seek exact solutions for several fractional partial differential equations including the space-time fractional (2 + 1)-dimensional dispersive long wave equations, the (2 + 1)-dimensional space-time fractional Nizhnik-Novikov-Veselov system, and the time fractional fifth-order Sawada-Kotera equation. The fractional derivative is defined in the sense of modified Riemann-liouville derivative. Based on a certain variable transformation, these fractional partial diffe...
Wei Li; Huizhang Yang; Bin He
2014-01-01
Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets
Yang, Xiao-Jun; Gao, Feng; Srivastava, H. M.
In the present paper, a family of the special functions via the celebrated Mittag-Leffler function defined on the Cantor sets is investigated. The nonlinear local fractional ODEs (NLFODEs) are presented by following the rules of local fractional derivative (LFD). The exact solutions for these problems are also discussed with the aid of the non-differentiable charts on Cantor sets. The obtained results are important for describing the characteristics of the fractal special functions.
Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
A new approach to exact solutions construction in scalar cosmology with a Gauss-Bonnet term
Fomin, I. V.; Chervon, S. V.
2017-08-01
We study the cosmological model based on Einstein-Gauss-Bonnet gravity with non-minimal coupling of a scalar field to a Gauss-Bonnet term in four-dimensional (4D) Friedmann universe. We show how constructing the exact solutions by the method based on a confrontation of the Hubble parameter in the model under consideration is achieved with that in a standard scalar field inflationary cosmology.
Compressible Flow Produced by Distributed Sources of Mass: An Exact Solution
Clarke, J. F.
1987-01-01
The paper considers the case of a one-dimensional isentropic unsteady compressible flow that is driven entirely by a distribution of sources in the left-hand half space of an unbounded domain. The right-hand half-space contains no sources, so that source-strength drops discontinuously to zero as one crosses from left to right-hand space. Exact solutions are obtained for those parts of the flow that remain isentropic.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used ...
Analytic P{sub 1} solutions for time-dependent, thermal radiative transfer in several geometries
Energy Technology Data Exchange (ETDEWEB)
McClarren, Ryan G. [Computational Physics and Methods Group (CCS-2), Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States)], E-mail: ryanmc@lanl.gov; Paul Holloway, James [Department of Nuclear Engineering and Radiological Sciences, College of Engineering, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 2104 (United States); Brunner, Thomas A. [Sandia National Laboratories, P.O. Box 5800, MS 1186, Albuquerque, NM 87185 1186 (United States)
2008-02-15
We present several solutions for the time-dependent P{sub 1} approximation (telegrapher's equation) coupled to thermal radiative transfer with C{sub v}{proportional_to}T{sup 3}. Our solutions are based on the energy density Green's function in slab geometry, which we derive exactly. The analytic P{sub 1} solution is compared with analytic transport and diffusion solutions on one of the Su-Olson benchmark problems. Also, we transform the slab geometry Green's function into the solution from a point source (the 1D spherical Green's function) and an infinite line source (the 1D cylindrical Green's function). We evaluate the P{sub 1} solution to the line source and compare the result with a solution generated by a P{sub n} numerical method.
Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates
Biasi, Anxo; Bizoń, Piotr; Craps, Ben; Evnin, Oleg
2017-11-01
The lowest Landau level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our paper provides a controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multivortex solutions.
Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries
Directory of Open Access Journals (Sweden)
Hugo Hernán Ortíz-Álvarez
2015-01-01
Full Text Available The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.
Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan
2018-01-01
In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.
Exact solutions of time fractional heat-like and wave-like equations with variable coefficients
Directory of Open Access Journals (Sweden)
Zhang Sheng
2016-01-01
Full Text Available In this paper, a variable-coefficient time fractional heat-like and wave-like equation with initial and boundary conditions is solved by the use of variable separation method and the properties of Mittag-Leffler function. As a result, exact solutions are obtained, from which some known special solutions are recovered. It is shown that the variable separation method can also be used to solve some others time fractional heat-like and wave-like equation in science and engineering.
Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption.
Lenzi, E K; Mendes, G A; Mendes, R S; da Silva, L R; Lucena, L S
2003-05-01
We analyze a nonlinear fractional diffusion equation with absorption by employing fractional spatial derivatives and obtain some more exact classes of solutions. In particular, the diffusion equation employed here extends some known diffusion equations such as the porous medium equation and the thin film equation. We also discuss some implications by considering a diffusion coefficient D(x,t)=D(t)/x/(-theta) (theta in R) and a drift force F=-k(1)(t)x+k(alpha)x/x/(alpha-1). In both situations, we relate our solutions to those obtained within the maximum entropy principle by using the Tsallis entropy.
Bezerra, V. B.; Christiansen, H. R.; Cunha, M. S.; Muniz, C. R.
2017-07-01
We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity's rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.
Some exact anisotropic solutions via Noether symmetry in f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Sharif, M., E-mail: msharif.math@pu.edu.pk; Nawazish, I., E-mail: iqranawazish07@gmail.com [University of the Punjab, Department of Mathematics (Pakistan)
2015-01-15
We attempt to find exact solutions of the Bianchi I model in f(R) gravity using the Noether symmetry approach. For this purpose, we take a perfect fluid and formulate conserved quantities for the power-law f(R) model. We discuss some cosmological parameters for the resulting solution which are responsible for expanding behavior of the universe. We also explore Noether gauge symmetry and the corresponding conserved quantity. It is concluded that symmetry generators as well as conserved quantities exist in all cases and the behavior of cosmological parameters shows consistency with recent observational data.
Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans
2011-04-01
Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the Lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris’ current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.
Exact solitary wave and quasi-periodic wave solutions of the KdV-Sawada-Kotera-Ramani equation
National Research Council Canada - National Science Library
Zhang, Lijun; Khalique, Chaudry Masood
2015-01-01
In this paper we derive new exact solitary wave solutions and quasi-periodic traveling wave solutions of the KdV-Sawada-Kotera-Ramani equation by using a method which we introduce here for the first time...
Migration of radionuclides through sorbing media analytical solutions--II
Energy Technology Data Exchange (ETDEWEB)
Pigford, T.H.; Chambre, P.L.; Albert, M.
1980-10-01
This report presents analytical solutions, and the results of such solutions, for the migration of radionuclides in geologic media. Volume 1 contains analytical solutions for one-dimensional equilibrium transport in infinite media and multilayered media. One-dimensional non-equilibrium transport solutions are also included. Volume 2 contains analytical solutions for transport in a one-dimensional field flow with transverse dispersion as well as transport in multi-dimensional flow. A finite element solution of the transport of radionuclides through porous media is discussed. (DMC)
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
Some exact solutions to the Lighthill-Whitham-Richards-Payne traffic flow equations
Rowlands, G.; Infeld, E.; Skorupski, A. A.
2013-09-01
We find a class of exact solutions to the Lighthill-Whitham-Richards-Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg-de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end.
Exact Travelling Wave Solutions for Isothermal Magnetostatic Atmospheres by Fan Subequation Method
Directory of Open Access Journals (Sweden)
Hossein Jafari
2012-01-01
ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. These equations transform to a single nonlinear elliptic equation for the magnetic vector potential . This equation depends on an arbitrary function of that must be specified. With choices of the different arbitrary functions, we obtain analytical solutions of elliptic equation using the Fan subequation method.
Discretization error estimation and exact solution generation using the method of nearby problems.
Energy Technology Data Exchange (ETDEWEB)
Sinclair, Andrew J. (Auburn University Auburn, AL); Raju, Anil (Auburn University Auburn, AL); Kurzen, Matthew J. (Virginia Tech Blacksburg, VA); Roy, Christopher John (Virginia Tech Blacksburg, VA); Phillips, Tyrone S. (Virginia Tech Blacksburg, VA)
2011-10-01
The Method of Nearby Problems (MNP), a form of defect correction, is examined as a method for generating exact solutions to partial differential equations and as a discretization error estimator. For generating exact solutions, four-dimensional spline fitting procedures were developed and implemented into a MATLAB code for generating spline fits on structured domains with arbitrary levels of continuity between spline zones. For discretization error estimation, MNP/defect correction only requires a single additional numerical solution on the same grid (as compared to Richardson extrapolation which requires additional numerical solutions on systematically-refined grids). When used for error estimation, it was found that continuity between spline zones was not required. A number of cases were examined including 1D and 2D Burgers equation, the 2D compressible Euler equations, and the 2D incompressible Navier-Stokes equations. The discretization error estimation results compared favorably to Richardson extrapolation and had the advantage of only requiring a single grid to be generated.
Analytical solution of linear ordinary differential equations by differential transfer matrix method
Directory of Open Access Journals (Sweden)
Sina Khorasani
2003-08-01
Full Text Available We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the $n$th-order differential equation to a system of $n$ linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method.
EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon–Mann–Whitney Test
Directory of Open Access Journals (Sweden)
Alexander Marx
2016-02-01
Full Text Available In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney (WMW test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD. We found that approximated P values were generally higher than the exact solution provided by EDISON-WMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.
Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity
Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.
2017-11-01
Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.
Interference effects in phased beam tracing using exact half-space solutions.
Boucher, Matthew A; Pluymers, Bert; Desmet, Wim
2016-12-01
Geometrical acoustics provides a correct solution to the wave equation for rectangular rooms with rigid boundaries and is an accurate approximation at high frequencies with nearly hard walls. When interference effects are important, phased geometrical acoustics is employed in order to account for phase shifts due to propagation and reflection. Error increases, however, with more absorption, complex impedance values, grazing incidence, smaller volumes and lower frequencies. Replacing the plane wave reflection coefficient with a spherical one reduces the error but results in slower convergence. Frequency-dependent stopping criteria are then applied to avoid calculating higher order reflections for frequencies that have already converged. Exact half-space solutions are used to derive two additional spherical wave reflection coefficients: (i) the Sommerfeld integral, consisting of a plane wave decomposition of a point source and (ii) a line of image sources located at complex coordinates. Phased beam tracing using exact half-space solutions agrees well with the finite element method for rectangular rooms with absorbing boundaries, at low frequencies and for rooms with different aspect ratios. Results are accurate even for long source-to-receiver distances. Finally, the crossover frequency between the plane and spherical wave reflection coefficients is discussed.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Energy Technology Data Exchange (ETDEWEB)
Nieto, M.M. [Los Alamos National Lab., NM (United States); Daboul, J. [Ben Gurion Univ. of the Negev, Beer Sheva (Israel)
1994-07-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = {minus}{gamma}/r{sup {nu}}, {gamma} > 0 and {minus}{infinity} < {nu} < {infinity}. When the angular momentum is non-zero, these solutions lead to the classical orbits {rho}(t) = [cos {mu}({var_phi}(t) {minus} {var_phi}{sub 0}(t))]{sup 1/{mu}}, with {mu} = {nu}/2 {minus} 1 {ne} 0. For {nu} > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when {nu} > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed.
Validation of ANUGA hydraulic model using exact solutions to shallow water wave problems
Mungkasi, S.; Roberts, S. G.
2013-04-01
ANUGA is an open source and free software developed by the Australian National University (ANU) and Geoscience Australia (GA). This software is a hydraulic numerical model used to solve the two-dimensional shallow water equations. The numerical method underlying it is a finite volume method. This paper presents some validation results of ANUGA with respect to exact solutions to shallow water flow problems. We identify the strengths of ANUGA and comment on future work that may be taken into account for ANUGA development.
Exact Solutions and Conserved Quantities in f(R,T) Gravity
Sharif, M
2016-01-01
This paper explores Noether and Noether gauge symmetries of anisotropic universe model in $f(R,T)$ gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.
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.
Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits
Directory of Open Access Journals (Sweden)
J. Niederle
2010-01-01
Full Text Available Two Maxwell-Chern-Simons (MCS models in the (1 + 3-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.
Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra
Merad, M.; Hadj Moussa, M.
2018-01-01
In this paper, we present the exact solution of the (1+1)-dimensional relativistic Klein-Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder-de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen-Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for α 1 and α 2 → 0 and are compared with those of literature.
Exact solutions of (3â¯+â¯1-dimensional generalized KP equation arising in physics
Directory of Open Access Journals (Sweden)
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
Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation
Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu
2016-01-01
Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The ex...
Investigation of ALEGRA shock hydrocode algorithms using an exact free surface jet flow solution.
Energy Technology Data Exchange (ETDEWEB)
Hanks, Bradley Wright.; Robinson, Allen C
2014-01-01
Computational testing of the arbitrary Lagrangian-Eulerian shock physics code, ALEGRA, is presented using an exact solution that is very similar to a shaped charge jet flow. The solution is a steady, isentropic, subsonic free surface flow with significant compression and release and is provided as a steady state initial condition. There should be no shocks and no entropy production throughout the problem. The purpose of this test problem is to present a detailed and challenging computation in order to provide evidence for algorithmic strengths and weaknesses in ALEGRA which should be examined further. The results of this work are intended to be used to guide future algorithmic improvements in the spirit of test-driven development processes.
Aman, Sidra; Zuki Salleh, Mohd; Ismail, Zulkhibri; Khan, Ilyas
2017-09-01
This article focuses on the flow of Maxwell nanofluids with graphene nanoparticles over a vertical plate (static) with constant wall temperature. Possessing high thermal conductivity, engine oil is useful to be chosen as base fluid with free convection. The problem is modelled in terms of PDE’s with boundary conditions. Some suitable non-dimensional variables are interposed to transform the governing equations into dimensionless form. The generated equations are solved via Laplace transform technique. Exact solutions are evaluated for velocity and temperature. These solutions are significantly controlled by some parameters involved. Temperature rises with elevation in volume fraction while Velocity decreases with increment in volume fraction. A comparison with previous published results are established and discussed. Moreover, a detailed discussion is made for influence of volume fraction on the flow and heat profile.
Noether symmetries and exact solutions of an Euler-Bernoulli beam model
Fatima, Aeeman; Mahomed, Fazal M.; Khalique, Chaudry Masood
2016-07-01
In this paper, a Noether symmetry analysis is carried out for an Euler-Bernoulli beam equation via the standard Lagrangian of its reduced scalar second-order equation which arises from the standard Lagrangian of the fourth-order beam equation via its Noether integrals. The Noether symmetries corresponding to the reduced equation is shown to be the inherited Noether symmetries of the standard Lagrangian of the beam equation. The corresponding Noether integrals of the reduced Euler-Lagrange equations are deduced which remarkably allows for three families of new exact solutions of the static beam equation. These are shown to contain all the previous solutions obtained from the standard Lie analysis and more.
Pazzona, Federico G.; Demontis, Pierfranco; Suffritti, Giuseppe B.
2014-08-01
The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013), 10.1103/PhysRevE.88.062144] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters ϕ and θ. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.
Yavorskii, N. I.
2017-09-01
Magnetohydrodynamic (MHD) flow of a viscous electrically conducting incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector normal to the surface is specified on the upper disk, and the lower disk is nonconducting. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameters: the electric current density on the upper plate Y and the Batchelor number (magnetic Prandtl number). It is assumed that there is no external source that produces an axial magnetic field. The problem is solved for a Batchelor number of 0-2. Fluid flow is caused by the electric current. It is shown that for small values of Y, the fluid velocity vector has only axial and radial components. The velocity of motion increases with increasing Y, and at a critical value of Y, there is a bifurcation of the new steady flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism for the bifurcation of rotation in MHD flow is found.
The exact solution of self-consistent equations in the scanning near-field optic microscopy problem
DEFF Research Database (Denmark)
Lozovski, Valeri; Bozhevolnyi, Sergey I.
1999-01-01
The macroscopic approach that allows one to obtain an exact solution of the self-consistent equation of the Lippmann-Schwinger type is developed. The main idea of our method consist in usage of diagram technque for exact summation of the infinite series corresponding to the iteration procedure fo...
Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method
Directory of Open Access Journals (Sweden)
Muhammad Shakeel
2014-01-01
Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.
Analytical solution for soil water redistribution during evaporation process.
Teng, Jidong; Yasufuku, Noriyuki; Liu, Qiang; Liu, Shiyu
2013-01-01
Simulating the dynamics of soil water content and modeling soil water evaporation are critical for many environmental and agricultural strategies. The present study aims to develop an analytical solution to simulate soil water redistribution during the evaporation process. This analytical solution was derived utilizing an exponential function to describe the relation of hydraulic conductivity and water content on pressure head. The solution was obtained based on the initial condition of saturation and an exponential function to model the change of surface water content. Also, the evaporation experiments were conducted under a climate control apparatus to validate the theoretical development. Comparisons between the proposed analytical solution and experimental result are presented from the aspects of soil water redistribution, evaporative rate and cumulative evaporation. Their good agreement indicates that this analytical solution provides a reliable way to investigate the interaction of evaporation and soil water profile.
Hopping conductivity of a one-dimensional bond-percolation model in a constant field: Exact solution
Khantha, M.; Balakrishnan, V.
1984-04-01
The recent work of Odagaki and Lax on the ac hopping conductivity in a one-dimensional bond-percolation model is generalized to include a constant applied field. The corresponding biased random-walk problem on a finite chain of arbitrary length and with properly terminated ends is solved analytically. The solution is extended to include all continuous-time random walks. (It is thus directly applicable, for instance, to spectral diffusion with asymmetric transfer rates and memory effects.) The diffusivity (and thence the conductivity and relative permittivity) on a chain of N sites is obtained exactly, in closed form. A configuration averaging over N yields the diffusivity and relative permittivity for the randomly interrupted infinite chain. Our analytic results are valid at all frequencies, and are in a form amenable to extensive numerical computation. This is done, and the noteworthy features of the results are displayed graphically. All the known results in the field-free case are recovered as special cases of the expressions presented here.
Analytical solutions of one-dimensional advection–diffusion ...
Indian Academy of Sciences (India)
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the ...
A Comprehensive Analytical Solution of the Nonlinear Pendulum
Ochs, Karlheinz
2011-01-01
In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…
Analytical travelling wave solutions and parameter analysis for the ...
Indian Academy of Sciences (India)
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams ...
Zhang, Zhizeng; Zhao, Zhao; Li, Yongtao
2016-06-01
This paper attempts to verify the correctness of the analytical displacement solution in transversely isotropic rock mass, and to determine the scope of its application. The analytical displacement solution of a circular tunnel in transversely isotropic rock mass was derived firstly. The analytical solution was compared with the numerical solution, which was carried out by FLAC3D software. The results show that the expression of the analytical displacement solution is correct, and the allowable engineering range is that the dip angle is less than 15 degrees.
Exact solutions to plaquette Ising models with free and periodic boundaries
Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard
2017-01-01
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) [1], who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) [2]. We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Majorana fermions in the nonuniform Ising-Kitaev chain: exact solution.
Narozhny, Boris
2017-05-03
A quantum computer based on Majorana qubits would contain a large number of zero-energy Majorana states. This system can be modelled as a connected network of the Ising-Kitaev chains alternating the "trivial" and "topological" regions, with the zero-energy Majorana fermions localized at their interfaces. The low-energy sector of the theory describing such a network can be formulated in terms of leading-order couplings between the Majorana zero modes. I consider a minimal model exhibiting effective couplings between four Majorana zero modes - the nonuniform Ising-Kitaev chain, containing two "topological" regions separated by a "trivial" region. Solving the model exactly, I show that for generic values of the model parameters the four zero modes are localized at the four interface points of the chain. In the special case where additional inversion symmetry is present, the Majorana zero modes are "delocalized" between two interface points. In both cases, the low-energy sector of the theory can be formulated in terms of the localized Majorana fermions, but the couplings between some of them are independent of their respective separations: the exact solution does not support the "nearest-neighbor" form of the effective low-energy Hamiltonian.
Exact solutions to plaquette Ising models with free and periodic boundaries
Energy Technology Data Exchange (ETDEWEB)
Mueller, Marco, E-mail: Marco.Mueller@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig (Germany); Johnston, Desmond A., E-mail: D.A.Johnston@hw.ac.uk [Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland (United Kingdom); Janke, Wolfhard, E-mail: Wolfhard.Janke@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig (Germany)
2017-01-15
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) , who later dubbed it the fuki-nuke, or “no-ceiling”, model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) . We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
Laplace transform obtained from literature. ... used in the literature. Keywords. Population balance; aggregation; breakage; auxiliary equation method; Laplace transform. PACS Nos 02.70.−c; 02.30.Mv; 02.30.Jr. 1. ...... assumptions proposed earlier, a more realistic representation of the solutions is obtained compared to the ...
Analytical Solutions To Describe Juxtaposed Sands | Adeniji ...
African Journals Online (AJOL)
... face flow rate, but can be extended, using convolution integral that can be deconvolved by Laplace transformation, to correct for storage capacity of the well bore and near well bore complexities. These solutions can improve design and analysis of interference testing. Type curves are presented to characterize flow regime ...
Exact solution to the steady-state dynamics of a periodically modulated resonator
Directory of Open Access Journals (Sweden)
Momchil Minkov
2017-07-01
Full Text Available We provide an analytic solution to the coupled-mode equations describing the steady-state of a single periodically modulated optical resonator driven by a monochromatic input. The phenomenology of this system was qualitatively understood only in the adiabatic limit, i.e., for low modulation speed. However, both in and out of this regime, we find highly non-trivial effects for specific parameters of the modulation. For example, we show complete suppression of the transmission even with zero detuning between the input and the static resonator frequency. We also demonstrate the possibility for complete, lossless frequency conversion of the input into the sideband frequencies, as well as for optimizing the transmitted signal towards a given target temporal waveform. The analytic results are validated by first-principle simulations.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-08-15
Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.
Analytical construction of peaked solutions for the nonlinear ...
African Journals Online (AJOL)
We obtain analytical solutions, by way of the homotopy analysis method, to a nonlinear wave equation describing the nonlinear evolution of a vector potential of an electromagnetic pulse propagating in an arbitrary pair plasma with temperature asymmetry. As the method is analytical, we are able to construct peaked ...
Energy Technology Data Exchange (ETDEWEB)
Kwok Sau Fa [Departamento de Fisica, Universidade Estadual de Maringa, Av. Colombo 5790, 87020-900 Maringa-PR (Brazil); Joni Fat, E-mail: kwok@dfi.uem.br [Jurusan Teknik Elektro-Fakultas Teknik, Universitas Tarumanagara, Jl. Let. Jend. S. Parman 1, Blok L, Lantai 3 Grogol, Jakarta 11440 (Indonesia)
2011-10-15
We consider the decoupled continuous-time random walk model with a finite characteristic waiting time and approximate jump length variance. We take the waiting time probability density function (PDF) given by a combination of the exponential and the Mittag-Leffler function. Using this waiting time PDF, we investigate the diffusion behavior for all times. We obtain exact solutions for the first two moments and the PDF for the force-free and linear force cases. Due to the finite characteristic waiting time and jump length variance, the model presents, for the force-free case, normal diffusive behavior in the long-time limit. Further, the model can describe anomalous behavior at intermediate times.
Exact solution of SU(4) non-equilibrium Kondo model at the Toulouse point.
Duki, Solomon; Mathur, Harsh
2007-03-01
SU(4) symmetry in quantum dots has become a growing interest in both semiconductor quantum dots and carbon nanotube quantum dots[1]. We investigate theoretically the properties of an SU(4) Kondo model out of equilibrium by solving the problem exactly at a special point in the parameter space. The solution reveals that, in contrast to the SU(2) model, there are two more excitations in the system other than the charge and spin excitations. We investigate the differential conductance for arbitrary voltage bias. [1] P. Jarillo-Herrero, J. Kong, H.S.J. van der Zant, C. Dekker, L.P. Kouwenhoven and S. De Franceschi, http://www.nature.com/openurl?urlver=Z39.88-2004&rftvalfmt=info:ofi/fmt:kev:mtx:journal&rft.genre=journal&rft. volume=434&rft.spage=484 &rft.date=2005 (Nature) 434, 484, (2005).
Mach, Patryk; Karkowski, Janusz
2013-01-01
We investigate spherical, isothermal and polytropic steady accretion models in the presence of the cosmological constant. Exact solutions are found for three classes of isothermal fluids, assuming the test gas approximation. The cosmological constant damps the mass accretion rate and - above certain limit - completely stops the steady accretion onto black holes. A "homoclinic-type" accretion flow of polytropic gas has been discovered in AdS spacetimes in the test-gas limit. These results can have cosmological connotation, through the Einstein--Straus vacuole model of embedding local structures into Friedman-Lemaitre-Robertson-Walker spacetimes. In particular one infers that steady accretion would not exist in the late phases of the Penrose's scenario of the evolution of the Universe, known as the Weyl curvature hypothesis.
Mach, Patryk; Malec, Edward; Karkowski, Janusz
2013-10-01
We investigate spherical, isothermal and polytropic steady accretion models in the presence of the cosmological constant. Exact solutions are found for three classes of isothermal fluids, assuming the test gas approximation. The cosmological constant damps the mass accretion rate and—above a certain limit—completely stops the steady accretion onto black holes. A “homoclinic-type” accretion flow of polytropic gas has been discovered in anti-de Sitter spacetimes in the test-gas limit. These results can have cosmological connotation, through the Einstein-Straus vacuole model of embedding local structures into Friedman-Lemaitre-Robertson-Walker spacetimes. In particular, one infers that steady accretion would not exist in the late phases of Penrose’s scenario of the evolution of the Universe, known as the Weyl curvature hypothesis.
Exact solutions for non-Hermitian Dirac-Pauli equation in an intensive magnetic field
Rodionov, V. N.
2015-04-01
We consider modified Dirac-Pauli equations that are entered using {{γ }5}-mass factorization, m\\to {{m}1}+/- {{γ }5}{{m}2}, of an ordinary Klein-Gordon operator. We also consider the interaction of fermions with an intensive uniform magnetic field, focusing on their (g-2) gyromagnetic factor. Due to effective research procedures, we derive the exact solutions of the enregy spectra of pseudo-Hermitian Hamiltonians, taking into account the spin of the fermions. The basic research methods are the elucidation of the new border areas of the unbroken PT symmetry of non-Hermitian Hamiltonians. In particular, it is shown that the reality energy spectrum of fermions at rest can be expressed by limiting the intensity of the magnetic field, H≤slant {{H}max }={{m}2}/(2Δ μ {{m}1}), where Δ μ is an anomalous magnetic moment of particles.
Ganguly, Moumita; Chakraborty, Aniruddha
2017-10-01
A diffusion theory for intramolecular reactions of polymer chain in dilute solution is formulated. We give a detailed analytical expression for calculation of rate of polymer looping in solution. The physical problem of looping can be modeled mathematically with the use of a Smoluchowski-like equation with a Dirac delta function sink of finite strength. The solution of this equation is expressed in terms of Laplace Transform of the Green's function for end-to-end motion of the polymer in absence of the sink. We have defined two different rate constants, the long term rate constant and the average rate constant. The average rate constant and long term rate constant varies with several parameters such as length of the polymer (N), bond length (b) and the relaxation time τR. The long term rate constant is independent of the initial probability distribution.
Parker, A.
1995-07-01
In this second of two articles (designated I and II), the bilinear transformation method is used to obtain stationary periodic solutions of the partially integrable regularized long-wave (RLW) equation. These solutions are expressed in terms of Riemann theta functions, and this approach leads to a new and compact expression for the important dispersion relation. The periodic solution (or cnoidal wave) can be represented as an infinite sum of sech2 ``solitary waves'': this remarkable property may be interpreted in the context of a nonlinear superposition principle. The RLW cnoidal wave approximates to a sinusoidal wave and a solitary wave in the limits of small and large amplitudes, respectively. Analytic approximations and error estimates are given which shed light on the character of the cnoidal wave in the different parameter regimes. Similar results are presented in brief for the related RLW Boussinesq (RLWB) equation.
First integrals and analytical solutions of the nonlinear fin problem ...
Indian Academy of Sciences (India)
2016-07-06
Jul 6, 2016 ... first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether's classical method, partial Noether ... Fin equation; Lie symmetry; first integrals; exact solutions. PACS Nos 02.20.Tw; 02.30.Hq. 1. ... to some new integrable systems via reciprocal trans- formations [1].
Analytical solutions of time–space fractional, advection–dispersion ...
Indian Academy of Sciences (India)
and time–space fractional Whitham–Broer–Kaup (FWBK) equation that have significant roles in hydrology. We introduce ... The symmetry reductions and exact independent solutions based on optimal system are investigated .... used travelling wave transformation to reduce (2) to a nonlinear system of third-order fractional ...
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... gested technique would be expected to perform better, with more exact solutions compared to the traditional exp(−ϕ(η))-expansion method. References. [1] N T Shawagfeh, Appl. Math. Comput. 31(2–3), 517 (2002). [2] A A Kilbas, H M Srivastava and J J Trujillo, Comput. Math. Appl. 204, 1079 (2006) ...
Dyons, Superstrings, and Wormholes: Exact Solutions of the Non-Abelian Dirac-Born-Infeld Action
Directory of Open Access Journals (Sweden)
Edward A. Olszewski
2015-01-01
Full Text Available We construct dyon solutions on coincident D4-branes, obtained by applying T-duality transformations to type I SO(32 superstring theory in 10 dimensions. These solutions, which are exact, are obtained from an action comprising the non-Abelian Dirac-Born-Infeld action and a Wess-Zumino-like action. When one spatial dimension of the D4-branes is taken to be vanishingly small, the dyons are analogous to the ’t Hooft/Polyakov monopole residing in a 3+1-dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar is reinterpreted as a Higgs boson transforming in the adjoint representation of the gauge group. Applying a T-duality transformation to the vanishingly small spatial dimension, we obtain a collection of D3-branes, not all of which are coincident. Two of the D3-branes, distinct from the others, acquire intrinsic, finite curvature and are connected by a wormhole. The dyons possess electric and magnetic charges whose values on each D3-brane are the negative of one another. The gravitational effects, which arise after the T-duality transformation, occur despite the fact that the action of the system does not explicitly include the gravitational interaction. These solutions provide a simple example of the subtle relationship between the Yang-Mills and gravitational interactions, that is, gauge/gravity duality.
Directory of Open Access Journals (Sweden)
Birol İbiş
2014-12-01
Full Text Available The purpose of this paper was to obtain the analytical approximate solution of time-fractional Fornberg–Whitham, equation involving Jumarie’s modified Riemann–Liouville derivative by the fractional variational iteration method (FVIM. FVIM provides the solution in the form of a convergent series with easily calculable terms. The obtained approximate solutions are compared with the exact or existing numerical results in the literature to verify the applicability, efficiency and accuracy of the method.
Directory of Open Access Journals (Sweden)
Mehmet Tarik Atay
2013-01-01
Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.
Energy Technology Data Exchange (ETDEWEB)
Segre, S.E. [Rome Univ. 2. Tor Vergata, Rome (Italy). Istituto Nazionale Fisica della Materia, Dipartimento di Fisica
2001-07-01
The known analytic expressions for the evolution of the polarization of electromagnetic waves propagating in a plasma with uniformly sheared magnetic field are extended to the case where the shear is not constant. Exact analytic expressions are found for the case when the space variations of the medium are such that the magnetic field components and the plasma density satisfy a particular condition (eq. 13), possibly in a convenient reference frame of polarization space. [Italian] Le espressioni, gia' note, per l'evoluzione della polarizzazione di onde elettromagnetiche propaganti in un plasma magnetizzato con shear costante vengono estese a casi in cui questo non e' costante. Si trovano soluzioni analitiche esatte per il caso in cui le variazioni spaziali del mezzo sono tali da soddisfare una particolare condizione (eq. 13), eventualmente in un opportuno sistema di riferimento nello spazio della polarizzazione (lo spazio di Poincare').
Second-order analytic solutions for re-entry trajectories
Kim, Eun-Kyou
1993-01-01
With the development of aeroassist technology, either for near-earth orbital transfer with or without a plane change or for planetary aerocapture, it is of interest to have accurate analytic solutions for reentry trajectories in an explicit form. Starting with the equations of motion of a non-thrusting aerodynamic vehicle entering a non-rotating spherical planetary atmosphere, a normalization technique is used to transform the equations into a form suitable for an analytic integration. Then, depending on the type of planar entry modes with a constant angle-of-attack, namely, ballistic fly-through, lifting skip, and equilibrium glide trajectories, the first-order solutions are obtained with the appropriate simplification. By analytic continuation, the second-order solutions for the altitude, speed, and flight path angle are derived. The closed form solutions lead to explicit forms for the physical quantities of interest, such as the deceleration and aerodynamic heating rates. The analytic solutions for the planar case are extended to three-dimensional skip trajectories with a constant bank angle. The approximate solutions for the heading and latitude are developed to the second order. In each type of trajectory examined, explicit relations among the principal variables are in a form suitable for guidance and navigation purposes. The analytic solutions have excellent agreement with the numerical integrations. They also provide some new results which were not reported in the existing classical theory.
Energy Technology Data Exchange (ETDEWEB)
Sun Wenbo E-mail: w.sun@larc.nasa.gov; Loeb, Norman G.; Fu Qiang
2004-02-01
A recently developed finite-difference time domain scheme is examined using the exact analytic solutions for light scattering by a coated sphere immersed in an absorbing medium. The relative differences are less than 1% in the extinction, scattering, and absorption efficiencies and less than 5% in the scattering phase functions. The definition of apparent single-scattering properties is also discussed.
Pandir, Yusuf; Duzgun, Hasan Huseyin
2016-06-01
In this study, we investigate some new analytical solutions to the fractional Sine-Gordon equation by using the new version of generalized F-expansion method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, new analytical solutions were obtained in terms Jacobi elliptic functions.
Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics
Energy Technology Data Exchange (ETDEWEB)
Allegra, Nicolas, E-mail: nicolas.allegra@univ-lorraine.fr
2015-05-15
In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model via the so-called height mapping and the nature of boundary conditions is unravelled. The complete and detailed fermionic solution of the dimer model on the square lattice with an arbitrary number of monomers is presented, and finite size effect analysis is performed to study surface and corner effects, leading to the extrapolation of the central charge of the model. The solution allows for exact calculations of monomer and dimer correlation functions in the discrete level and the scaling behavior can be inferred in order to find the set of scaling dimensions and compare to the bosonic theory which predicts particular features concerning corner behaviors. Finally, some combinatorial and numerical properties of partition functions with boundary monomers are discussed, proved and checked with enumeration algorithms.
Applications of, and Extensions to, Selected Exact Solutions in General Relativity
Cropp, Bethan
2011-01-01
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime ...
Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics
Directory of Open Access Journals (Sweden)
Nicolas Allegra
2015-05-01
Full Text Available In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model via the so-called height mapping and the nature of boundary conditions is unravelled. The complete and detailed fermionic solution of the dimer model on the square lattice with an arbitrary number of monomers is presented, and finite size effect analysis is performed to study surface and corner effects, leading to the extrapolation of the central charge of the model. The solution allows for exact calculations of monomer and dimer correlation functions in the discrete level and the scaling behavior can be inferred in order to find the set of scaling dimensions and compare to the bosonic theory which predicts particular features concerning corner behaviors. Finally, some combinatorial and numerical properties of partition functions with boundary monomers are discussed, proved and checked with enumeration algorithms.
Rugate filter design: An analytical approach using uniform WKB solutions
Perelman, N.; Averbukh, I.
1996-03-01
An analytical approach to the design of rugate filters with a smooth amplitude modulation of the sine-wave index is developed. The approach is based on the uniform WKB solutions (asymptotic expansions) of the coupled-wave equations. A closed-form solution for the inverse problem (finding the refractive index profile for a given reflectance shape inside the stop band) is found.
Analytical solutions for one-dimensional advection–dispersion ...
Indian Academy of Sciences (India)
We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0.
CSIR Research Space (South Africa)
Shatalov, M
2012-09-01
Full Text Available Exact solutions of equations of longitudinal vibration of conical and exponential rod are analyzed for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the method...
Analytic solution of simplified Cardan's shaft model
Directory of Open Access Journals (Sweden)
Zajíček M.
2014-12-01
Full Text Available Torsional oscillations and stability assessment of the homokinetic Cardan shaft with a small misalignment angle is described in this paper. The simplified mathematical model of this system leads to the linearized equation of the Mathieu's type. This equation with and without a stationary damping parameter is considered. The solution of the original differential equation is identical with those one of the Fredholm’s integral equation with degenerated kernel assembled by means of a periodic Green's function. The conditions of solvability of such problem enable the identification of the borders between stability and instability regions. These results are presented in the form of stability charts and they are verified using the Floquet theory. The correctness of oscillation results for the system with periodic stiffness is then validated by means of the Runge-Kutta integration method.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-01-15
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.
Transmission Line Adapted Analytical Power Charts Solution
Sakala, Japhet D.; Daka, James S. J.; Setlhaolo, Ditiro; Malichi, Alec Pulu
2017-08-01
The performance of a transmission line has been assessed over the years using power charts. These are graphical representations, drawn to scale, of the equations that describe the performance of transmission lines. Various quantities that describe the performance, such as sending end voltage, sending end power and compensation to give zero voltage regulation, may be deduced from the power charts. Usually required values are read off and then converted using the appropriate scales and known relationships. In this paper, the authors revisit this area of circle diagrams for transmission line performance. The work presented here formulates the mathematical model that analyses the transmission line performance from the power charts relationships and then uses them to calculate the transmission line performance. In this proposed approach, it is not necessary to draw the power charts for the solution. However the power charts may be drawn for the visual presentation. The method is based on applying derived equations and is simple to use since it does not require rigorous derivations.
A comprehensive analytical solution of the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Ochs, Karlheinz, E-mail: ochs@ieee.org [Chair of Communications, Department of Electrical Engineering and Information Technology, Ruhr-University Bochum (Germany)
2011-03-15
In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.
Bouallègue, Fayçal Ben; Crouzet, Jean-François; Comtat, Claude; Fourcade, Marjolaine; Mohammadi, Bijan; Mariano-Goulart, Denis
2007-07-01
This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.
Pan, Supriya
2018-01-01
Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.
Energy Technology Data Exchange (ETDEWEB)
Wang, Y. B. [Department of Mathematics, ShaoXing University, No.900, ChengNan Avenue 312000, ShaoXing, Zhejiang (China); Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn [School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073 (China); Dai, H. H. [Department of Mathematics, City University of HongKong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong (China)
2016-08-15
Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.
Dattani, Justine; Barahona, Mauricio
2017-01-01
Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells with time-varying (stochastic or deterministic) transcription and degradation rates. Such rates can be understood as upstream cellular drives representing the effect of different aspects of the cellular environment. We show that the full solution of the master equation contains two components: a model-specific, upstream effective drive, which encapsulates the effect of cellular drives (e.g. entrainment, periodicity or promoter randomness) and a downstream transcriptional Poissonian part, which is common to all models. Our analytical framework treats cell-to-cell and dynamic variability consistently, unifying several approaches in the literature. We apply the obtained solution to characterize different models of experimental relevance, and to explain the influence on gene transcription of synchrony, stationarity, ergodicity, as well as the effect of time scales and other dynamic characteristics of drives. We also show how the solution can be applied to the analysis of noise sources in single-cell data, and to reduce the computational cost of stochastic simulations. © 2017 The Authors.
Directory of Open Access Journals (Sweden)
P. Darania
2006-01-01
Full Text Available We study the exact solution of some classes of nonlinear integral equations by series of some invertible transformations and RF-pair operations. We show that this method applies to several classes of nonlinear Volterra integral equations as well and give some useful invertible transformations for converting these equations into differential equations of Emden-Fowler type. As a consequence, we analyze the effect of the proposed operations on the exact solution of the transformed equation in order to find the exact solution of the original equation. Some applications of the method are also given. This approach is effective to find a great number of new integrable equations, which thus far, could not be integrated using the classical methods.
Rui, Weiguo
2017-06-01
By using a counterexample, we proved the fractional chain rule appeared in many references does not hold under Riemann-Liouville definition and Caputo definition of fractional derivative. It shows that this chain rule is invalid in investigating exact solutions of nonlinear fractional partial differential equations (PDEs). In this paper, based on the homogenous balanced principle, the function-expansion method of separation variable type are introduced. By using this method, a series of nonlinear time fractional PDEs such as time fractional KdV equation and Burgers equation, time fractional diffusion-convection equations are studied from mathematical viewpoint. The dynamical properties of these exact solutions are discussed and the profiles of several representative exact solutions are illustrated.
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
conditions and user information, which makes the data sets very sizable and the analytics complex. Data mining and emerging cloud computing technologies make collecting, processing, and analyzing the so-called big data possible. This paper proposes an innovative ICT-solution to streamline smart meter data...... analytics. The proposed solution offers an information integration pipeline for ingesting data from smart meters, a scalable platform for processing and mining big data sets, and a web portal for visualizing analytics results. The implemented system has a hybrid architecture of using Spark or Hive for big......Smart meters are increasingly used worldwide. Smart meters are the advanced meters capable of measuring energy consumption at a fine-grained time interval, e.g., every 15 min. Smart meter data are typically bundled with social economic data in analytics, such as meter geographic locations, weather...
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
Smart meters are increasingly used worldwide. Smart meters are the advanced meters capable of measuring energy consumption at a fine-grained time interval, e.g., every 15 min. Smart meter data are typically bundled with social economic data in analytics, such as meter geographic locations, weather...... conditions and user information, which makes the data sets very sizable and the analytics complex. Data mining and emerging cloud computing technologies make collecting, processing, and analyzing the so-called big data possible. This paper proposes an innovative ICT-solution to streamline smart meter data...... analytics. The proposed solution offers an information integration pipeline for ingesting data from smart meters, a scalable platform for processing and mining big data sets, and a web portal for visualizing analytics results. The implemented system has a hybrid architecture of using Spark or Hive for big...
Malkov, Mikhail
2017-10-01
Propagation of energetic particles through magnetized turbulent media is reconsidered using the exact solution of Fokker-Planck equation [PRD, 2017]. It shows that the cosmic ray (CR) transport in weakly scattering media is nondiffusive. Poor understanding of the CR transport obscures their sources and acceleration mechanisms. We present a simplified approximate version of the exact solution of Fokker-Planck equation that accurately describes a ballistic, diffusive and transdiffusive (intermediate between the first two) propagation regimes. The transdiffusive phase lasts up to 5-7 collision times and starts at about one-half of collision time. Since the scattering rate is energy-dependent, a large part of the energy spectrum propagates neither diffusively nor ballistically. Its treatment should rely on the exact solution. Significant parts of the spectra affected by the heliospheric modulation, for example, falls into this category. We present a new approximation of an exact Fokker-Planck propagator. It conveniently unifies the ballistic and Gaussian propagators, currently used (separately) in major Solar modulation and other CR transport models. The maximum deviation of the new propagator from the exact solution is less than a few percents. Supported by the NASA Astrophysics Theory Program, Grant No. NNX14AH36G.
Analytical solutions of basic models in quantum optics
Braak, Daniel
2015-01-01
The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the complex domain (Fuchsian equations). The linking concept is provided by the Bargmann Hilbert space of analytic functions, which is isomorphic to $L^2(\\mathbb{R})$, the standard Hilbert space for a single continuous degree of freedom in quantum mechanics. I...
Exact solutions to a spatially extended model of kinase-receptor interaction
Szopa, Piotr; Lipniacki, Tomasz; Kazmierczak, Bogdan
2011-10-01
B and Mast cells are activated by the aggregation of the immune receptors. Motivated by this phenomena we consider a simple spatially extended model of mutual interaction of kinases and membrane receptors. It is assumed that kinase activates membrane receptors and in turn the kinase molecules bound to the active receptors are activated by transphosphorylation. Such a type of interaction implies positive feedback and may lead to bistability. In this study we apply the Steklov eigenproblem theory to analyze the linearized model and find exact solutions in the case of non-uniformly distributed membrane receptors. This approach allows us to determine the critical value of receptor dephosphorylation rate at which cell activation (by arbitrary small perturbation of the inactive state) is possible. We found that cell sensitivity grows with decreasing kinase diffusion and increasing anisotropy of the receptor distribution. Moreover, these two effects are cooperating. We showed that the cell activity can be abruptly triggered by the formation of the receptor aggregate. Since the considered activation mechanism is not based on receptor crosslinking by polyvalent antigens, the proposed model can also explain B cell activation due to receptor aggregation following binding of monovalent antigens presented on the antigen presenting cell.
Snijkers, F.
2016-03-31
We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.
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.
Multi-analyte validation in heterogeneous solution by ELISA.
Lakshmipriya, Thangavel; Gopinath, Subash C B; Hashim, Uda; Murugaiyah, Vikneswaran
2017-12-01
Enzyme Linked Immunosorbent Assay (ELISA) is a standard assay that has been used widely to validate the presence of analyte in the solution. With the advancement of ELISA, different strategies have shown and became a suitable immunoassay for a wide range of analytes. Herein, we attempted to provide additional evidence with ELISA, to show its suitability for multi-analyte detection. To demonstrate, three clinically relevant targets have been chosen, which include 16kDa protein from Mycobacterium tuberculosis, human blood clotting Factor IXa and a tumour marker Squamous Cell Carcinoma antigen. Indeed, we adapted the routine steps from the conventional ELISA to validate the occurrence of analytes both in homogeneous and heterogeneous solutions. With the homogeneous and heterogeneous solutions, we could attain the sensitivity of 2, 8 and 1nM for the targets 16kDa protein, FIXa and SSC antigen, respectively. Further, the specific multi-analyte validations were evidenced with the similar sensitivities in the presence of human serum. ELISA assay in this study has proven its applicability for the genuine multiple target validation in the heterogeneous solution, can be followed for other target validations. Copyright © 2017 Elsevier B.V. All rights reserved.
Lekner, John; Andrejic, Petar
2018-01-01
Solutions of the Helmholtz equation which describe electromagnetic beams (and also acoustic or particle beams) are discussed. We show that an exact solution which reproduces the Gaussian beam waveform on the beam axis does not exist. This is surprising, since the Gaussian beam is a solution of the paraxial equation, and thus supposedly accurate on and near the beam axis. Likewise, a solution of the Helmholtz equation which exactly reproduces the Gaussian beam in the focal plane does not exist. We show that the last statement also holds for Bessel-Gauss beams. However, solutions of the Helmholtz equation (one of which is discussed in detail) can approximate the Gaussian waveform within the central focal region.
On the Analytic Solution for a Steady Magnetohydrodynamic Equation
Soltanalizadeh, Babak; Ghehsareh, Hadi Roohani; Yıldırım, Ahmet; Abbasbandy, Saeid
2013-07-01
The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate results. The presented results through tables and figures show the efficiency and accuracy of the proposed technique.
Chernov, A. A.; Pil'nik, A. A.
2018-02-01
Analytical solution of the segregation problem is found for the arbitrary crystal growth law using the quasi-steady-state approximation. The segregation in this case is caused by the displacement of dissolved gas by moving plane crystallization front. The effect of solidification shrinkage on the crystallization process was taken into account. The comparison made between obtained solution and existing exact solutions shows good agreement. It is shown that in the case of "equilibrium crystallization" (when the growth rate is inversely proportional to time) the solution of the problem becomes self-similar. In this case gas concentration at the crystallization front instantly increases to a certain value and than stays the same during the whole process. At the same time the diffusion layer thickness increases proportionally to time. The conditions for the inevitability of gaseous release leading to the formation of pores in solidified material is formulated for the general case.
Qiu, Shanwen
2013-09-01
In this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.
Analytic solution to variance optimization with no short positions
Kondor, Imre; Papp, Gábor; Caccioli, Fabio
2017-12-01
We consider the variance portfolio optimization problem with a ban on short selling. We provide an analytical solution by means of the replica method for the case of a portfolio of independent, but not identically distributed, assets. We study the behavior of the solution as a function of the ratio r between the number N of assets and the length T of the time series of returns used to estimate risk. The no-short-selling constraint acts as an asymmetric \
Analytic solutions for tachyon condensation with general projectors
Energy Technology Data Exchange (ETDEWEB)
Okawa, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Rastelli, L. [C.N. Yang Institute for Theoretical Physics, Stony Brook, NY (United States); Zwiebach, B. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Center for Theoretical Physics
2006-11-15
The tachyon vacuum solution of Schnabl is based on the wedge states, which close under the star product and interpolate between the identity state and the sliver projector. We use reparameterizations to solve the long-standing problem of finding an analogous family of states for arbitrary projectors and to construct analytic solutions based on them. The solutions simplify for special projectors and allow explicit calculations in the level expansion. We test the solutions in detail for a one-parameter family of special projectors that includes the sliver and the butterfly. Reparameterizations further allow a one-parameter deformation of the solution for a given projector, and in a certain limit the solution takes the form of an operator insertion on the projector. We discuss implications of our work for vacuum string field theory. (orig.)
Directory of Open Access Journals (Sweden)
Ping Liu
2015-08-01
Full Text Available The symmetry reduction equations, similarity solutions, sub-groups and exact solutions of the (3+1-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations with viscosity (INHBV equations, which describe the atmospheric gravity waves, are researched in this paper. Calculation on symmetry shows that the equations are invariant under the Galilean transformations, scaling transformations, rotational transformations and space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1-dimensional INHBV equations are proposed. Traveling wave solutions of the INHBV equations are demonstrated by means of symmetry method. The evolutions on the wind velocities and temperature perturbation are demonstrated by figures.
An Analytical Method For The Solution Of Reactor Dynamic Equations
African Journals Online (AJOL)
In this paper, an analytical method for the solution of nuclear reactor dynamic equations is presented. The method is applied to a linearised high-order deterministic model of a pressurised water reactor plant driven by step-reactivity insertion. A comparison of this method with two other techniques (the matrix exponential and ...
Foam for Enhanced Oil Recovery : Modeling and Analytical Solutions
Ashoori, E.
2012-01-01
Foam increases sweep in miscible- and immiscible-gas enhanced oil recovery by decreasing the mobility of gas enormously. This thesis is concerned with the simulations and analytical solutions for foam flow for the purpose of modeling foam EOR in a reservoir. For the ultimate goal of upscaling our
An analytical solution of compressible charged porous media
Malakpoor, K.; Huyghe, J.M.
2009-01-01
A one-dimensional analytical solution is derived for saturated charged compressible porous media. The equations describe infinitesimal deformation of charged porous media saturated with a fluid with dissolved cations and anions. In the one-dimensional case the governing equations reduce to a coupled
Analytical solutions of coupled-mode equations for microring ...
Indian Academy of Sciences (India)
The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a 4 × 4 linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics ...
Directory of Open Access Journals (Sweden)
Chen Han-Lin
2013-01-01
Full Text Available With the aid of Maple symbolic computation and Lie group method, (2+1-dimensional PBLMP equation is reduced to some (1+1-dimensional PDE with constant coefficients. Using the homoclinic test technique and auxiliary equation methods, we obtain new exact nontraveling solution with arbitrary functions for the PBLMP equation.
Fulcher, Lewis P.
1979-01-01
Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)
Analytic solutions for seismic travel time and ray path geometry through simple velocity models.
Energy Technology Data Exchange (ETDEWEB)
Ballard, Sanford
2007-12-01
The geometry of ray paths through realistic Earth models can be extremely complex due to the vertical and lateral heterogeneity of the velocity distribution within the models. Calculation of high fidelity ray paths and travel times through these models generally involves sophisticated algorithms that require significant assumptions and approximations. To test such algorithms it is desirable to have available analytic solutions for the geometry and travel time of rays through simpler velocity distributions against which the more complex algorithms can be compared. Also, in situations where computational performance requirements prohibit implementation of full 3D algorithms, it may be necessary to accept the accuracy limitations of analytic solutions in order to compute solutions that satisfy those requirements. Analytic solutions are described for the geometry and travel time of infinite frequency rays through radially symmetric 1D Earth models characterized by an inner sphere where the velocity distribution is given by the function V (r) = A-Br{sup 2}, optionally surrounded by some number of spherical shells of constant velocity. The mathematical basis of the calculations is described, sample calculations are presented, and results are compared to the Taup Toolkit of Crotwell et al. (1999). These solutions are useful for evaluating the fidelity of sophisticated 3D travel time calculators and in situations where performance requirements preclude the use of more computationally intensive calculators. It should be noted that most of the solutions presented are only quasi-analytic. Exact, closed form equations are derived but computation of solutions to specific problems generally require application of numerical integration or root finding techniques, which, while approximations, can be calculated to very high accuracy. Tolerances are set in the numerical algorithms such that computed travel time accuracies are better than 1 microsecond.
Exact solutions of time-fractional heat conduction equation by the fractional complex transform
Directory of Open Access Journals (Sweden)
Li Zheng-Biao
2012-01-01
Full Text Available The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.
New Approximate Analytical Solutions of the Falkner-Skan Equation
Directory of Open Access Journals (Sweden)
Beong In Yun
2012-01-01
Full Text Available We propose an iterative method for solving the Falkner-Skan equation. The method provides approximate analytical solutions which consist of coefficients of the previous iterate solution. By some examples, we show that the presented method with a small number of iterations is competitive with the existing method such as Adomian decomposition method. Furthermore, to improve the accuracy of the proposed method, we suggest an efficient correction method. In practice, for some examples one can observe that the correction method results in highly improved approximate solutions.
Analytical solutions for Tokamak equilibria with reversed toroidal current
Energy Technology Data Exchange (ETDEWEB)
Martins, Caroline G. L.; Roberto, M.; Braga, F. L. [Departamento de Fisica, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, Sao Paulo 12228-900 (Brazil); Caldas, I. L. [Instituto de Fisica, Universidade de Sao Paulo, 05315-970 Sao Paulo, SP (Brazil)
2011-08-15
In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile.
Saïdou, Abdoulkary; Alidou, Mohamadou; Ousmanou, Dafounansou; Serge Yamigno, Doka
2014-12-01
We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete (G'/G)-expansion method, we solve the nonlinear differential—difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.
Russell, John
2000-11-01
A modified Orr-Sommerfeld equation that applies to the asymptotic suction boundary layer was reported by Bussmann & Münz in a wartime report dated 1942 and by Hughes & Reid in J.F.M. ( 23, 1965, p715). Fundamental systems of exact solutions of the Orr-Sommerfeld equation for this mean velocity distribution were reported by D. Grohne in an unpublished typescript dated 1950. Exact solutions of the equation of Bussmann, Münz, Hughes, & Reid were reported by P. Baldwin in Mathematika ( 17, 1970, p206). Grohne and Baldwin noticed that these exact solutions may be expressed either as Barnes integrals or as convolution integrals. In a later paper (Phil. Trans. Roy. Soc. A, 399, 1985, p321), Baldwin applied the convolution integrals in the contruction of large-Reynolds number asymptotic approximations that hold uniformly. The present talk discusses the subtleties that arise in the construction of such convolution integrals, including several not reported by Grohne or Baldwin. The aim is to recover the full set of seven solutions (one well balanced, three balanced, and three dominant-recessive) postulated by W.H. Reid in various works on the uniformly valid solutions.
Raslan, K. R.; EL-Danaf, Talaat S.; Ali, Khalid K.
2017-07-01
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.
Exact solutions of a two-dimensional cubic–quintic discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Khare, Avinash; Rasmussen, Kim Ø; Samuelsen, Mogens Rugholm
2011-01-01
We show that a two-dimensional generalized cubic–quintic Ablowitz–Ladik lattice admits periodic solutions that can be expressed in analytical form. The framework for the stability analysis of these solutions is developed and applied to reveal the intricate stability behavior of this nonlinear sys...
On the Partial Analytical Solution of the Kirchhoff Equation
Michels, Dominik L.
2015-09-01
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.
Analytic solution of an oscillatory migratory α2 stellar dynamo
Brandenburg, A.
2017-02-01
Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α. Aims: We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods: We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. Results: The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α. Conclusions: The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α.
Analytic solutions of integral moving least squares for polygon soups.
Park, Taejung; Lee, Sung-Ho; Kim, Chang-Hun
2012-10-01
This paper presents analytic solutions to the integral moving least squares (MLS) equations originally proposed by Shen et al. by choosing another specific weighting function that renders the numerator in the MLS equation unitless. In addition, we analyze the original method to show that their approximation surfaces (i.e., enveloping surfaces with nonzero values in the weighting function) often form zero isosurfaces near concavities behind the triangle-soup models. This paper also presents error terms for the integral MLS formulations against signed distance fields. Based on our analytic solutions, we show that our method provides both interpolation and approximation surfaces faster and more efficiently. Because our method computes solutions for integral MLS equations directly, it does not rely on numerical steps that might have numerical-accuracy issues. In particular, unlike the original method that deals with incorrect approximation surfaces by iteratively adjusting parameters, this paper proposes faster and more efficient approximations to surfaces without needing iterative routines. We also present computational efficiency comparisons, in which our method is 15-fold faster in computing integrations, even with conservative assumptions. Finally, we show that the surface normal vectors on the implicit surfaces formed by our analytic solutions are identical to the angle-weighted pseudonormal vectors.
Directory of Open Access Journals (Sweden)
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.
Muttalib, K. A.; Khatun, M.; Barry, J. H.
2017-11-01
Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility χ⊥ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled χ⊥ can be used as a quantitative measure of the degree of frustration in Ising spin systems.
Ivanov, A. N.; Cronenberg, G.; Höllwieser, R.; Jenke, T.; Pitschmann, M.; Wellenzohn, M.; Abele, H.
2016-10-01
We calculate the chameleon field profile, confined between two parallel plates, filled with air at pressure P =10-4 mbar and room temperature and separated by the distance L , in the chameleon field theory with Ratra-Peebles self-interaction potential with index n =1 . We give the exact analytical solution in terms of Jacobian elliptic functions, depending on the mass density of the ambient matter. The obtained analytical solution can be used in qBounce experiments, measuring transition frequencies between quantum gravitational states of ultracold neutrons and also for the calculation of the chameleon field induced Casimir force for the CANNEX experiment. We show that the chameleon-matter interactions with coupling constants β ≤1 04 can be probed by qBounce experiments with sensitivities Δ E ≤10-18 eV . At L =30.1 μ m we reproduce the result β <5.8 ×1 08 , obtained by Jenke et al. [Phys. Rev. Lett. 112, 151105 (2014)] at sensitivity Δ E ˜10-14 eV . In the vicinity of one of the plates our solution coincides with the solution, obtained by Brax and Pignol [Phys. Rev. Lett. 107, 111301 (2011)] [see also Ivanov et al. Phys. Rev. D 87, 105013 (2013)] above a plate at zero density of the ambient matter.
Exact solutions to plaquette Ising models with free and periodic boundaries
Directory of Open Access Journals (Sweden)
Marco Mueller
2017-01-01
We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Approximate Analytical Solutions to the Relativistic Isothermal Gas Spheres
Saad, A. S.; Nouh, M. I.; Shaker, A. A.; Kamel, T. M.
2017-10-01
In this paper we introduce a novel analytical solution to Tolman-Oppenheimer-Volkoff (TOV) equation, which is ultimately a hydrostatic equilibrium equation derived from general relativity in the framework of relativistic isothermal spheres. To improve the convergence radii of the obtained series solutions, a combination of an Euler-Abel transformation and a Padé approximation has been done. The solutions are given in the ξ-θ and ξ-ν phase planes taking into account the general relativistic effects σ=0.1, 0.2 and 0.3. A comparison between the results obtained by the suggested approach and the numerical one indicates a good agreement, with a maximum relative error of order 10-3, which establishes the validity and accuracy of the method. The proposed procedure accelerated the power series solution about ten times that of the traditional one. An application to a neutron star is presented.
Analytic solutions of a class of nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Eugenia N. Petropoulou
2015-08-01
Full Text Available We study a class of nonlinear partial differential equations, which can be connected with wave-type equations and Laplace-type equations, by using a functional-analytic technique. We establish primarily the existence and uniqueness of bounded solutions in the two-dimensional Hardy-Lebesque space of analytic functions with independent variables lying in the open unit disc. However these results can be modified to expand the domain of definition. The proofs have a constructive character enabling the determination of concrete and easily verifiable conditions, and the determination of the coefficients appearing in the power series solution. Illustrative examples are given related to the sine-Gordon equation, the Klein-Gordon equation, and to equations with nonlinear terms of algebraic, exponential and logistic type.
Nearly perfect nonmagnetic invisibility cloaking: Analytic solutions and parametric studies
Castaldi, Giuseppe; Gallina, Ilaria; Galdi, Vincenzo
2009-09-01
Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous “transformation medium” capable of suitably rerouting the energy flux around the region to conceal without causing any scattering in the exterior region. It is well known that the inherently magnetic properties of such medium limit the high-frequency scaling of practical “metamaterial” implementations based on subwavelength inclusions (e.g., split-ring resonators). Thus, for the optical range, nonmagnetic implementations, based on approximate reductions of the constitutive parameters, have been proposed. In this paper, we present an alternative approach to nonmagnetic coordinate-transformation cloaking, based on the mapping from a nearly transparent, anisotropic and spatially inhomogeneous virtual domain. We show that, unlike its counterparts in the literature, our approach is amenable to exact analytic treatment, and that its overall performance is comparable to that of a nonideal (lossy, dispersive, parameter truncated) implementation of standard (magnetic) cloaking.
Analytical Solution for the Time-Fractional Telegraph Equation
Directory of Open Access Journals (Sweden)
F. Huang
2009-01-01
Full Text Available We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.
A block Krylov subspace time-exact solution method for linear ordinary differential equation systems
Bochev, Mikhail A.
2013-01-01
We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of
Electrostatics of a Point Charge between Intersecting Planes: Exact Solutions and Method of Images
Mei, W. N.; Holloway, A.
2005-01-01
In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…
A block Krylov subspace time-exact solution method for linear ODE systems
Bochev, Mikhail A.
We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial
Analytic solution of the Starobinsky model for inflation
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)
2017-07-15
We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lemaitre-Robertson-Walker metric constitute an integrable system. The analytical solution in terms of a Painleve series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Williams, Todd O [Los Alamos National Laboratory
2009-01-01
The exact solution for the history-dependent behavior of laminated plates subjected to cylindrical bending is presented. The solution represents the extension of Pagano's solution to consider arbitrary types of constitutive behaviors for the individual lamina as well as arbitrary types of cohesive zones models for delamination behavior. Examples of the possible types of material behavior are plasticity, viscoelasticity, viscoplasticity, and damaging. Examples of possible CZMs that can be considered are linear, nonlinear hardening, as well as nonlinear with softening. The resulting solution is intended as a benchmark solution for considering the predictive capabilities of different plate theories. Initial results are presented for several types of history-dependent material behaviors. It is shown that the plate response in the presence of history-dependent behaviors can differ dramatically from the elastic response. These results have strong implications for what constitutes an appropriate plate theory for modeling such behaviors.
Solute transport with multiprocess nonequilibrium: a semi-analytical solution approach
Neville, Christopher J.; Ibaraki, Motomu; Sudicky, Edward A.
2000-07-01
A semi-analytical solution for the simulation of one-dimensional subsurface solute transport incorporating multiple nonequilibrium processes is presented. The solution is based on the theory developed by Brusseau et al. (1992) [Brusseau, M.L., Jessup, R.E., Rao, P.S.C., 1992. Modeling solute transport influenced by multiprocess nonequilibrium and transformation reactions. Water Resources Research 28 (1), 175-182.] which is a generalized combination of two-site and two-region model. In addition to developing a semi-analytical complement to their numerical solution, we extend the range of boundary and initial conditions considered. The semi-analytical solution can represent domains of both finite and semi-infinite extent and accommodates nonzero initial concentrations. The solution is derived in Laplace space and final results are obtained using an accurate and robust numerical inversion algorithm. The solution is particularly well suited for interpreting experimental results obtained under controlled laboratory conditions. Identification of the input parameters for the solution is examined by simulating a column experiment by van Genuchten (1974) [van Genuchten, M., 1974. Mass Transfer Studies in Sorbing Porous Media. PhD thesis, New Mexico State University, Las Cruces, NM.].
A full analytic solution of SO(10)-inspired leptogenesis
Di Bari, Pasquale; Fiorentin, Michele Re
2017-10-01
Recent encouraging experimental results on neutrino mixing parameters prompt further investigation on SO(10)-inspired leptogenesis and on the associated strong thermal solution that has correctly predicted a non-vanishing reactor mixing angle, it further predicts sin δ ≲ 0, now supported by recent results at ˜ 95% C.L., normally ordered neutrino masses and atmospheric mixing angle in the first octant, best fit results in latest global analyses. Extending a recent analytical procedure, we account for the mismatch between the Yukawa basis and the weak basis, that in SO(10)-inspired models is described by a CKM-like unitary transformation V L , obtaining a full analytical solution that provides useful insight and reproduces accurately all numerical results, paving the way for future inclusion of different sources of theoretical uncertainties and for a statistical analysis of the constraints. We show how muon-dominated solutions appear for large values of the lightest neutrino mass in the range (0 .01-1) eV but also how they necessarily require a mild fine tuning in the seesaw relation. For the dominant (and untuned) tauon-dominated solutions we show analytically how, turning on V L ≃ V CKM, some of the constraints on the low energy neutrino parameters get significantly relaxed. In particular we show how the upper bound on the atmospheric neutrino mixing angle in the strong thermal solution gets relaxed from θ 23 ≲ 41° to θ 23 ≲ 44°, an important effect in the light of the most recent NO νA, T2K and IceCube results.
Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on Jumarie’s modified Riemann-Liouville derivative, the fractional complex transformation is used to transform fractional differential equations to ordinary differential equations. Exact solutions including the hyperbolic functions, the trigonometric functions, and the rational functions for the space-time fractional bidirectional wave equations are obtained using the (G′/G-expansion method. The method provides a promising tool for solving nonlinear fractional differential equations.
General scalar-tensor cosmology: analytical solutions via noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-02-15
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system. (orig.)
Viñales, A D; Despósito, M A
2006-01-01
We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.
Exact Solutions of Space-time Fractional EW and modified EW equations
Korkmaz, Alper
2016-01-01
The bright soliton solutions and singular solutions are constructed for space-time fractional EW and modified EW equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. Then, implementation of ansatz method the solutions are constructed.
Exact solutions of space-time fractional EW and modified EW equations
Korkmaz, Alper
2017-03-01
The bright soliton solutions and singular solutions are constructed for space-time fractional EW and modified EW equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. Then, implementation of ansatz method the solutions are constructed.
Exact solutions for the Wick-type stochastic Kersten-Krasil'shchik coupled KdV-mKdV equations
Singh, S.; Saha Ray, S.
2017-11-01
In this article, exact solutions of Wick-type stochastic Kersten-Krasil'shchik coupled KdV-mKdV equations have been obtained by using the Jacobian elliptic function expansion method. We have used the Hermite transform for transforming the Wick-type stochastic Kersten-Krasil'shchik coupled KdV-mKdV equation into a deterministic partial differential equation. Also, we have applied the inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.
The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes
Birkandan, T.; Hortaçsu, M.
2018-03-01
Heun-type exact solutions emerge for both the radial and the angular equations for the case of a scalar particle coupled to the zero mass limit of both the Kerr and Kerr-(anti)de-Sitter spacetime. Since any type D metric has Heun-type solutions, it is interesting that this property is retained in the zero mass case. This work further refutes the claims that M going to zero limit of the Kerr metric is both locally and globally the same as the Minkowski metric.
Directory of Open Access Journals (Sweden)
Changfeng Xue
2008-01-01
Full Text Available The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.
On exact solutions of a heat-wave type with logarithmic front for the porous medium equation
Kazakov, A. L.; Lempert, A. A.; Orlov, S. S.; Orlov, S. S.
2017-10-01
The paper deals with a nonlinear second-order parabolic equation with partial derivatives, which is usually called “the porous medium equation”. It describes the processes of heat and mass transfer as well as filtration of liquids and gases in porous media. In addition, it is used for mathematical modeling of growth and migration of population. Usually this equation is studied numerically like most other nonlinear equations of mathematical physics. So, the construction of exact solution in an explicit form is important to verify the numerical algorithms. The authors deal with a special solutions which are usually called “heat waves”. A new class of heat-wave type solutions of one-dimensional (plane-symmetric) porous medium equation is proposed and analyzed. A logarithmic heat wave front is studied in details. Considered equation has a singularity at the heat wave front, because the factor of the highest (second) derivative vanishes. The construction of these exact solutions reduces to the integration of a nonlinear second-order ordinary differential equation (ODE). Moreover, the Cauchy conditions lead us to the fact that this equation has a singularity at the initial point. In other words, the ODE inherits the singularity of the original problem. The qualitative analysis of the solutions of the ODE is carried out. The obtained results are interpreted from the point of view of the corresponding heat waves’ behavior. The most interesting is a damped solitary wave, the length of which is constant, and the amplitude decreases.
Directory of Open Access Journals (Sweden)
Zulfiqar Ali
2013-01-01
Full Text Available We find exact solutions of the Generalized Modified Boussinesq (GMB equation, the Kuromoto-Sivashinsky (KS equation the and, Camassa-Holm (CH equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.
Analytical solutions of laminar swirl decay in a straight pipe
Yao, Shanshan; Fang, Tiegang
2012-08-01
In this work, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles. Based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles, the swirl velocity equation is solved by the separation of variable technique for a rather general inlet swirl velocity distribution, which includes a forced vortex in the core and a free vortex near the wall. The solutions are expressed by the Bessel function for the slug flow and by the generalized Laguerre function for the developed parabolic velocity. Numerical examples are calculated and plotted for different combinations of influential parameters. The effects of the Reynolds number, the pipe axial distance, and the inlet swirl profiles on the swirl velocity distribution and the swirl decay are analyzed. The current results offer analytical equations to estimate the decay rate and the outlet swirl intensity and velocity distribution for the design of swirl flow devices.
Analytical solutions of transport problems in anisotropic media
Energy Technology Data Exchange (ETDEWEB)
Lapenta, G.; Ravetto, P.; Rostagno, M.M.
2000-07-01
Recently, the problem of neutron transport in anisotropic media has received new attention in connection with safety studies of water reactors and design of gas-cooled systems. In situations presenting large voided regions, as the axial streaming is dominating with respect to the transverse one, the average properties of the homogenized material should physically account for such macroscopic anisotropy. Hence, it is suggested that cell calculations produce anisotropic average cross sections, e.g., axial ({sigma}{sub A}) and transverse ({sigma}{sub T}) values. Since material anisotropy is due to leakage, as a first-step approximation, the medium can be considered isotropic with respect to scattering phenomena. Transport codes are currently being adapted to include anisotropic cross sections. An important aspect of code development is the validation of algorithms by analytical benchmarks. For that purpose, the present work is devoted to the fully analytical solution of transport problems in slab geometry.
Speeding Up Exact Solutions of Interactive Dynamic Influence Diagrams Using Action Equivalence
DEFF Research Database (Denmark)
Zeng, Yifeng; Prashant, Doshi
2009-01-01
Interactive dynamic influence diagrams (I-DIDs) are graphical models for sequential decision making in partially observable settings shared by other agents. Algorithms for solving I-DIDs face the challenge of an exponentially growing space of candidate models ascribed to other agents, over time. ...... at a single time step. We show how to update these augmented classes and prove that our method is exact. The new approach enables us to bound the aggregated model space by the cardinality of other agents' actions. We evaluate its performance and provide empirical results in support....
An exact solution to the draining reservoir problem of the incompressible and non-viscous liquid
Energy Technology Data Exchange (ETDEWEB)
Hong, Seok-In [Department of Science Education, Gyeongin National University of Education, Anyang 430-739 (Korea, Republic of)], E-mail: sihongtao@hanmail.net
2009-03-15
The exact expressions for the drain time and the height, velocity and acceleration of the free surface are found for the draining reservoir problem of the incompressible and non-viscous liquid. Contrary to the conventional approximate results, they correctly describe the initial time dependence of the liquid velocity and acceleration. Torricelli's law does not hold in the initial transient region, which imposes restrictions on the validity of the analogy between the drain system and the electric circuit (Ohm's law)
Switching synchronization in one-dimensional memristive networks: An exact solution
Slipko, V. A.; Pershin, Y. V.
2017-12-01
We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high- to low-resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of nonlinear equations describing the memristors dynamics is solved exactly, without any approximations. The time dependencies of memristances are found, and it is shown that the voltage falls across memristors are proportional to their threshold voltages. A compact expression for the network switching time is derived.
Giriraj MEHTI
2017-01-01
Aim of the paper is to obtain solution of parabolic, elliptical and coupled partial differential equation using Reduced Differential Transform Method (RDTM). The results are compared with solution obtained by other methods. It is observed that RDTM is easy to implement, accurate and efficient. It reduces volume of computation and save time.
Directory of Open Access Journals (Sweden)
Giriraj MEHTI
2017-04-01
Full Text Available Aim of the paper is to obtain solution of parabolic, elliptical and coupled partial differential equation using Reduced Differential Transform Method (RDTM. The results are compared with solution obtained by other methods. It is observed that RDTM is easy to implement, accurate and efficient. It reduces volume of computation and save time.
On the exact solutions of nonlinear diffusion-reaction equations with ...
Indian Academy of Sciences (India)
It is interesting to note that the linearly independent solutions C++ and C+− of eq. (16) respectively represent the kink and antikink-shaped soliton solutions in analogy with other versions of the nonlinear D-R equations studied in the literature. (see p. 289 of [4]). The kink and antikink-shaped solitons resulting from these.
Painlevé test for integrability and exact solutions for the field ...
Indian Academy of Sciences (India)
SUSANTO CHAKRABORTY1 and PRANAB KRISHNA CHANDA2. 1Central Drugs Laboratory, 3 Kyd Street, Kolkata 700 016, India. 2Siliguri B.Ed. College, .... Equations (1.4) with a physical origin stated have been found to have interesting solutions and mathematical characteristics. Charap [2] obtained solutions for (1.4).
Stable, Time-Dependent, Exact Solutions for Brane Models with a Bulk Scalar Field
Lee, S; Olive, Keith A; Kanti, Panagiota; Lee, Seokcheon; Olive, Keith A.
2003-01-01
We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflationary, time-dependent solutions of the 3D scale factor on the brane. We also derive the constraints necessary for the stability of these solutions under time-dependent perturbations of the radion field, and we demonstrate the existence of phenomenologically interesting, stable solutions with a positive cosmological constant on the brane.
Analytical solution for irradiance due to inhomogeneous Lambertian polygonal emitters.
Chen, Min; Arvo, James
2003-05-01
We present an analytic solution for the irradiance at a point due to a polygonal Lambertian emitter with radiant exitance that varies with position according to a polynomial of arbitrary degree. This is a basic problem that arises naturally in radiative transfer and more specifically in global illumination, a subfield of computer graphics. Our solution is closed form except for a single nonalgebraic special function known as the Clausen integral. We begin by deriving several useful formulas for high-order tensor analogs of irradiance, which are natural generalizations of the radiation pressure tensor. We apply the resulting tensor formulas to linearly varying emitters, obtaining a solution that exhibits the general structure of higher-degree cases, including the dependence on the Clausen integral. We then generalize to higher-degree polynomials with a recurrence formula that combines solutions for lower-degree polynomials; the result is a generalization of Lambert's formula for homogeneous diffuse emitters, a well-known formula with many applications in radiative transfer and computer graphics. Similar techniques have been used previously to derive closed-form solutions for the irradiance due to homogeneous polygonal emitters with directionally varying radiance. The present work extends this previous result to include inhomogeneous emitters, which proves to be significantly more challenging to solve in closed form. We verify our theoretical results with numerical approximations and briefly discuss their potential applications.
Analytical solutions for tsunami runup on a plane beach
DEFF Research Database (Denmark)
Madsen, Per A.; Schäffer, Hemming Andreas
2010-01-01
In the literature it has so far been common practice to consider solitary waves N-waves (composed of solitary waves) as the appropriate model of tsunamis approaching the shoreline. Unfortunately, this approach is based on a tie between the nonlinearity and the horizontal length scale (or duration......) of the wave, which is not realistic for geophysical tsunamis. To resolve this problem, we first derive analytical solutions to the nonlinear shallow-water (NSW) equations for the runup/rundown of single waves, where the duration and the wave height can be specified separately. The formulation is then extended...
Fock space, symbolic algebra, and analytical solutions for small stochastic systems
Santos, Fernando A. N.; Gadêlha, Hermes; Gaffney, Eamonn A.
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Exact solution for the fractional cable equation with nonlocal boundary conditions
Bazhlekova, Emilia; Dimovski, Ivan
2013-10-01
The fractional cable equation is studied on a bounded space domain. One of the prescribed boundary conditions is of Dirichlet type, the other is of a general form, which includes the case of nonlocal boundary conditions. In real problems nonlocal boundary conditions are prescribed when the data on the boundary can not be measured directly. We apply spectral projection operators to convert the problem to a system of integral equations in any generalized eigenspace. In this way we prove uniqueness of the solution and give an algorithm for constructing the solution in the form of an expansion in terms of the generalized eigenfunctions and three-parameter Mittag-Leffler functions. Explicit representation of the solution is given for the case of double eigenvalues. We consider some examples and as a particular case we recover a recent result. The asymptotic behavior of the solution is also studied.
Self-regulatory gene: An exact solution for the gene gate model
Vandecan, Yves; Blossey, Ralf
2013-04-01
The stochastic dynamics of gene expression is often described by highly abstract models involving only the key molecular actors DNA, RNA, and protein, neglecting all further details of the transcription and translation processes. One example of such models is the “gene gate model,” which contains a minimal set of actors and kinetic parameters, which allows us to describe the regulation of a gene by both repression and activation. Based on this approach, we formulate a master equation for the case of a single gene regulated by its own product—a transcription factor—and solve it exactly. The obtained gene product distributions display features of mono- and bimodality, depending on the choice of parameters. We discuss our model in the perspective of other models in the literature.
An exact solution for the Hawking effect in a dispersive fluid
Philbin, T G
2016-01-01
We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact scattering coefficients for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1+1-dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal.
Directory of Open Access Journals (Sweden)
S. Hoseinzadeh
2017-10-01
Full Text Available We introduce a four-dimensional extension of the Poincaré algebra (N in (1+1-dimensional space-time and obtain a (1+1-dimensional gauge symmetric gravity model using the algebra N. We show that the obtained gravity model is dual (canonically transformed to the (1+1-dimensional anti de Sitter (AdS gravity. We also obtain some black hole and Friedmann–Robertson–Walker (FRW solutions by solving its classical equations of motion. Then, we study A4,8A1⊗A1 gauged Wess–Zumino–Witten (WZW model and obtain some exact black hole and cosmological solutions in string theory. We show that some obtained black hole and cosmological metrics in string theory are same as the metrics obtained in solutions of our gauge symmetric gravity model.
Hoseinzadeh, S.; Rezaei-Aghdam, A.
2017-10-01
We introduce a four-dimensional extension of the Poincaré algebra (N) in (1 + 1)-dimensional space-time and obtain a (1 + 1)-dimensional gauge symmetric gravity model using the algebra N. We show that the obtained gravity model is dual (canonically transformed) to the (1 + 1)-dimensional anti de Sitter (AdS) gravity. We also obtain some black hole and Friedmann-Robertson-Walker (FRW) solutions by solving its classical equations of motion. Then, we study A4,8A1/⊗A1 gauged Wess-Zumino-Witten (WZW) model and obtain some exact black hole and cosmological solutions in string theory. We show that some obtained black hole and cosmological metrics in string theory are same as the metrics obtained in solutions of our gauge symmetric gravity model.
Baecklund transformations and exact soliton solutions for nonlinear Schroedinger-type equations
Energy Technology Data Exchange (ETDEWEB)
Khater, A. H. [Cairo Univ. (Egypt). Faculty of science, Dept. of Mathematics]|[Antwerp Univ. (Belgium). Dept. of Physics; Callebaut, D. K. [Antwerp Univ. (Belgium). Dept. of Physics; El-Kalaawy, O. H. [Cairo Univ. (Egypt). Faculty of science, Dept. of Mathematics
1998-09-01
Using the Baecklund transformations (BTs) and the Darboux-Bargmann technique, the Authors consider the nonlinear Schroedinger-type (NLS-type) equations solvable by the inverse scattering method of Zakharov-Shabat/Ablowitz-Kaup-Newell-Segur (ZS/AKNS) system and the ZS/AKNS wave functions corresponding to the soliton solutions of NLS-type equations. Thus, families of new soliton solutions for NLS- type equations are obtained.
On two exact solutions of time fractional heat equations using different transforms
Directory of Open Access Journals (Sweden)
Ibrahim Rabha W.
2015-01-01
Full Text Available Two solutions of time fractional differential equations are illustrated. The first one converges to functional space in term of Weyl transform in L2(R, while the second solution approaches to the Fox function with respect to time, by using the Fourier and Laplace-Mellin transforms. The fractional calculus is taken in the sense of the Riemann-Liouville fractional differential operator.
Exact Solutions on Twisted Rings for the 3D Navier-Stokes Equations
Funaro, Daniele
2011-01-01
The problem of describing the behavior of the solutions to the Navier-Stokes equations in three space dimensions has always been borderline. From one side, due to the viscosity term, smooth data seem to produce solutions with an everlasting regular behavior. On the other hand, the lack of a convincing theoretical analysis suggests the existence of possible counterexamples. In particular, one cannot exclude the blowing up of solutions in finite time even in presence of smooth data. Here we give examples of explicit solutions of the non-homogeneous equations. These are defined on a Hill's type vortex where the flow is rotating and swirling at the same time, inducing the flux to spiraling at a central node. Despite the appearance, the solution still remains very regular at the agglomeration point. The analysis may lead to a better understanding of the subtle problem of characterizing the solution space of the 3D Navier-Stokes equations. For instance, this result makes more narrow the path to the search of counte...
Benchmarking the invariant embedding method against analytical solutions in model transport problems
Directory of Open Access Journals (Sweden)
Wahlberg Malin
2006-01-01
Full Text Available The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.
Directory of Open Access Journals (Sweden)
Qazi Mahmood Ul Hassan
2014-01-01
Full Text Available We use the fractional derivatives in Caputo’s sense to construct exact solutions to fractional fifth order nonlinear evolution equations. A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.
Analytical Solutions for Corrosion-Induced Cohesive Concrete Cracking
Directory of Open Access Journals (Sweden)
Hua-Peng Chen
2012-01-01
Full Text Available The paper presents a new analytical model to study the evolution of radial cracking around a corroding steel reinforcement bar embedded in concrete. The concrete cover for the corroding rebar is modelled as a thick-walled cylinder subject to axisymmetrical displacement constraint at the internal boundary generated by expansive corrosion products. A bilinear softening curve reflecting realistic concrete property, together with the crack band theory for concrete fracture, is applied to model the residual tensile stress in the cracked concrete. A governing equation for directly solving the crack width in cover concrete is established for the proposed analytical model. Closed-form solutions for crack width are then obtained at various stages during the evolution of cracking in cover concrete. The propagation of crack front with corrosion progress is studied, and the time to cracking on concrete cover surface is predicted. Mechanical parameters of the model including residual tensile strength, reduced tensile stiffness, and radial pressure at the bond interface are investigated during the evolution of cover concrete cracking. Finally, the analytical predictions are examined by comparing with the published experimental data, and mechanical parameters are analysed with the progress of reinforcement corrosion and through the concrete cover.
Decision exploration lab: a visual analytics solution for decision management.
Broeksema, Bertjan; Baudel, Thomas; Telea, Arthur G; Crisafulli, Paolo
2013-12-01
We present a visual analytics solution designed to address prevalent issues in the area of Operational Decision Management (ODM). In ODM, which has its roots in Artificial Intelligence (Expert Systems) and Management Science, it is increasingly important to align business decisions with business goals. In our work, we consider decision models (executable models of the business domain) as ontologies that describe the business domain, and production rules that describe the business logic of decisions to be made over this ontology. Executing a decision model produces an accumulation of decisions made over time for individual cases. We are interested, first, to get insight in the decision logic and the accumulated facts by themselves. Secondly and more importantly, we want to see how the accumulated facts reveal potential divergences between the reality as captured by the decision model, and the reality as captured by the executed decisions. We illustrate the motivation, added value for visual analytics, and our proposed solution and tooling through a business case from the car insurance industry.
Exact Solutions to the Double Travelling Salesman Problem with Multiple Stacks
DEFF Research Database (Denmark)
Petersen, Hanne L.; Archetti, Claudia; Speranza, M. Grazia
2010-01-01
In this paper we present mathematical programming formulations and solution approaches for the optimal solution of the Double Travelling Salesman Problem with Multiple Stacks (DTSPMS). A set of orders is given, each one requiring transportation of one item from a customer in a pickup region...... to a customer in a delivery region. The vehicle available for the transportation in each region carries a container. The container is organized in rows of given length. Each row is handled independently from the others according to a LIFO (Last In First Out) stack policy. The DTSPMS problem consists...... of determining the pickup tour, the loading plan of the container and the delivery tour in such a way that the total length of the two tours is minimized. The formulations are based on different modelling ideas and each formulation gives rise to a specific solution approach. We present computational results...
Spherical and nonspherical models of primordial black hole formation: exact solutions
Harada, Tomohiro
2015-01-01
We construct spacetimes which provide spherical and nonspherical models of black hole formation in the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with the Lemaitre-Tolman-Bondi solution and the Szekeres quasispherical solution, respectively. These dust solutions may contain both shell-crossing and shell-focusing naked singularities. These singularities can be physically regarded as the breakdown of dust description, where strong pressure gradient force plays a role. We adopt the simultaneous big bang condition to extract a growing mode of adiabatic perturbation in the flat FLRW universe. If the density perturbation has a sufficiently homogeneous central region and a sufficiently sharp transition to the background FLRW universe, its central shell-focusing singularity is globally covered. If the density concentration is {\\it sufficiently large}, there appears no shell-crossing singularity and a black hole is formed. If the density concentration is {\\it not sufficiently large}, there appears shell-...
Directory of Open Access Journals (Sweden)
Emrullah Yaşar
2016-01-01
Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method.
Energy Technology Data Exchange (ETDEWEB)
Khater, A.H.; El-Kalaawy, O.H. [Cairo Univ., Beni-Suef (Egypt). Dept. of Mathematics; Callebaut, D.K. [Universitaire Instelling Antwerpen, Wilrijk (Belgium). Dept. of Physics
1998-12-01
Nonlinear Alfven waves, propagating along a homogeneous magnetic field, are studied using relativistic isotropic hydrodynamics. Alfven solitons of the moving-wave and wave packet types are considered for modified Korteweg-de Vries (mKdV) equation and the nonlinear Schroedinger (NLS) equation, respectively. The method of characteristics is used and the Baecklund transformations (BTs) are employed to generate new solutions from the old ones. Thus, families of new solutions for the mKdV and the NLS equations are obtained. The question arises which solitons exist in the pulsar atmosphere. (orig.) 37 refs.
On the exact solutions of nonlinear diffusion-reaction equations with ...
Indian Academy of Sciences (India)
Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding ...
Exact Solution of the Two-Level System and the Einstein Solid in the Microcanonical Formalism
Bertoldi, Dalia S.; Bringa, Eduardo M.; Miranda, E. N.
2011-01-01
The two-level system and the Einstein model of a crystalline solid are taught in every course of statistical mechanics and they are solved in the microcanonical formalism because the number of accessible microstates can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials. In…
Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line
Aslan, İsmail
2016-09-01
Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.
Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n,n ...
Indian Academy of Sciences (India)
2013-12-05
Dec 5, 2013 ... 2Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,. Babolsar, Iran. ∗ ... into the physical aspects of problems and may be easily used in other applications. In mathematics, for a nonlinear partial differential equation (PDE), usually the travelling wave solutions are ...
Directory of Open Access Journals (Sweden)
Shibib Khalid S.
2017-01-01
Full Text Available The exact analytical solution of axis-symmetry transient temperature and Tresca failure stress in pulsed mode solid-state laser rod is derived using integral transform method. The result obtained from this work is compared with previously published data and good agreement is found. The effect of increasing period is studied, and it is found that at constant pulse width as the period is increased, the allowable pumping power is increased too. Furthermore, the effect of changing pulse width with a constant period is studied, and it is found that as the pulse width is increased, the allowable pumping power is decreased. The effect of duty cycle is studied also and it is found that as duty cycle is increased the allowable pumping power is decreased. This work permits proper selection of pulse width, period and duty cycle to avoid laser rod fracture while obtaining maximum output laser power in the designing of laser system.
Symmetry Analysis and Exact Solutions of the 2D Unsteady Incompressible Boundary-Layer Equations
Han, Zhong; Chen, Yong
2017-01-01
To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attributed to the classification of the corresponding Lie subalgebras. The comprehensiveness and inequivalence of the optimal system are shown clearly under different values of invariants. Then by virtue of the optimal system obtained, the boundary-layer equations are directly reduced to a system of ordinary differential equations (ODEs) by only one step. It has been shown that not only do we recover many of the known results but also find some new reductions and explicit solutions, which may be previously unknown. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072, 11435005, 11675054, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213
Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
Energy Technology Data Exchange (ETDEWEB)
Tierz, Miguel [Departamento de Matemática, Grupo de Física Matemática,Faculdade de Ciências, Universidade de Lisboa,Campo Grande, Edifício C6, 1749-016 Lisboa (Portugal)
2016-04-27
We solve for finite N the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N{sub f} fundamental and N{sub f} anti-fundamental chiral multiplets of R-charge 1/2 and of mass m, by identifying it with an average of inverse characteristic polynomials in a Stieltjes-Wigert ensemble. This requires the computation of the Cauchy transform of the Stieltjes-Wigert polynomials, which we carry out, finding a relationship with Mordell integrals, and hence with previous analytical results on the matrix model. The semiclassical limit of the model is expressed, for arbitrary N{sub f}, in terms of a single Hermite polynomial. This result also holds for more general matter content, involving matrix models with double-sine functions.
Khalid, Asma; Jiann, Lim Yeou; Khan, Ilyas; Shafie, Sharidan
2017-04-01
The purpose of this paper is to study the unsteady convection flow of carbon nanotubes (CNTs) induced by free convection with oscillating plate condition. Single-wall CNTs are used with water as base fluids. The governing partial differential equations and boundary conditions are transformed into a set of ordinary differential equations using suitable dimensionless variables. These equations are solved analytically using Laplace transform technique to obtain the velocity and temperature profiles. Results for velocity and temperature are shown in various graphs and discussed for the embedded flow parameters in detail. It is observed that, velocity decreases with increasing CNTs volume fraction and an increase in CNTs volume fraction increases the nanofluid temperature, which leads to an increase in the heat transfer rates.
Li, Yanning
2013-10-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
Analytical solution to the circularity problem in the discounted cash flow valuation framework
Directory of Open Access Journals (Sweden)
Felipe Mejía-Peláez
2011-12-01
Full Text Available In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E, cost of levered equity (Ke, levered firm value (V, and the weighted average cost of capital (WACC. We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular “Rolling WACC” ignoring the circularity issue, setting a target leverage (usually constant with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors.
Ciotti, Luca; Pellegrini, Silvia
2017-10-01
One of the most active fields of research of modern-day astrophysics is that of massive black hole formation and coevolution with the host galaxy. In these investigations, ranging from cosmological simulations, to semi-analytical modeling, to observational studies, the Bondi solution for accretion on a central point-mass is widely adopted. In this work we generalize the classical Bondi accretion theory to take into account the effects of the gravitational potential of the host galaxy, and of radiation pressure in the optically thin limit. Then, we present the fully analytical solution, in terms of the Lambert-Euler W-function, for isothermal accretion in Jaffe and Hernquist galaxies with a central black hole. The flow structure is found to be sensitive to the shape of the mass profile of the host galaxy. These results and the formulae that are provided, most importantly, the one for the critical accretion parameter, allow for a direct evaluation of all flow properties, and are then useful for the abovementioned studies. As an application, we examine the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the black hole, under the hypothesis of classical Bondi accretion. An overestimate is obtained from regions close to the black hole, and an underestimate outside a few Bondi radii; the exact position of the transition between the two kinds of departure depends on the galaxy model.
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Orhan DÖNMEZ
2016-12-01
Full Text Available The wave properties in a dusty space plasma consisting of positively and negatively charged dust as well as distributed nonisothermal electrons are investigated by using the exact traveling wave solutions of the Schamel-KdV equation. The analytic solutions are obtained by the different types $(G'/G$-expansion methods and direct integration. The nonlinear dynamics of ion-acoustic waves for the various values of phase speed $V_p$, plasma parameters $\\alpha$, $\\sigma$, and $\\sigma_d$, and the source term $\\mu$ are studied. We have observed different types of waves from the different analytic solutions obtained from the different methods. Consequently, we have found the discontinuity, shock or solitary waves. It is also concluded that these parameters play an important role in the presence of solitary waves inside the plasma. Depending on plasma parameters, the discontinuity wave turns into solitary wave solution for the certain values of the phase speed and plasma parameters. Additionally, exact solutions of the Schamel-KdV equation may also be used to understand the wave types and properties in the different plasma systems.
Approximate explicit analytic solution of the Elenbaas-Heller equation
Liao, Meng-Ran; Li, Hui; Xia, Wei-Dong
2016-08-01
The Elenbaas-Heller equation describing the temperature field of a cylindrically symmetrical non-radiative electric arc has been solved, and approximate explicit analytic solutions are obtained. The radial distributions of the heat-flux potential and the electrical conductivity have been figured out briefly by using some special simplification techniques. The relations between both the core heat-flux potential and the electric field with the total arc current have also been given in several easy explicit formulas. Besides, the special voltage-ampere characteristic of electric arcs is explained intuitionally by a simple expression involving the Lambert W-function. The analyses also provide a preliminary estimation of the Joule heating per unit length, which has been verified in previous investigations. Helium arc is used to examine the theories, and the results agree well with the numerical computations.
Measurement of Actinides in Molybdenum-99 Solution Analytical Procedure
Energy Technology Data Exchange (ETDEWEB)
Soderquist, Chuck Z. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Weaver, Jamie L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2015-11-01
This document is a companion report to a previous report, PNNL 24519, Measurement of Actinides in Molybdenum-99 Solution, A Brief Review of the Literature, August 2015. In this companion report, we report a fast, accurate, newly developed analytical method for measurement of trace alpha-emitting actinide elements in commercial high-activity molybdenum-99 solution. Molybdenum-99 is widely used to produce ^{99m}Tc for medical imaging. Because it is used as a radiopharmaceutical, its purity must be proven to be extremely high, particularly for the alpha emitting actinides. The sample of ^{99}Mo solution is measured into a vessel (such as a polyethylene centrifuge tube) and acidified with dilute nitric acid. A gadolinium carrier is added (50 µg). Tracers and spikes are added as necessary. Then the solution is made strongly basic with ammonium hydroxide, which causes the gadolinium carrier to precipitate as hydrous Gd(OH)_{3}. The precipitate of Gd(OH)_{3} carries all of the actinide elements. The suspension of gadolinium hydroxide is then passed through a membrane filter to make a counting mount suitable for direct alpha spectrometry. The high-activity ^{99}Mo and ^{99m}Tc pass through the membrane filter and are separated from the alpha emitters. The gadolinium hydroxide, carrying any trace actinide elements that might be present in the sample, forms a thin, uniform cake on the surface of the membrane filter. The filter cake is first washed with dilute ammonium hydroxide to push the last traces of molybdate through, then with water. The filter is then mounted on a stainless steel counting disk. Finally, the alpha emitting actinide elements are measured by alpha spectrometry.
Directory of Open Access Journals (Sweden)
Ninghu Su
2017-01-01
Full Text Available This paper presents solutions of the fractional partial differential equation (fPDE for analysing water movement in soils. The fPDE explains processes equivalent to the concept of symmetrical fractional derivatives (SFDs which have two components: the forward fractional derivative (FFD and backward fractional derivative (BFD of water movement in soils with the BFD representing the micro-scale backwater effect in porous media. The distributed-order time-space fPDE represents water movement in both swelling and non-swelling soils with mobile and immobile zones with the backwater effect operating at two time scales in large and small pores. The concept of flux-concentration relation is now updated to account for the relative fractional flux of water movement in soils.
Matagne, E.
1994-07-01
This paper reports an exact solution of the Einstein-Maxwell equations. This solution has at the origin of the spatial coordinates a singularity of the Reissner-Nordström type. Far outside, it is a uniform electric field embedded into a Melvin metric. The entire solution is static, but an acceleration with the classical value qE/m can be shown.
Trifonov, E. V.
2017-07-01
We propose a procedure for multiplying solutions of linear and nonlinear one-dimensional wave equations, where the speed of sound can be an arbitrary function of one variable. We obtain exact solutions. We show that the functional series comprising these solutions can be used to solve initial boundary value problems. For this, we introduce a special scalar product.
Mostafa M.A. Khater; Dipankar Kumar
2017-01-01
The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann–Liouville derivative sense. Applying the generalized Kudryashov method through with symbolic computer maple package, numerous new exact solutions ar...
Bulatov, Vitaly V
2012-01-01
The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density and the shape of the floor are modeled with specific functions. In a general case when the characteristics of stratified media and the boundary conditions are arbitrary, the dynamics of internal waves can be only approximated with numerical methods. However, numerical solutions do not describe the wave field qualitatively. At the same time, the need for a qualitative analysis of the far field of internal waves arises in studies applying remote sensing methods in space-based radar applications. In this case, the dynamics of internal waves can be described using asymptotic models. In this paper, we derive asymptotic solutions to the problem of characterizing the far field of internal gravity waves propagating in a stratified medium with a smoothly varying floor.
On the stability of the exact solutions of the dual-phase lagging model of heat conduction
Ordonez-Miranda, Jose; Alvarado-Gil, Juan Jose
2011-12-01
The dual-phase lagging (DPL) model has been considered as one of the most promising theoretical approaches to generalize the classical Fourier law for heat conduction involving short time and space scales. Its applicability, potential, equivalences, and possible drawbacks have been discussed in the current literature. In this study, the implications of solving the exact DPL model of heat conduction in a three-dimensional bounded domain solution are explored. Based on the principle of causality, it is shown that the temperature gradient must be always the cause and the heat flux must be the effect in the process of heat transfer under the dual-phase model. This fact establishes explicitly that the single- and DPL models with different physical origins are mathematically equivalent. In addition, taking into account the properties of the Lambert W function and by requiring that the temperature remains stable, in such a way that it does not go to infinity when the time increases, it is shown that the DPL model in its exact form cannot provide a general description of the heat conduction phenomena.
Food Adulteration: From Vulnerability Assessment to New Analytical Solutions.
Cavin, Christophe; Cottenet, Geoffrey; Blancpain, Carine; Bessaire, Thomas; Frank, Nancy; Zbinden, Pascal
2016-01-01
Crises related to the presence of melamine in milk or horse meat in beef have been a wake-up call to the whole food industry showing that adulteration of food raw materials is a complex issue. By analysing the situation, it became clear that the risk-based approach applied to ensure the safety related to chemical contaminants in food is not adequate for food fraud. Therefore, a specific approach has been developed to evaluate adulteration vulnerabilities within the food chain. Vulnerabilities will require the development of new analytical solutions. Fingerprinting methodologies can be very powerful in determining the status of a raw material without knowing the identity of each constituent. Milk adulterated by addition of adulterants with very different chemical properties could be detected rapidly by Fourier-transformed mid-infrared spectroscopy (FT-mid-IR) fingerprinting technology. In parallel, a fast and simple multi-analytes liquid-chromatography tandem mass-spectrometry (LC/MS-MS) method has been developed to detect either high levels of nitrogen-rich compounds resulting from adulteration or low levels due to accidental contamination either in milk or in other sensitive food matrices. To verify meat species authenticity, DNA-based methods are preferred for both raw ingredients and processed food. DNA macro-array, and more specifically the Meat LCD Array have showed efficient and reliable meat identification, allowing the simultaneous detection of 32 meat species. While the Meat LCD Array is still a targeted approach, DNA sequencing is a significant step towards an untargeted one.
Directory of Open Access Journals (Sweden)
Asma Khalid
2015-01-01
Full Text Available The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.
Dlugach, Janna M.; Mishchenko, Michael I.
2017-01-01
In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.
Directory of Open Access Journals (Sweden)
Maria Cristina Carrisi
2016-01-01
Full Text Available A new model for Polyatomic Gases with an arbitrary but fixed number of moments has been recently proposed and investigated in the framework of Extended Thermodynamics; the arbitrariness of the number of moments is linked to a number N and the resulting model is called an N-Model. This model has been elaborated in order to take into account the entropy principle, the Galilean relativity principle, and some symmetry conditions. It has been proved that the solution for all these conditions exists, but it has not been written explicitly because hard notation is necessary; it has only been shown how the theory is self-generating in the sense that if we know the closure of the N-Model, then we will be able to find that of (N+1-Model. Up to now only a single particular solution has been found in this regard. Instead of this, we find here a numberable set of exact solutions which hold for every fixed number N.
Steady-State Thermoelastic Analytical Solutions for Insulated Pipelines
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M. Fraldi
2016-01-01
Full Text Available A steady-state thermoelastic analytical solution for a multilayer hollow cylinder, composed of an arbitrary number of phases and subject to both radial pressure and temperature gradient, is presented. By assuming each phase to be homogeneous and thermally isotropic and by varying the mechanical and thermal constitutive parameters, a sensitivity analysis has been performed with the aim of finally applying the study to the mechanical behaviour of an industrial pipeline composed of three phases (steel, insulating coating, and polyethylene under the action of the above-mentioned load conditions. By making reference to a classical Hencky-von Mises criterion, the stress profiles along the thickness of the layers have been carried out, also localizing the onset of plasticity as a function of the temperature variations, material properties, and geometrical features characterizing the composite structure of interest. At the end, some numerical results of practical interest in the engineering applications have been specialized to three different insulated coating materials (expanded polyurethane, laminate glass, and syntactic foam, to highlight the cases in which thermal properties and loads can significantly interfere with the mechanical response in pipes, in terms of stresses, in this way suggesting possible strategies for avoiding unexpected failure and supporting the optimal structural design of these systems.
Electronic states of graphene nanoribbons and analytical solutions
Directory of Open Access Journals (Sweden)
Katsunori Wakabayashi, Ken-ichi Sasaki, Takeshi Nakanishi and Toshiaki Enoki
2010-01-01
Full Text Available Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.
Approximate analytical solutions to the condensation-coagulation equation of aerosols
DEFF Research Database (Denmark)
Smith, Naftali R.; Shaviv, Nir J.; Svensmark, Henrik
2016-01-01
to the coagulation limit plus a condensation correction. Our solutions are then compared with numerical results. We show that the solutions can be used to estimate the sensitivity of the cloud condensation nuclei number density to the nucleation rate of small condensation nuclei and to changes in the formation rate......We present analytical solutions to the steady state nucleation-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical solutions. For example, we provide an analytic solution...
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H H Ortíz Álvarez
2012-12-01
Full Text Available In solving practical problems in science and engineering arises as a direct consequence differential equations that explains the dynamics of the phenomena.Finding exact solutions to this equations provides importan informationabout the behavior of physical systems. The Lie symmetry method allows tofind invariant solutions under certain groups of transformations for differentialequations.This method not very well known and used is of great importance inthe scientific community. By this approach it was possible to find several exactinvariant solutions for the Klein Gordon Equation uxx − utt = k(u. A particularcase, The Kolmogorov equation uxx − utt = k1u + k2un was considered.These equations appear in the study of relativistic and quantum physics. Thegeneral solutions found, could be used for future explorations on the study forother specific K(u functions. En la solución de problemas prácticos de las ciencias y la ingeniería surgen como consecuencia directa ecuaciones diferenciales que dan razón de la dinámica de los fenómenos. El encontrar soluciones exactas a estas ecuaciones proporciona información importante sobre el comportamiento de sistemas físicos. El método de las simetrías de Lie permite encontrar soluciones invariantes bajo ciertos grupos de transformaciones para ecuaciones diferenciales. Mediante este método fue posible encontrar familias de soluciones exactas invariantes para la ecuación de Klein Gordon uxx- utt = k(u: En particular, se consideró la ecuación de Kolmogorov uxx - utt = k1u + k2u n. Estas ecuaciones aparecen en el estudio de la física relativista y cuántica. Las soluciones generales encontradas podrían emplearse en futuros desarrollos en el estudio para otro tipo de funciones k(u.
An analytical solution for the Marangoni mixed convection boundary layer flow
DEFF Research Database (Denmark)
Moghimi, M. A.; Kimiaeifar, Amin; Rahimpour, M.
2010-01-01
In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier-Stokes equations to a set of nonlinear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM...... the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....
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Chao Lu
2016-01-01
Full Text Available This paper is concerned with the scheduling of Electrical Multiple Units (EMUs under the condition of their utilization on one sector or within several interacting sectors. Based on the introduction of the train connection graph which describes the possible connection relationship between trains, the integer programming model of EMU circulation planning is constructed. In order to analyzing the resolution of the model, a heuristic which shares the characteristics with the existing methods is introduced first. This method consists of two stages: one is a greedy strategy to construct a feasible circulation plan fragment, and another is to apply a stochastic disturbance to it to generate a whole feasible solution or get a new feasible solution. Then, an exact branch and bound method which is based on graph designing is proposed. Due to the complexity, the lower bound is computed through a polynomial approximation algorithm which is a modification from the one solving the degree constraint minimum 1-tree problem. Then, a branching strategy is designed to cope with the maintenance constraints. Finally, we report extensive computational results on a railway corridor in which the sectors possess the basic feature of railway networks.
Exact solution of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain
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L. Čanová
2009-01-01
Full Text Available The geometric frustration in a class of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chains is investigated by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. The ground state, the magnetization process and the specific heat as a function of the external magnetic field are particularly examined for different strengths of the geometric frustration. It is shown that the increase of the Heisenberg spin value S raises the number of intermediate magnetization plateaux, which emerge in magnetization curves provided that the ground state is highly degenerate on behalf of a sufficiently strong geometric frustration. On the other hand, all intermediate magnetization plateaux merge into a linear magnetization versus magnetic field dependence in the limit of classical Heisenberg spin S → ∞. The enhanced magnetocaloric effect with cooling rate exceeding the one of paramagnetic salts is also detected when the disordered frustrated phase constitutes the ground state and the external magnetic field is small enough.
CSIR Research Space (South Africa)
Shatalov, M
2011-07-01
Full Text Available New exact solutions of equations of longitudinal vibration of conical and exponential rod are obtained for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown...
Classical charged fluids at equilibrium near an interface: Exact ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 64; Issue 5. Classical charged fluids at equilibrium near an interface: Exact analytical density profiles and surface tension. Françoise Cornu. Invited Talks:- Topic 1. Rigorous results and exact solutions; general aspects of statistical physics; thermodynamics Volume 64 ...
Transient Analytic Element Solutions for Flexible Aquifer Test Analyses
Kuhlman, K. L.; Neuman, S. P.
2007-12-01
We present three extensions to the 2D Laplace transform analytic element method (LT-AEM), introduced by Furman and Neuman (2003), which exemplify the types of problems that are easily solved using the LT-AEM, and are useful for performing flexible aquifer test analyses. First, we give the equation for a simplified leaky aquifer- aquitard LT-AEM system, similar to that used by Hantush (1960); in this example the source term is proportional to the drawdown in the aquifer (dual-domain flow is another example). Secondly, we present an approximate unconfined integrodifferential equation, as initially proposed by Boulton (1954) and generalized by Herrera, et al (1978). This solution illustrates how problems defined by convolution integrals are easily handled using LT-AEM (leaky systems can also be represented using convolution integrals). Finally, we present a damped-wave generalization of the diffusion equation that arises from considering a more general form of Darcy's law. The effects of inertia in the aquifer can be considered and may be important near sources in very course materials (e.g., gravel packed envelopes surrounding pumping wells). This final example shows how higher-order time derivatives may be handled in a simple and elegant fashion using LT-AEM techniques; solving the wave equation is as straightforward as solving the diffusion equation in Laplace space. Each of the LT-AEM problems presented here can be solved using any developed LT-AEM element (e.g., point, line, or area sources) or any combination of them, with little modification to the method used to solve the standard diffusion equation.
Zhang, Bo; Chen, Tianning; Zhao, Yuyuan; Zhang, Weiyong; Zhu, Jian
2012-09-01
On the basis of the work of Wilson et al. [J. Acoust. Soc. Am. 84, 350-359 (1988)], a more exact numerical approach was constructed for predicting the nonlinear sound propagation and absorption properties of rigid porous media at high sound pressure levels. The numerical solution was validated by the experimental results for sintered fibrous porous steel samples and its predictions were compared with the numerical solution of Wilson et al. An approximate analytical solution was further put forward for the normalized surface acoustic admittance of rigid air-saturated porous materials with infinite thickness, based on the wave perturbation method developed by Lambert and McIntosh [J. Acoust. Soc. Am. 88, 1950-1959 (1990)]. Comparisons were made with the numerical results.
DEFF Research Database (Denmark)
Andriollo, Tito; Thorborg, Jesper; Hattel, Jesper Henri
2016-01-01
In the present paper, for the first time in literature an exact analytical solution to Lemaitre's isotropic damage model is developed for the special case of uniaxial tensile testing. This is achieved by taking advantage of a convenient formulation of the isotropic hardening function, which allows...... obtaining an integral relationship between total strain and effective stress. By means of the generalized binomial theorem, an expression in terms of infinite series is subsequently derived. The solution is found to simplify considerably existing techniques for material parameters identification based...... on optimization, as all issues associated with classical numerical solution procedures of the constitutive equations are eliminated. In addition, an implicit implementation of the plane stress projected version of Lemaitre's model is discussed, showing that the resulting algebraic system can be reduced...
Analytical Solution for facilitated transport across a membrane
Al-marzouqi, M.; Hogendoorn, Kees; Versteeg, Geert
2002-01-01
An analytical expression for the facilitation factor of component A across a liquid membrane is derived in case of an instantaneous reaction A(g)+B(l)AB(l) inside the liquid membrane. The present expression has been derived based on the analytical results of Olander (A.I.Ch.E. J. 6(2) (1960) 233)
Analytical solution for facilitated transport across a membrane
Marzouqi, Mohamed Hassan Al-; Hogendoorn, Kees J.A.; Versteeg, Geert F.
2002-01-01
An analytical expression for the facilitation factor of component A across a liquid membrane is derived in case of an instantaneous reaction A(g) + B(l) ⇔ AB(l) inside the liquid membrane. The present expression has been derived based on earlier analytical results obtained for the enhancement factor
Energy Technology Data Exchange (ETDEWEB)
Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Noether symmetries and analytical solutions in f(T) cosmology: A complete study
Basilakos, S.; Capozziello, S.; De Laurentis, M.; Paliathanasis, A.; Tsamparlis, M.
2013-11-01
We investigate the main features of the flat Friedmann-Lemaître-Robertson-Walker cosmological models in the f(T) modified gravity regime. In particular, a general approach to find out exact cosmological solutions in f(T) gravity is discussed. Instead of taking into account phenomenological models, we consider as a selection criterion, the existence of Noether symmetries in the cosmological f(T) pointlike Lagrangian. We find that only the f(T)=f0Tn model admits extra Noether symmetries. The existence of extra Noether integrals can be used in order to simplify the system of differential equations (equations of motion) as well as to determine the integrability of the f(T)=f0Tn cosmological model. Within this context, we can solve the problem analytically and thus we provide the evolution of the main cosmological functions such as the scale factor of the Universe, the Hubble expansion rate, the deceleration parameter, and the linear matter perturbations. We show that the f(T)=f0Tn cosmological model suffers from two basic problems. The first problem is related to the fact that the deceleration parameter is constant which means that it never changes sign, and therefore the Universe always accelerates or always decelerates depending on the value of n. Second, we find that the clustering growth rate remains always equal to unity implying that the recent growth data disfavor the f(T)=f0Tn gravity. Finally, we prove that the f(T)=f0Tn gravity can be cosmologically equivalent with the f(R)=Rn gravity model and the time varying vacuum model Λ(H)=3γH2 (for n-1=1-γ) because the above cosmological scenarios share exactly the same Hubble expansion, despite the fact that the three models have a different geometrical origin. Finally, some important differences with power-law f(R) gravity are pointed out.
Feng, Lian-Li; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian
2016-09-01
In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method. Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No. XZD201602, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527
Directory of Open Access Journals (Sweden)
Sunday O. Edeki
2015-10-01
Full Text Available In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM resulting from the modification of the classical Differential Transformation Method (DTM is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algorithm can be followed for European put options. It is shown that PDTM is more efficient, reliable and better than the classical DTM and other semi-analytical methods since less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs encountered in financial mathematics.
Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations
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Seyma Tuluce Demiray
2015-01-01
Full Text Available We make use of the so-called Sumudu transform method (STM, a type of ordinary differential equations with both integer and noninteger order derivative. Firstly, we give the properties of STM, and then we directly apply it to fractional type ordinary differential equations, both homogeneous and inhomogeneous ones. We obtain exact solutions of fractional type ordinary differential equations, both homogeneous and inhomogeneous, by using STM. We present some numerical simulations of the obtained solutions and exhibit two-dimensional graphics by means of Mathematica tools. The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions.
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Heng Wang
2016-01-01
Full Text Available By using the method of dynamical system, the exact travelling wave solutions of the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms are studied. Based on this method, all phase portraits of the system in the parametric space are given with the aid of the Maple software. All possible bounded travelling wave solutions, such as solitary wave solutions, kink and anti-kink wave solutions, and periodic travelling wave solutions, are obtained, respectively. The results presented in this paper improve the related previous conclusions.
Analytical mechanics solutions to problems in classical physics
Merches, Ioan
2014-01-01
Fundamentals of Analytical Mechanics Constraints Classification Criteria for Constraints The Fundamental Dynamical Problem for a Constrained Particle System of Particles Subject to Constraints Lagrange Equations of the First KindElementary Displacements Generalities Real, Possible and Virtual Displacements Virtual Work and Connected Principles Principle of Virtual WorkPrinciple of Virtual Velocities Torricelli's Principle Principles of Analytical Mechanics D'alembert's Principle Configuration Space Generalized Forces Hamilton's Principle The Simple Pendulum Problem Classical (Newtonian) Formal
Ding, Xiao-Li; Nieto, Juan J.
2017-11-01
In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.
A tilted and warped inner accretion disc around a spinning black hole: an analytical solution
Chakraborty, Chandrachur; Bhattacharyya, Sudip
2017-08-01
Inner accretion disc around a black hole provides a rare, natural probe to understand the fundamental physics of the strong gravity regime. A possible tilt of such a disc, with respect to the black hole spin equator, is important. This is because such a tilt affects the observed spectral and timing properties of the disc X-ray emission via Lense-Thirring precession, which could be used to test the theoretical predictions regarding the strong gravity. Here, we analytically solve the steady, warped accretion disc equation of Scheurer and Feiler, and find an expression of the radial profile of the disc tilt angle. In our exact solution, considering a prograde disc around a slowly spinning black hole, we include the inner part of the disc, which was not done earlier in this formalism. Such a solution is timely, as a tilted inner disc has recently been inferred from X-ray spectral and timing features of the accreting black hole H1743-322. Our tilt angle radial profile expression includes observationally measurable parameters, such as black hole mass and Kerr parameter, and the disc inner edge tilt angle Win, and hence can be ideal to confront observations. Our solution shows that the disc tilt angle in 10-100 gravitational radii is a significant fraction of the disc outer edge tilt angle, even for Win = 0. Moreover, tilt angle radial profiles have humps in ˜10-1000 gravitational radii for some sets of parameter values, which should have implications for observed X-ray features.
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M. T. Mustafa
2014-01-01
Full Text Available A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.
Can We Remove Secular Terms for Analytical Solution of Groundwater Response under Tidal Influence?
Munusamy, Selva Balaji
2016-01-01
This paper presents a secular term removal methodology based on the homotopy perturbation method for analytical solutions of nonlinear problems with periodic boundary condition. The analytical solution for groundwater response to tidal fluctuation in a coastal unconfined aquifer system with the vertical beach is provided as an example. The non-linear one-dimensional Boussinesq's equation is considered as the governing equation for the groundwater flow. An analytical solution is provided for non-dimensional Boussinesq's equation with cosine harmonic boundary condition representing tidal boundary condition. The analytical solution is obtained by using homotopy perturbation method with a virtual embedding parameter. The present approach does not require pre-specified perturbation parameter and also facilitates secular terms elimination in the perturbation solution. The solutions starting from zeroth-order up to third-order are obtained. The non-dimensional expression, $A/D_{\\infty}$ emerges as an implicit parame...
Timonin, A. M.
2016-09-01
Based on the finite-layer method, a method for evaluating the stress-strain state and energy release rate for specimens with delaminations in double-cantilever beam and end-notched flexure tests is proposed. Exact numerical solutions of boundary-value problems for the "stiff" systems of differential equations describing deformations of test specimens are obtained. The distributions of forces, moments, displacements, and rotations in the specimens and the distributions of normal and tangential stresses on their midline are presented. New closed-form expressions for these functions and for compliance of the specimens are developed. Calculation results for the energy release rate obtained by a numerical differentiation and from analytical relations are presented. Two new techniques for estimating the energy release rate are proposed: (1) using the calculated values of peak stress and jumps of displacements at the tip of delamination; (2) by evaluation of indeterminacy at the tip of delamination with the use of stresses and derivatives of stresses and displacements. The effect of the transverse shear and Poisson ratio on the results is estimated. A comparison of the numerical and analytical solutions obtained with known results and the ASTM standard is presented.
Analytical solution for two-phase flow in a wellbore using the drift-flux model
Energy Technology Data Exchange (ETDEWEB)
Pan, L.; Webb, S.W.; Oldenburg, C.M.
2011-11-01
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO{sub 2} leakage problem as well as to field data from a CO{sub 2} production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO{sub 2} is leaking upward responds to the mass flow rate of CO{sub 2}-water mixture.
Wexler, Eliezer J.
1992-01-01
Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems having uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of selected solutions, source codes for the computer programs, and samples of program input and output also are included.
Li, Yajun
2011-08-01
Nonparaxial ray tracing through Risley prisms of four different configurations is performed to give the exact solution of the inverse problem arisen from applications of Risley prisms to free space communications. Predictions of the exact solution and the third-order theory [Appl. Opt.50, 679 (2011)APOPAI0003-693510.1364/AO.50.000679] are compared and results are shown by curves for systems using prisms of different materials. The exact solution for the problem of precision pointing is generalized to investigate the synthesis of the scan pattern, i.e., to create a desirable scan pattern on some plane perpendicular to the optical axis of the system by controlling the circular motion of the two prisms.
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Dimitrios E. Panayotounakos
2011-01-01
Full Text Available We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel's nonlinear differential equations (ODEs of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind (Neumann functions, as well as of the free member of the considered ODE; the parameter being introduced furnishes the order of the above Bessel functions and defines also the desired solutions of the considered ODE as one-parameter family of surfaces. The nonlinear initial or boundary value problems are also investigated. Finally, introducing a relative mathematical methodology, we construct the exact parametric or closed form solutions for several degenerate Abel's equation of the first kind.
Energy Technology Data Exchange (ETDEWEB)
An, Deuk Man [Pusan Nat’l Univ., Busan (Korea, Republic of)
2017-01-15
In this study, we develop the exact field of modeⅠin an infinitely deep crack in a half-plane. Using this field, we obtain the exact stress intensity factor KⅠ. From the tractions on the crack faces induced by exact field, we calculate the stress intensity factor of this field. We compare the results with the stress intensity factor calculated using Bueckner’s weight function formula and that calculated by using Tada’s formula listed in “The Stress Analysis of Cracks Handbook” It was found that Bueckner’s formula yields accurate results. However, the results obtained using Tada’s formula exhibit inaccurate behavior.
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M. K. Bahar
2013-01-01
Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...
The Analytical Solution of Parabolic Volterra Integro-Differential Equations in the Infinite Domain
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Yun Zhao
2016-09-01
Full Text Available This article focuses on obtaining analytical solutions for d-dimensional, parabolic Volterra integro-differential equations with different types of frictional memory kernel. Based on Laplace transform and Fourier transform theories, the properties of the Fox-H function and convolution theorem, analytical solutions for the equations in the infinite domain are derived under three frictional memory kernel functions. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, the Fox-H function and the convolution form of the Fourier transform. In addition, graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equations with a power-law memory kernel. It can be seen that the solution curves are subject to Gaussian decay at any given moment.
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Lev Abolnikov
2000-01-01
Full Text Available A bulk M/G/1 system is considered that responds to large increases (decreases of the queue during the service act by alternating between two service modes. The switching rule is based on two up and down thresholds for total arrivals over the service act. A necessary and sufficient condition for the ergodicity of a Markov chain embedded into the main queueing process is found. Both complex-analytic and matrix-analytic solutions are obtained for the steady-state distribution. Under the assumption of the same service time distribution in both modes, a combined complex-matrix-analytic method is introduced. The technique of matrix unfolding is used, which reduces the problem to a matrix iteration process with the block size much smaller than in the direct application of the matrix-analytic method.
A family of analytical solutions of a nonlinear diffusion-convection equation
Hayek, Mohamed
2018-01-01
Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.
Verhoest, N.E.C.; Pauwels, V.R.N.; Troch, P.A.; Troch, De F.P.
2002-01-01
This paper presents two analytical solutions of the linearized Boussinesq equation for an inclined aquifer, drained by ditches, subjected to a constant recharge rate. These solutions are based on different initial conditions. First, the transient solution is obtained for an initially fully saturated
Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo
2017-06-01
This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009
Analytic Solutions to Coherent Control of the Dirac Equation
Campos, Andre G.; Cabrera, Renan; Rabitz, Herschel A.; Bondar, Denys I.
2017-10-01
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies.
Analytical solutions for the radial Scarf II potential
Lévai, G.; Baran, Á.; Salamon, P.; Vertse, T.
2017-06-01
The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for l = 0 by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the S0 (k)s-wave S-matrix, the poles of which supply the k values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. It is shown that the generalized Woods-Saxon potential can be generated from the Rosen-Morse II potential in the same way as the radial Scarf II potential is obtained from its one-dimensional correspondent. Based on this analogy, possible applications are also pointed out.
Analytical solutions of the electrostatically actuated curled beam problem
Younis, Mohammad I.
2014-07-24
This works presents analytical expressions of the electrostatically actuated initially deformed cantilever beam problem. The formulation is based on the continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximation. In such cases, multi-mode reduced order models are shown to yield accurate results. © 2014 Springer-Verlag Berlin Heidelberg.
Vacaru, Sergiu I.; Yazici, Enis
2014-01-01
We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.
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Mostafa M.A. Khater
2017-09-01
Full Text Available The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann–Liouville derivative sense. Applying the generalized Kudryashov method through with symbolic computer maple package, numerous new exact solutions are successfully obtained. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions with the integer and fractional order.
Exact solutions for STO and (3+1-dimensional KdV-ZK equations using Gâ²G2-expansion method
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Sadaf Bibi
Full Text Available This article deals with finding some exact solutions of nonlinear fractional differential equations (NLFDEs by applying a relatively new method known as Gâ²G2-expansion method. Solutions of spaceâtime fractional Sharma-Tasso-Olever (STO equation of fractional order and (3+1-dimensional KdV-Zakharov Kuznetsov (KdV-ZK equation of fractional order are reckoned to demonstrate the validity of this method. The fractional derivative version of modified RiemannâLiouville, linked with Fractional complex transform is employed to transform fractional differential equations into the corresponding ordinary differential equations. Keywords: Sharma Tasso-Olever (STO equation, (3+1-Dimensional KdV-Zakharov Kuznetsov (KdV-ZK equation, Exact solutions, Gâ²G2-expansion method
Muriel, Amador
2017-01-01
There have been several papers published which show exact solutions of the Navier-Stokes equation. None of the solutions admit any possibility of turbulence. It is strongly suggested that the Navier-Stokes equation is not the correct problem definition for turbulence. Yet, by contrast, in a simple example, it s shown that turbulence can result quite directly by using two or more species of fluids. The species are in fact identical atoms with different quantum states, provoking the strong suggestion that a plausible explanation for the origin of turbulence is quantum mechanical. This suggestion is heavily supported by actual modern pipe flow experiments [Muriel, Quantum Theory of Turbulence, Harvard Book Store (2011),which may be downloaded from (Muriel, ResearchGate)] The most general exact solutions of the Navier-Stokes equation will be displayed. In addition, experiments supporting a quantum interpretation will be reviewed.
Analytical Solutions for Predicting Underwater Explosion Gas Bubble Behaviour
2010-11-01
décrit différents modèles analytiques élaborés antérieurement pour prévoir la croissance et l’implosion radiales en champ libre des bulles gazeuses...9.80665 Air pressure (kPa), Pair 101.325 101.325 4.4 Code Development The visualization software IDL was used to develop a code for calculating the...models and assumptions provide better predictions. Using the visualization software IDL the various analytical models and similitude equations, a code
Analytical solution of a stochastic content-based network model
Energy Technology Data Exchange (ETDEWEB)
Mungan, Muhittin [Department of Physics, Faculty of Arts and Sciences, Bogazici University, 34342 Bebek Istanbul (Turkey); Guersey Institute, PO Box 6, Cengelkoey, 34680 Istanbul (Turkey); Kabakoglu, Alkan [Department of Physics, Faculty of Arts and Sciences, Koc University, 34450 Sariyer Istanbul (Turkey); Dipartimento di Fisica, Universita di Padova, I-35131 Padova (Italy); Balcan, Duygu [Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 34469, Istanbul (Turkey); Erzan, Ayse [Guersey Institute, PO Box 6, Cengelkoey, 34680 Istanbul (Turkey); Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 34469, Istanbul (Turkey)
2005-11-04
We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.
Analytical solutions for transport processes fluid mechanics, heat and mass transfer
Brenn, Günter
2017-01-01
This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field. .
Lunin, Andrei; Grudiev, Alexej
2011-01-01
Analytical solutions are derived for transient and steady state gradient distributions in the travelling wave accelerating structures with arbitrary variation of parameters over the structure length. The results of both the unloaded and beam loaded cases are presented.
A Quantum Dot with Spin-Orbit Interaction--Analytical Solution
Basu, B.; Roy, B.
2009-01-01
The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
National Research Council Canada - National Science Library
Thiago Antonini Alves; Ricardo Alan Verdú Ramos; Cassio Roberto Macedo Maia
2015-01-01
In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT...
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Semi-Analytic Solution of HIV and TB Co-Infection Model BOLARIN ...
African Journals Online (AJOL)
ADOWIE PERE
. +. −. + +. +. +. +. − + +. +. −. +. +. −. +. (66). RESULTS AND DISCUSSION. In this section, we use maple software to plot the graph of semi-analytic solution of our model equations. Since, most of the parameters were not readily available ...
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
Halil Özer; Özkan Öz
2014-01-01
This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using fou...
Korkmaz, Alper
2017-05-01
Exact solutions to conformable time fractional (3+1)-dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo–Miwa, the Zakharov–Kuznetsov, and the modified Zakharov–Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.
Analytical solution of groundwater waves in unconfined aquifers with ...
Indian Academy of Sciences (India)
Selva Balaji Munusamy
2017-07-29
Jul 29, 2017 ... vertical beach face. However, in natural systems the beach face is normally sloped. Nielsen [2] used a linearized. Boussinesq equation to provide solutions for a coastal aquifer with sloping beach face. Nielsen [2] assumed a fixed location boundary condition and the perturbation parameter included.
Explicit Analytical Solution of a Pendulum with Periodically Varying Length
Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu
2010-01-01
A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…
Analytical solutions of weakly coupled map lattices using recurrence relations
Energy Technology Data Exchange (ETDEWEB)
Sotelo Herrera, Dolores, E-mail: dsh@dfmf.uned.e [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); San Martin, Jesus [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); Dep. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9-28040 Madrid (Spain)
2009-07-20
By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C{sup 2} function.
Analytical solution of mass transfer effects on unsteady flow past an ...
African Journals Online (AJOL)
This paper discussed the analytical solution of unsteady free convection and mass transfer flow past an accelerated infinite vertical porous flat plate with suction, heat generation and chemical species when the plate accelerates in its own plane. The governing equations are solved analytically using perturbation technique.
Saha Ray, S.
2016-09-01
In this article, the Jacobi elliptic function method viz. the mixed dn-sn method has been presented for finding the travelling wave solutions of the Davey-Stewartson equations. As a result, some solitary wave solutions and doubly periodic solutions are obtained in terms of Jacobi elliptic functions. Moreover, solitary wave solutions are obtained as simple limits of doubly periodic functions. These solutions can be useful to explain some physical phenomena, viz. evolution of a three-dimensional wave packet on water of finite depth. The proposed Jacobi elliptic function method is efficient, powerful and can be used in order to establish newer exact solutions for other kinds of nonlinear fractional partial differential equations arising in mathematical physics.
Analytical solutions of stellar winds in B-A type supergiants stars
Araya, Ignacio; Cure, Michel
2013-06-01
An analytical solution for the δ-slow hydrodynamic solution (Cure et al. 2011) in B-A type supergiants stars is developed. The methodology is based on the analytical solutions of a) Villata (1992), which is described in terms of the stellar and wind parameters and b) Muller & Vink (2008), which is described in terms of fitting parameters from a numerical solution (hydrodynamic). These methodologies only apply for fast solutions, for that reason the line acceleration term (gL) of Muller & Vink method is modified in order to obtain an analytical solution for the δ-slow solution. To find a relationship between the parameters from the fit and the stellar and wind parameters, a computational grid, based on the grid of stellar models from Ekstrom et al. (2012), is created for B-A type supergiants stars with δ-slow hydrodynamic solution. Finally, an analytical solution for B-A type supergiants stars is obtained based on the Lambert W function (Corless et al. 1996). Comparing with the numerical solutions, the terminal velocity has a median relative error below 4% and the mass loss rate has a median relative error below 5%. In addition, we calculated the wind-momentum luminosity relationship (WLR) with the models from the computational grid and compared with the observations, showing a very good agreement.
Power Control at Grid Connected Converters and Analytical Solution of Steady States
Viktor Valouch; Jiří Škramlík; Zdeněk Muller; Jan Švec; Josef Tlustý
2015-01-01
The paper presents a power control technique at grid connected converters under unbalanced voltage conditions. The current positive and negative sequences during grid voltage sags are controlled to ensure a proper exchange of active and reactive powers without power ripples. An analytical solution in a closed form of the B6 and B4 converters working with an optimized half a period switching symmetry is presented. The analytical solution may be applied for the converters connected to highly un...
Mustafa, M.T.; Arif, A.F.M.; Masood, Khalid
2014-01-01
A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars...
Analytic solution of neural network with disordered lateral inhibition
Hamaguchi, Kosuke; Hatchett, J. P. L.; Okada, Masato
2006-05-01
The replica method has played a key role in analyzing systems with disorder, e.g., the Sherrington-Kirkpatrick (SK) model, and associative neural networks. Here we study the influence of disorder in the lateral inhibition type interactions on the cooperative and uncooperative behavior of recurrent neural networks by using the replica method. Although the interaction between neurons has a dependency on distance, our model can be solved analytically. Bifurcation analysis identifies the boundaries between paramagnetic, ferromagnetic, spin-glass, and localized phases. In the localized phase, the network shows a bump like activity, which is often used as a model of spatial working memory or columnar activity in the visual cortex. Simulation results show that disordered interactions can stabilize the drift the of bump position, which is commonly observed in conventional lateral inhibition type neural networks.
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 ...
Directory of Open Access Journals (Sweden)
Mark A Lau
2016-09-01
Full Text Available This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions.
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares
2015-07-01
This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)