Non-linear Dynamics Commons^™

Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi

mohammad najafi

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

Starting Radial Subdiffusion From A Central Point Through A Diverging Medium (A Sphere): Heat-Balance Integral Method, Jordan Hristov

Jordan Hristov

The work presents an integral solution of the time-fractional subdiffusion equation as alternative approach to those employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer) well known from the heat diffusion and hydrodynamics. The profile satisfies the boundary conditions imposed at the boundary of the boundary layer that allows its coefficients to be expressed through the boundary layer depth as unique parameter describing the profile. The technique is demonstrated by a solution of a time fractional radial equation concerning anomalous diffusion from a central point source in a …

Formation Of Organized Nanostructures From Unstable Bilayers Of Thin Metallic Liquids, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman

Mikhail Khenner

Dewetting of pulsed-laser irradiated, thin (< 20 nm), optically reflective metallic bilayers on an optically transparent substrate with a reflective support layer is studied within the lubrication equations model. A steady-state bilayer film thickness (h) dependent temperature profile is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Large thermocapillary forces are observed along the plane of the liquid-liquid and liquid-gas interfaces due to this h-dependent temperature, which, in turn, is strongly influenced by the h-dependent laser light reflection and absorption. Consequently the dewetting is a result of the competition between thermocapillary and intermolecular forces. A linear analysis of the dewetting length scales established that the non-isothermal calculations better predict the experimental results as compared to the isothermal case within the bounding Hamaker coefficients. Subsequently, a computational non-linear dynamics study of the dewetting pathway was performed for Ag/Co and Co/Ag bilayer systems to predict the morphology evolution. We found that the systems evolve towards formation of different morphologies, including core-shell, embedded, or stacked nanostructure morphologies.

Transient Flow Of A Generalized Second Grade Fluid Due To A Constant Surface Shear Stress: An Approximate Integral-Balance Solution, Jordan Hristov

Jordan Hristov

Integral balance solution to start-up problem of a second grade viscoelastic fluid caused by a constant surface stress at the surface has been developed by an entire-domain parabolic profile with an unspecified exponent. The closed form solution explicitly defines two dimensionless similarity variables ξ = y ν t and 2 D0 p t= χ = ν β , responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed, as well comparison with the existing …

Concentration Oscillations In The Processes Of Unsaturated Compounds Oxidative Carbonylation. 2. Oxidative Carbonylation Of Alkynes In The Palladium Halogen Complexes Solutions (In Russian), Sergey N. Gorodsky

Sergey N. Gorodsky

No abstract provided.

Physics Of Quasi-Monoenergetic Laser-Plasma Acceleration Of Electrons In The Blowout Regime, Serguei Y. Kalmykov, Bradley A. Shadwick, Arnaud Beck, Erik Lefebvre

Serge Youri Kalmykov

No abstract provided.

Some New Exact Solutions Of The (3+1)-Dimensional Breaking Soliton Equation By The Exp-Function Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi

mohammad najafi

This paper applies the Exp-function method to search for new exact traveling wave solutions of the (3+1)-dimensional breaking soliton equation, their physical expantions are given graphically.

Testing For Weak Form Market Efficiency In Indian Foreign Exchange Makret, Anoop Sasikumar

Anoop Sasikumar

This paper attempts to examine the weak form of market efficiency in the Indian foreign exchange market using a family of variance ratio tests. Monthly Nominal Effective Exchange Rate (NEER) data from April 1993-June 2010 were used for the analysis. NEER series was considered for the analysis as it is supposed to capture more information compared to the bilateral exchange rates. Three individual variance ratio tests as well as three joint variance ratio tests were used for the purpose of analysis. After analyzing the results from both individual and joint variance ratio test, it was concluded that Indian foreign exchange …

Concentration Oscillations In The Processes Of Unsaturated Compounds Oxidative Carbonylation. 1. Processes Of Acetylene And Phenylacetylene Oxidative Carbonylation (In Russian), Sergey N. Gorodsky, Katarina Novakovic

Sergey N. Gorodsky

This review describes the processes of oxidative carbonylation of acetylene and phenylacetylene, occurring in the oscillatory mode under conditions of homogeneous catalysis by palladium complexes.

Analytical Solutions For Nonlinear Lateral Sloshing In Partiallyfilled Elliptical Tankers, Hassan Askari

No abstract provided.

Applications Of Local Fractional Calculus To Engineering In Fractal Time-Space: Local Fractional Differential Equations With Local Fractional Derivative, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.

A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent’s series of complex functions in complex fractal space, and generalized residue theorems are investigated.

Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.

A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun

Xiao-Jun Yang

It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.

Electron Self-Injection Into An Evolving Plasma Bubble: Quasi-Monoenergetic Laser-Plasma Acceleration In The Blowout Regime, Serguei Y. Kalmykov, Arnaud Beck, Sunghwan A. Yi, Vladimir N. Khudik, Michael C. Downer, Erik Lefebvre, Bradley A. Shadwick, Donald P. Umstadter

Donald P. Umstadter

An electron density bubble driven in a rarefied uniform plasma by a slowly evolving laser pulse goes through periods of adiabatically slow expansions and contractions. Bubble expansion causes robust self-injection of initially quiescent plasma electrons, whereas stabilization and contraction terminate self-injection thus limiting injected charge; concomitant phase space rotation reduces the bunch energy spread. In regimes relevant to experiments with hundred terawatt- to petawatt-class lasers, bubble dynamics and, hence, the self-injection process are governed primarily by the driver evolution. Collective transverse fields of the trapped electron bunch reduce the accelerating gradient and slow down phase space rotation. Bubble expansion followed …

Electron Self-Injection Into An Evolving Plasma Bubble: Quasi-Monoenergetic Laser-Plasma Acceleration In The Blowout Regime, Serguei Y. Kalmykov, Arnaud Beck, Sunghwan A. Yi, Vladimir N. Khudik, Michael C. Downer, Erik Lefebvre, Bradley A. Shadwick, Donald P. Umstadter

Serge Youri Kalmykov

An electron density bubble driven in a rarefied uniform plasma by a slowly evolving laser pulse goes through periods of adiabatically slow expansions and contractions. Bubble expansion causes robust self-injection of initially quiescent plasma electrons, whereas stabilization and contraction terminate self-injection thus limiting injected charge; concomitant phase space rotation reduces the bunch energy spread. In regimes relevant to experiments with hundred terawatt- to petawatt-class lasers, bubble dynamics and, hence, the self-injection process are governed primarily by the driver evolution. Collective transverse fields of the trapped electron bunch reduce the accelerating gradient and slow down phase space rotation. Bubble expansion followed …

A Modification Of Extended Homoclinic Test Approach To Solve The (3+1)-Dimensional Potential-Ytsf Equation, Mohammad Najafi, Mohammad Taghi Darvishi

mohammad najafi

By means of the extended homoclinic test approach (EHTA) one can solve some nonlinear partial differential equations (NLPDEs) in their bilinear forms. When an NLPDE has no bilinear closed form we can not use this method. We modify the idea of EHTA to obtain some analytic solutions for the (3+1)-dimensional potential-Yu- Toda-Sasa-Fukuyama (YTSF) equation by obtaining a bilinear closed form for it. By comparison of this method and other analytic methods, like HAM, HTA and three-wave methods, we can see that the new idea is very easy and straightforward

Local Fractional Functional Analysis And Its Applications, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional functional analysis is a totally new area of mathematics, and a totally new mathematical world view as well. In this book, a new approach to functional analysis on fractal spaces, which can be used to interpret fractal mathematics and fractal engineering, is presented. From Cantor sets to fractional sets, real line number and the spaces of local fractional functions are derived. Local fractional calculus of real and complex variables is systematically elucidated. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach's spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental …

Local Fractional Laplace’S Transform Based Local Fractional Calculus, Yang Xiaojun

Xiao-Jun Yang

In this paper, a new modeling for the local fractional Laplace’s transform based on the local fractional calculus is proposed in fractional space. The properties of the local fractional Laplace’s transform are obtained and an illustrative example for the local fractional system is investigated in detail.

Fundamentals Of Local Fractional Iteration Of The Continuously Nondifferentiable Functions Derived Form Local Fractional Calculus, Yang Xiaojun

Xiao-Jun Yang

A new possible modeling for the local fractional iteration process is proposed in this paper. Based on the local fractional Taylor’s series, the fundamentals of local fractional iteration of the continuously non-differentiable functions are derived from local fractional calculus in fractional space.

Local Fractional Integral Transforms, Yang X

Xiao-Jun Yang

Over the past ten years, the local fractional calculus revealed to be a useful tool in various areas ranging from fundamental science to various engineering applications, because it can deal with local properties of non-differentiable functions defined on fractional sets. In fractional spaces, a basic theory of number and local fractional continuity of non-differentiable functions are presented, local fractional calculus of real and complex variables is introduced. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach’s spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental introduction to Yang-Fourier transforms, Yang-Laplace transforms, local …

Optimal Control Of Switched Autonomous Systems In Microbial Fed-Batch Cultures, Chongyang Liu, Enmin Feng

Chongyang Liu

A switched autonomous system is proposed to formulate the fed-batch culture process by taking the switching instants between the feed and batch processes as control variables. To maximize the concentration of 1,3-propanediol (1,3-PD) at the terminal time, an optimal control model subject to our proposed switched autonomous system and continuous state inequality constraints is then presented.Acomputational approach is developed to find the optimal switching instants in two aspects. On the one hand, the constraint transcription and smoothing techniques are applied to dealing with the continuous state inequality constraints; on the other hand, the first and the second derivatives of the …

An Analysis Of Presence Of Long Memory In The Indian Foreign Exchange Market, Anoop Sasikumar

Anoop Sasikumar

This paper seeks to analyze the presence of long memory in the Indian foreign exchange market using a family of tests. The study has used Nominal Effective Exchange Rate (NEER) series as the data source to check the possible presence of long memory. Three R/S statistics viz. Hurst, Mandelbrot’s and Lo’s modified R/S statistics as well as two semi-parametric tests viz. Robinson’s Gaussian semi-parametric estimate and Andrews-Guggenberger modified GPH estimator are used for the purpose of analysis. All the results conclusively prove the presence of strong version of long memory in the Indian foreign exchange market.

Influence Of Most Important Radicals On The Numericaly Simulated Belousov-Zhabotinsky Oscillatory Reaction Under Batch Conditions, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Structures Of Chaos In Open Reaction Systems, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Dynamic Behavior Of The Bray-Liebhafsky Oscillatory Reaction Controlled By Sulfuric Acid And Temperature, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

The Stability Of The Extended Model Of Hypothalamic-Pituitary-Adrenal (Hpa) Axis Examined By Stoichiometric Network Analysis, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Kinetics Of The Bray-Liebhafsky Oscillatory Reaction Perturbed By Polymer Supported Cobalt Catalyst, Zeljko D. Cupic

Zeljko D Cupic

The Bray-Liebhafsky (BL) oscillatory reaction generated in the batch reactor at 62-68 degree C was perturbed by cobalt(II)-nitrate, supported on the macroreticular copolymer of poly-4-vinylpyridine with divinylbenzene (Co-PVPDVB). The kinetic data was analyzed of the complex pathways of the hydrogen peroxide decomposition in the examined BL reaction. The obtained results confirm that the kinetics of the BL reaction in the presence Co-PVPDVB comes partially from the Co-catalyst and partially from the macroreticular copolymer support.

Predictive Modeling Of The Hypothalamic-Pituitary-Adrenal (Hpa) Axis Response To Acute And Chronic Stress, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Termodynamika Procesowa (Dla Me Aparatura Procesowa) Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.