Mechanika Płynów Lab.,
2014
Wroclaw University of Technology
Mechanika Płynów Lab., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Integrability, Recursion Operators And Soliton Interactions,
2014
Bulgarian Academy of Sciences
Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov
Book chapter/book
This volume contains selected papers based on the talks,presentedat the Conference Integrability, Recursion Operators and Soliton Interactions, held in Sofia, Bulgaria (29-31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. …
Abstract Functional Stochastic Evolution Equations Driven By Fractional Brownian Motion,
2014
West Chester University of Pennsylvania
Abstract Functional Stochastic Evolution Equations Driven By Fractional Brownian Motion, Mark A. Mckibben, Micah Webster
Mathematics Faculty Publications
We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownianmotion in a real separable Hilbert space.Global existence results concerningmild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.
Hamiltonian Approach To The Modeling Of Internal Geophysical Waves With Vorticity,
2014
Technological University Dublin
Hamiltonian Approach To The Modeling Of Internal Geophysical Waves With Vorticity, Alan Compelli
Articles
We examine a simplified model of internal geophysical waves in a rotational 2-dimensional water-wave system, under the influence of Coriolis forces and with gravitationally induced waves. The system consists of a lower medium, bound underneath by an impermeable flat bed, and an upper lid. The 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of its conjugate variables and perform a variable transformation to show that it has canonical Hamiltonian structure. We then linearize the system, …
Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems,
2014
INRNE, Sofia, Bulgaria
Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi
Articles
We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.
Infinitely Many Rotationally Symmetric Solutions To A Class Of Semilinear Laplace-Beltrami Equations On The Unit Sphere,
2014
Harvey Mudd College
Infinitely Many Rotationally Symmetric Solutions To A Class Of Semilinear Laplace-Beltrami Equations On The Unit Sphere, Emily M. Fischer
HMC Senior Theses
I show that a class of semilinear Laplace-Beltrami equations has infinitely many solutions on the unit sphere which are symmetric with respect to rotations around some axis. This equation corresponds to a singular ordinary differential equation, which we solve using energy analysis. We obtain a Pohozaev-type identity to prove that the energy is continuously increasing with the initial condition and then use phase plane analysis to prove the existence of infinitely many solutions.
Matrix G-Strands,
2014
Imperial College London
Matrix G-Strands, Darryl Holm, Rossen Ivanov
Articles
We discuss three examples in which one may extend integrable Euler–Poincare ordinary differential equations to integrable Euler–Poincare partial differential
equations in the matrix G-Strand context. After describing matrix G-Strand examples for SO(3) and SO(4) we turn our attention to SE(3) where the matrix G-Strand equations recover the exact rod theory in the convective representation. We then find a zero curvature representation of these equations and establish the conditions under which they are completely integrable. Thus, the G-Strand equations turn out to be a rich source of integrable systems. The treatment is meant to be expository and most concepts are explained …
Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface,
2014
Technological University Dublin
Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli
Articles
We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.
Computational Models For Nanosecond Laser Ablation,
2014
Embry-Riddle Aeronautical University
Computational Models For Nanosecond Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades
Publications
Laser ablation in an ambient environment is becoming increasingly important in science and technology. It is used in applications ranging from chemical analysis via mass spectroscopy, to pulsed laser deposition and nanoparticle manufacturing. We describe numerical schemes for a multiphase hydrodynamic model of nanosecond laser ablation expressing energy, momentum, and mass conservation in the target material, as well as in the expanding plasma plume, along with collisional and radiative processes for laser-induced breakdown (plasma formation). Numerical simulations for copper in a helium background gas are presented and the efficiency of various ODE integrators is compared.
Graphic Illustration Of The Transmission Resonances For The Dkp Particles,
2013
Université Badji-Mokhtar
Graphic Illustration Of The Transmission Resonances For The Dkp Particles, B. Boutabia-Chéraitia, Abdenacer Makhlouf
Applications and Applied Mathematics: An International Journal (AAM)
We consider the Duffin-Kemmer-Petiau (DKP) equation in the presence of a spatially one-dimensional Woods-Saxon (WS) potential and we show by graphics how the zero-reflection condition on the Klein interval depends on the shape of the potential.
Exponentially Fitted Variants Of The Two-Step Adams-Bashforth Method For The Numerical Integration Of Initial Problems,
2013
Panjab University
Exponentially Fitted Variants Of The Two-Step Adams-Bashforth Method For The Numerical Integration Of Initial Problems, Gurjinder Singh, V. Kanwar, Saurabh Bhatia
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step Adams- Moulton methods respectively.
Dispersion Of A Solute In Hartmann Two-Fluid Flow Between Two Parallel Plates,
2013
Gulbarga University
Dispersion Of A Solute In Hartmann Two-Fluid Flow Between Two Parallel Plates, J. P. Kumar, J. C. Umavathi
Applications and Applied Mathematics: An International Journal (AAM)
The paper presents an analytical solution for the dispersion of a solute in a conducting immiscible fluid flowing between two parallel plates in the presence of a transverse magnetic field. The fluids in both the regions are incompressible, electrically conducting and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The results are tabulated for various values of viscosity ratio, pressure gradient and Hartman number on the effective Taylor dispersion coefficient and volumetric …
Exact Traveling Wave Solutions Of Nonlinear Pdes In Mathematical Physics Using The Modified Simple Equation Method,
2013
Zagazig University
Exact Traveling Wave Solutions Of Nonlinear Pdes In Mathematical Physics Using The Modified Simple Equation Method, E. M. E. Zayed, A. H. Arnous
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we apply the modified simple equation method to find the exact solutions with parameters of the (1+1)-dimensional nonlinear Burgers-Huxley equation, the (2+1) dimensional cubic nonlinear Klein-Gordon equation and the (2+1)-dimensional nonlinear Kadomtsev- Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The new exact solutions of these three equations are obtained. When these parameters are given special values, the solitary solutions are obtained.
Application Of The Optimal Homotopy Asymptotic Method For Solving The Cauchy Reaction-Diffusion Problem,
2013
University of Mazandaran
Application Of The Optimal Homotopy Asymptotic Method For Solving The Cauchy Reaction-Diffusion Problem, H. Jafari, S. Gharbavy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the optimal homotopy asymptotic method is applied on the Cauchy reaction-diffusion problems to check the effectiveness and performance of the method. The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. Moreover, this technique does not require any discretization or linearization and therefore it reduces significantly the numerical computations. The results reveal that the method is explicit.
Maxwell’S Equations On Cantor Sets: A Local Fractional Approach,
2013
Y. Zhao
Maxwell’S Equations On Cantor Sets: A Local Fractional Approach, Yang Xiaojun
Xiao-Jun Yang
Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell’s equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.
Application Of The Local Fractional Series Expansion Method And The Variational Iteration Method To The Helmholtz Equation Involving Local Fractional Derivative Operators,
2013
H. M. Srivastava
Application Of The Local Fractional Series Expansion Method And The Variational Iteration Method To The Helmholtz Equation Involving Local Fractional Derivative Operators, Yang Xiaojun
Xiao-Jun Yang
We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.
Computation Sequences For Series And Polynomials,
2013
The University of Western Ontario
Computation Sequences For Series And Polynomials, Yiming Zhang
Electronic Thesis and Dissertation Repository
Approximation to the solutions of non-linear differential systems is very useful when the exact solutions are unattainable. Perturbation expansion replaces the system with a sequences of smaller problems, only the first of which is typically nonlinear. This works well by hand for the first few terms, but higher order computations are typically too demanding for all but the most persistent. Symbolic computation is thus attractive; however, symbolic computation of the expansions almost always encounters intermediate expression swell, by which we mean exponential growth in subexpression size or repetitions. A successful management of spatial complexity is vital to compute meaningful results. …
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators,
2013
Y. Zhao
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Xiao-Jun Yang
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction,
2013
University of Mosul
Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for...
Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation,
2013
University of Mosul
Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation, Abdulghafor M. Al-Rozbayani Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the discrete Adomian decomposition method (DADM) is applied to a fully implicit scheme of the generalized Burger’s–Huxley equation. The numerical results of two test problems are compared with the exact solutions. The comparisons reveal that the proposed method is very accurate and effective for this kind of problems.
