Open Access. Powered by Scholars. Published by Universities.®

Non-linear Dynamics Commons™

Open Access. Powered by Scholars. Published by Universities.®

PDF

2009

Discipline
Institution
Keyword
Publication
Publication Type

Articles 1 - 30 of 33

Full-Text Articles in Non-linear Dynamics

A Variation Of The Carleman Embedding Method For Second Order Systems., Charles Nunya Dzacka Dec 2009

A Variation Of The Carleman Embedding Method For Second Order Systems., Charles Nunya Dzacka

Electronic Theses and Dissertations

The Carleman Embedding is a method that allows us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for higher order nonlinear ordinary differential equations, it is difficult to use the Carleman Embedding method. This project will examine the Carleman Embedding and a variation of the method which is very convenient in applying to second order systems of nonlinear equations.

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner Dec 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner Dec 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner Dec 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner Dec 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mikhail Khenner

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Go to article

Modeling In Microbial Batch Culture And Its Parameter Identification, Zhaohua Gong, Chongyang Liu, Enmin Feng Nov 2009

Modeling In Microbial Batch Culture And Its Parameter Identification, Zhaohua Gong, Chongyang Liu, Enmin Feng

Chongyang Liu

In this paper, the nonlinear dynamical system of batch fermentation is investigated in the bioconversion of glycerol to 1,3-propanediol(1,3-PD) by Klebsiella pneumoniae. Taking account of the kinetic behavior and experimental results in the batch cultures, we propose a two-stage dynamical system to formulate the fermentation process. Then some properties of the proposed system are proved. In view of the big errors between observations and numerical simulation results, we subsequently establish a parameter identification model to identify parameters in the system. The identifiability of the model is also discussed. Finally, in order to find the optimal parameters of the identification model, …

Go to article

Electron Self-Injection And Trapping Into An Evolving Plasma Bubble, Serguei Y. Kalmykov, Sunghwan A. Yi, Vladimir N. Khudik, Gennady Shvets Sep 2009

Electron Self-Injection And Trapping Into An Evolving Plasma Bubble, Serguei Y. Kalmykov, Sunghwan A. Yi, Vladimir N. Khudik, Gennady Shvets

Serge Youri Kalmykov

The blowout (or bubble) regime of laser wakefield acceleration is promising for generating monochromatic high-energy electron beams out of low-density plasmas. It is shown analytically and by particle-in-cell simulations that self-injection of the background plasma electrons into the quasistatic plasma bubble can be caused by slow temporal expansion of the bubble. Sufficient criteria for the electron trapping and bubble’s expansion rate are derived using a semianalytic nonstationary Hamiltonian theory. It is further shown that the combination of bubble’s expansion and contraction results in monoenergetic electron beams.

Go to article

Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne Aug 2009

Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne

Electronic Theses and Dissertations

The two variable Fitzhugh Nagumo model behaves qualitatively like the four variable Hodgkin-Huxley space clamped system and is more mathematically tractable than the Hodgkin Huxley model, thus allowing the action potential and other properties of the Hodgkin Huxley system to be more readily be visualized. In this thesis, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol's model of nonlinear oscillation, which are both finite nonlinear systems of differential equations. The Carleman technique can thus be used to obtain approximate solutions of the Fitzhugh Nagumo model and …

Go to article

Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun Jun 2009

Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun

Xiao-Jun Yang

Since Mandelbrot proposed the concept of fractal in 1970s’, fractal has been applied in various areas such as science, economics, cultures and arts because of the universality of fractal phenomena. It provides a new analytical tool to reveal the complexity of the real world. Nowadays the calculus in a fractal space becomes a hot topic in the world. Based on the established definitions of fractal derivative and fractal integral, the fundamental theorems of fractal derivatives and fractal integrals are investigated in detail. The fractal double integral and fractal triple integral are discussed and the variational principle in fractal space has …

Go to article

All-Optical Control Of Nonlinear Focusing Of Laser Beams In Plasma Beat Wave Accelerator, Serguei Y. Kalmykov, Sunghwan A. Yi, Gennady Shvets Jan 2009

All-Optical Control Of Nonlinear Focusing Of Laser Beams In Plasma Beat Wave Accelerator, Serguei Y. Kalmykov, Sunghwan A. Yi, Gennady Shvets

Serge Youri Kalmykov

Nonlinear focusing of a bi-color laser in plasma can be controlled by varying the difference frequency \Omega. The driven electron density perturbation forms a co-moving periodic focusing (de-focusing) channel if \Omega is below (above) the electron Langmuir frequency \omega_p. Hence, the beam focusing is enhanced for \Omega < \omega_p and is suppressed otherwise. In particular, a catastrophic relativistic self-focusing of a high-power laser beam can be prevented all-optically by a second, much weaker, co-propagating beam shifted in frequency by \Omega > \omega_p. A bi-envelope equation describing the early stage of the mutual de-focusing is derived and analyzed. Later stages, characterized by a well-developed electromagnetic cascade, are investigated numerically. Stable propagation of the over-critical laser pulse over several Rayleigh lengths is predicted. The non-resonant plasma beat wave (\Omega \not= \omega_p) can accelerate pre-injected electrons above …

Go to article

Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov Jan 2009

Poisson Structures Of Equations Associated With Groups Of Diffeomorphisms, Rossen Ivanov

Conference papers

A class of equations describing the geodesic flow for a right-invariant metric on the group of diffeomorphisms of Rn is reviewed from the viewpoint of their Lie-Poisson structures. A subclass of these equations is analogous to the Euler equations in hydrodynamics (for n = 3), preserving the volume element of the domain of fluid flow. An example in n = 1 dimension is the Camassa-Holm equation, which is a geodesic flow equation on the group of diffeomorphisms, preserving the H1 metric.

Go to article

Two Component Integrable Systems Modelling Shallow Water Waves, Rossen Ivanov Jan 2009

Two Component Integrable Systems Modelling Shallow Water Waves, Rossen Ivanov

Conference papers

Our aim is to describe the derivation of shallow water model equations for the constant vorticity case and to demonstrate how these equations can be related to two integrable systems: a two component integrable generalization of the Camassa-Holm equation and the Kaup - Boussinesq system.

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner Jan 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner Jan 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Go to article

The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun Jan 2009

The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun

Xiao-Jun Yang

Based on the theory of Jumarie’s fractional calculus, local fractional derivative is modified in detail and its fundamentals of local fractional derivative are proposed in this paper. The uniqueness of local fractional derivative is obtained and the Rolle’s theorem, the mean value theorem, the Cauchy’s generalized mean value theorem and the L’Hospital’s rules are proved.

Go to article

Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun Jan 2009

Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun

Xiao-Jun Yang

A local fractional Newton’s method, which is derived from the modified local fractional calculus , is proposed in the present paper. Its iterative function is obtained and the convergence of the iterative function is discussed. The comparison between the classical Newton iteration and the local fractional Newton iteration has been carried out. It is shown that the iterative value of the local fractional Newton method better approximates the real-value than that of the classical one.

Go to article

Computational Method For Inferring Objective Function Of Glycerol Metabolism In Klebsiella Pneumoniae, Zhaohua Gong, Chongyang Liu, Enmin Feng, Qingrui Zhang Jan 2009

Computational Method For Inferring Objective Function Of Glycerol Metabolism In Klebsiella Pneumoniae, Zhaohua Gong, Chongyang Liu, Enmin Feng, Qingrui Zhang

Chongyang Liu

Flux balance analysis (FBA) is an effective tool in the analysis of metabolic network. It can predict the flux distribution of engineered cells, whereas the accurate prediction depends on the reasonable objective function. In this work, we propose two nonlinear bilevel programming models on anaerobic glycerol metabolism in Klebsiella pneumoniae (K. pneumoniae) for 1,3-propanediol (1,3-PD) production. One intends to infer the metabolic objective function, and the other is to analyze the robustness of the objective function. In view of the models’ characteristic an improved genetic algorithm is constructed to solve them, where some techniques are adopted to guarantee all chromosomes …

Go to article

Modelling And Optimal Control For Nonlinear Multistage Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2009

Modelling And Optimal Control For Nonlinear Multistage Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In this paper, we propose a new controlled multistage system to formulate the fed-batch culture process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by regarding the feeding rate of glycerol as a control function. Compared with the previous systems, this system doesn’t take the feeding process as an impulsive form, but a time-continuous process, which is much closer to the actual culture process. Some properties of the above dynamical system are then proved. To maximize the concentration of 1,3-PD at the terminal time, we develop an optimal control model subject to our proposed controlled multistage system and continuous state inequality constraints. …

Go to article

Optimal Control And Properties Of Nonlinear Multistage Dynamical System For Planning Horizontal Well Paths, Zhaohua Gong, Chongyang Liu, Enmin Feng Jan 2009

Optimal Control And Properties Of Nonlinear Multistage Dynamical System For Planning Horizontal Well Paths, Zhaohua Gong, Chongyang Liu, Enmin Feng

Chongyang Liu

The goal of planning a horizontal well path is to obtain a trajectory that arrives at a given target subject to various constraints. In this paper, the optimal control problem subject to a nonlinear multistage dynamical system (NMDS) for horizontal well paths is investigated. Some properties of the multistage system are proved. In order to derive the optimality conditions, we transform the optimal control problem into one with control constraints and inequality-constrained trajectories by defining some functions. The properties of these functions are then discussed and optimality conditions for optimal control problem are also given. Finally, an improved simplex method …

Go to article

Optimal Control For Nonlinear Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu Jan 2009

Optimal Control For Nonlinear Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu

Chongyang Liu

In fed-batch culture of glycerol bio-dissimilation to 1, 3-propanediol (1, 3-PD), the aim of adding glycerol is to obtain as much 1, 3-PD as possible. So a proper feeding rate is required during the process. Taking the concentration of 1, 3-PD at the terminal time as the performance index and the feeding rate of glycerol as the control function, we propose an optimal control model subject to a nonlinear dynamical system and constraints of continuous state and non-stationary control. A computational approach is constructed to seek the solution of the above model in two aspects. On the one hand we …

Go to article

Temperature Influence On The Malonic Acid Decomposition In The Belousov-Zhabotinsky Reaction, Zeljko D. Cupic Jan 2009

Temperature Influence On The Malonic Acid Decomposition In The Belousov-Zhabotinsky Reaction, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Go to article

Activity Of Polymer Supported Cobalt Catalyst In The Bray-Liebhafsky Oscillator, Zeljko D. Cupic Jan 2009

Activity Of Polymer Supported Cobalt Catalyst In The Bray-Liebhafsky Oscillator, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Go to article

Large Deviation Spectra Of Chaotic Time Series From Bray–Liebhafsky Reaction, Zeljko D. Cupic Jan 2009

Large Deviation Spectra Of Chaotic Time Series From Bray–Liebhafsky Reaction, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Go to article

Predictive Modeling Of The Hypothalamic-Pituitary-Adrenal (Hpa) Function. Dynamic Systems Theory Approach By Stoichiometric Network Analysis And Quenching Small Amplitude Oscillations, Zeljko D. Cupic Jan 2009

Predictive Modeling Of The Hypothalamic-Pituitary-Adrenal (Hpa) Function. Dynamic Systems Theory Approach By Stoichiometric Network Analysis And Quenching Small Amplitude Oscillations, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Go to article

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner Jan 2009

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mikhail Khenner

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Go to article

Conceptual Circuit Models Of Neurons, Bo Deng Jan 2009

Conceptual Circuit Models Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

A systematic circuit approach tomodel neurons with ion pump is presented here by which the voltage-gated current channels are modeled as conductors, the diffusion-induced current channels are modeled as negative resistors, and the one-way ion pumps are modeled as one-way inductors. The newly synthesized models are different from the type of models based on Hodgkin-Huxley (HH) approach which aggregates the electro, the diffusive, and the pump channels of each ion into one conductance channel. We show that our new models not only recover many known properties of the HH type models but also exhibit some new that cannot be extracted …

Go to article

Equations Of The Camassa-Holm Hierarchy, Rossen Ivanov Jan 2009

Equations Of The Camassa-Holm Hierarchy, Rossen Ivanov

Articles

The squared eigenfunctions of the spectral problem associated with the CamassaHolm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized Fourier transform (GFT). All the fundamental properties of the CH equation, such as the integrals of motion, the description of the equations of the whole hierarchy, and their Hamiltonian structures, can be naturally expressed using the completeness relation and the recursion operator, whose eigenfunctions are the squared solutions. Using the GFT, we explicitly describe some members of the CH hierarchy, including integrable deformations for the CH …

Go to article

Generalised Fourier Transform And Perturbations To Soliton Equations, Georgi Grahovski, Rossen Ivanov Jan 2009

Generalised Fourier Transform And Perturbations To Soliton Equations, Georgi Grahovski, Rossen Ivanov

Articles

A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton …

Go to article

Nonlinear Dynamics Of Infant Sitting Postural Control, Joan E. Deffeyes Jan 2009

Nonlinear Dynamics Of Infant Sitting Postural Control, Joan E. Deffeyes

Department of Psychology: Dissertations, Theses, and Student Research

Sitting is one of the first developmental milestones that an infant achieves. Thus measurements of sitting posture present an opportunity to assess sensorimotor development at a young age, in order to identify infants who might benefit from therapeutic intervention, and to monitor the efficacy of the intervention. Sitting postural sway data was collected using a force plate from infants with typical development, and from infants with delayed development, where the delay in development was due to cerebral palsy in most of the infants in the study. The center of pressure time series from the infant sitting was subjected to a …

Go to article

Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov Jan 2009

Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov

Articles

In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of mass conservation, the simplest bottom and surface conditions and the constant vorticity condition. The approximate model equations are generated by introduction of suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order. The so obtained equations can be related to three different integrable systems: a two component generalization of the Camassa-Holm equation, the Zakharov-Ito system and the Kaup-Boussinesq system. The …

Go to article

Next Last