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Non-linear Dynamics

2012

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Articles 31 - 60 of 67

Full-Text Articles in Physical Sciences and Mathematics

A Short Introduction To Yang-Laplace Transforms In Fractal Space, Yang Xiaojun Jan 2012

A Short Introduction To Yang-Laplace Transforms In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The Yang-Laplace transforms [W. P. Zhong, F. Gao, In: Proc. of the 2011 3rd International Conference on Computer Technology and Development, 209-213, ASME, 2011] in fractal space is a generalization of Laplace transforms derived from the local fractional calculus. This letter presents a short introduction to Yang-Laplace transforms in fractal space. At first, we present the theory of local fractional derivative and integral of non-differential functions defined on cantor set. Then the properties and theorems for Yang-Laplace transforms are tabled, and both the initial value theorem and the final value theorem are investigated. Finally, some applications to the wave equation …

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Local Fractional Integral Equations And Their Applications, Yang Xiaojun Jan 2012

Local Fractional Integral Equations And Their Applications, Yang Xiaojun

Xiao-Jun Yang

This letter outlines the local fractional integral equations carried out by the local fractional calculus (LFC). We first introduce the local fractional calculus and its fractal geometrical explanation. We then investigate the local fractional Volterra/ Fredholm integral equations, local fractional nonlinear integral equations, local fractional singular integral equations and local fractional integro-differential equations. Finally, their applications of some integral equations to handle some differential equations with local fractional derivative and local fractional integral transforms in fractal space are discussed in detail.

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Local Fractional Partial Differential Equations With Fractal Boundary Problems, Yang Xiaojun Jan 2012

Local Fractional Partial Differential Equations With Fractal Boundary Problems, Yang Xiaojun

Xiao-Jun Yang

This letter points out the new alternative approaches to processing local fractional partial differential equations with fractal boundary conditions. Applications of the local fractional Fourier series, the Yang-Fourier transforms and the Yang-Laplace transforms to solve of local fractional partial differential equations with fractal boundary conditions are investigated in detail.

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Local Fractional Kernel Transform In Fractal Space And Its Applications, Yang Xiaojun Jan 2012

Local Fractional Kernel Transform In Fractal Space And Its Applications, Yang Xiaojun

Xiao-Jun Yang

In the present paper, we point out the local fractional kernel transform based on local fractional calculus (FLC), and its applications to the Yang-Fourier transform, the Yang-Laplace transform, the local fractional Z transform, the local fractional Stieltjes transform, the local fractional volterra/ Fredholm integral equations, the local fractional volterra/ Fredholm integro-differential equations, the local fractional variational iteration algorithms, the local fractional variational iteration algorithms with an auxiliary fractal parameter, the modified local fractional variational iteration algorithms, and the modified local fractional variational iteration algorithms with an auxiliary fractal parameter.

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A New Viewpoint To Fourier Analysis In Fractal Space, Yang Xiaojun Jan 2012

A New Viewpoint To Fourier Analysis In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

Fractional analysis is an important method for mathematics and engineering [1-21], and fractional differentiation inequalities are great mathematical topic for research [22-24]. In the present paper we point out a new viewpoint to Fourier analysis in fractal space based on the local fractional calculus [25-58], and propose the local fractional Fourier analysis. Based on the generalized Hilbert space [48, 49], we obtain the generalization of local fractional Fourier series via the local fractional calculus. An example is given to elucidate the signal process and reliable result.

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Generalized Sampling Theorem For Fractal Signals, Yang Xiaojun Jan 2012

Generalized Sampling Theorem For Fractal Signals, Yang Xiaojun

Xiao-Jun Yang

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The local fractional Fourier series is a generalization of Fourier series in fractal space, and the Yang-Fourier transform is a generalization of Fourier transform in fractal space. This letter points out the generalized sampling theorem for fractal signals (local fractional continuous signals) by using the local fractional Fourier series and Yang-Fourier transform techniques based on the local fractional calculus. This result is applied to process the local fractional continuous signals.

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Picard’S Approximation Method For Solving A Class Of Local Fractional Volterra Integral Equations, Yang Xiaojun Jan 2012

Picard’S Approximation Method For Solving A Class Of Local Fractional Volterra Integral Equations, Yang Xiaojun

Xiao-Jun Yang

In this letter, we fist consider the Picard’s successive approximation method for solving a class of the Volterra integral equations in local fractional integral operator sense. Special attention is devoted to the Picard’s successive approximate methodology for handling local fractional Volterra integral equations. An illustrative paradigm is shown the accuracy and reliable results.

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Local Fractional Calculus And Its Applications, Yang Xiaojun Jan 2012

Local Fractional Calculus And Its Applications, Yang Xiaojun

Xiao-Jun Yang

In this paper we point out the interpretations of local fractional derivative and local fractional integration from the fractal geometry point of view. From Cantor set to fractional set, local fractional derivative and local fractional integration are investigated in detail, and some applications are given to elaborate the local fractional Fourier series, the Yang-Fourier transform, the Yang-Laplace transform, the local fractional short time transform, the local fractional wavelet transform in fractal space.

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Fast Yang-Fourier Transforms In Fractal Space, Yang Xiaojun Jan 2012

Fast Yang-Fourier Transforms In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform based on the Yang-Fourier transform in fractal space. In the present letter we point out a new fractal model for the algorithm for fast Yang-Fourier transforms of discrete Yang-Fourier transforms. It is shown that the classical fast Fourier transforms is a special example in fractal dimension a=1.

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Local Fractional Fourier Analysis, Yang Xiaojun Jan 2012

Local Fractional Fourier Analysis, Yang Xiaojun

Xiao-Jun Yang

Local fractional calculus (LFC) deals with everywhere continuous but nowhere differentiable functions in fractal space. In this letter we point out local fractional Fourier analysis in generalized Hilbert space. We first investigate the local fractional calculus and complex number of fractional-order based on the complex Mittag-Leffler function in fractal space. Then we study the local fractional Fourier analysis from the theory of local fractional functional analysis point of view. We finally propose the fractional-order trigonometric and complex Mittag-Leffler functions expressions of local fractional Fourier series

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A Generalized Model For Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun Jan 2012

A Generalized Model For Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus is a generalization of Fourier transform in fractal space. In this paper, local fractional continuous non-differentiable functions in fractal space are studied, and the generalized model for the Yang-Fourier transforms derived from the local fractional calculus are introduced. A generalized model for the Yang-Fourier transforms in fractal space and some results are proposed in detail.

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Generalized Local Taylor's Formula With Local Fractional Derivative, Yang Xiao-Jun Jan 2012

Generalized Local Taylor's Formula With Local Fractional Derivative, Yang Xiao-Jun

Xiao-Jun Yang

In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional integrals and derivatives has been dealt with fractal and continuously non-differentiable functions, and has been successfully applied in engineering problems. It points out the proof of the generalized local fractional Taylor formula, and is devoted to the applications of the generalized local fractional Taylor formula to the generalized local fractional series and the approximation of functions. Finally, it is shown that local fractional Taylor …

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Traveling Wave Solutions For The (3+1)-Dimensional Breaking Soliton Equation By (G'/G)-Expansion Method And Modified F-Expansion Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi Jan 2012

Traveling Wave Solutions For The (3+1)-Dimensional Breaking Soliton Equation By (G'/G)-Expansion Method And Modified F-Expansion Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi

mohammad najafi

In this paper, using (G'/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

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Some Complexiton Type Solutions Of The (3+1)-Dimensional Jimbo-Miwa Equation, Mohammad Najafi, Mohammad Taghi Darvishi Jan 2012

Some Complexiton Type Solutions Of The (3+1)-Dimensional Jimbo-Miwa Equation, Mohammad Najafi, Mohammad Taghi Darvishi

mohammad najafi

By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

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Optimal Switching Control Of A Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2012

Optimal Switching Control Of A Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

Considering the hybrid nature in fed-batch culture of glycerol biconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, we propose a state-based switching dynamical system to describe the fermentation process. To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to our proposed switching system and constraints of continuous state inequality and control function is presented. Because the number of the switchings is not known a priori, we reformulate the above optimal control problem as a two-level optimization problem. An optimization algorithm is developed to seek the optimal solution on the basis of a heuristic approach …

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Nonlinear Dynamical Systems Of Fed-Batch Fermentation And Their Optimal Control, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2012

Nonlinear Dynamical Systems Of Fed-Batch Fermentation And Their Optimal Control, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In this article, we propose a controlled nonlinear dynamical system with variable switching instants, in which the feeding rate of glycerol is regarded as the control function and the moments between the batch and feeding processes as switching instants, to formulate the fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD). Some important properties of the proposed system and its solution are then discussed. Taking the concentration of 1,3-PD at the terminal time as the cost functional, we establish an optimal control model involving the controlled nonlinear dynamical system and subject to continuous state inequality constraints. The existence of the optimal …

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Modeling And Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects In Glycerol Continuous Fermentation, Zhaohua Gong, Chongyang Liu, Yongsheng Yu Jan 2012

Modeling And Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects In Glycerol Continuous Fermentation, Zhaohua Gong, Chongyang Liu, Yongsheng Yu

Chongyang Liu

Mathematical modeling and parameter estimation are critical steps in the optimization of biotechnological processes. In the 1,3-propanediol (1,3-PD )production by glycerol fermentation process under anaerobic conditions, 3-hydroxypropionaldehyde (3-HPA) accumulation would arouse an irreversible cessation of the fermentation process. Considering 3-HPA inhibitions to cells growth and to activities of enzymes, we propose a novel mathematical model to describe glycerol continuous cultures. Some properties of the above model are discussed. On the basis of the concentrations of extracellular substances, a parameter identification model is established to determine the kinetic parameters in the presented system. Through the penalty function technique combined with an …

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Optimal Control Of A Fed-Batch Fermentation Involving Multiple Feeds, Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen Jan 2012

Optimal Control Of A Fed-Batch Fermentation Involving Multiple Feeds, Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen

Chongyang Liu

A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3-PD concentration at the terminal time.

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Kinetic Analytical Method For Determination Of Uric Acid In Human Urine Using Analyte Pulse Perturbation Technique, Zeljko D. Cupic Jan 2012

Kinetic Analytical Method For Determination Of Uric Acid In Human Urine Using Analyte Pulse Perturbation Technique, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

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Influence Of Non-Linearity To The Optimal Experimental Design Demonstrated By A Biological System, René Schenkendorf, Andreas Kremling, Michael Mangold Jan 2012

Influence Of Non-Linearity To The Optimal Experimental Design Demonstrated By A Biological System, René Schenkendorf, Andreas Kremling, Michael Mangold

René Schenkendorf

A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is …

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Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski Jan 2012

Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

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Materiały Odstresowujące, Wojciech M. Budzianowski Jan 2012

Materiały Odstresowujące, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

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Oxidative Carbonylation Of 2-Propyn-1-Ol And 2-Methyl-3-Butyn-2-Ol In An Oscillatory Mode, Sergey N. Gorodsky Jan 2012

Oxidative Carbonylation Of 2-Propyn-1-Ol And 2-Methyl-3-Butyn-2-Ol In An Oscillatory Mode, Sergey N. Gorodsky

Sergey N. Gorodsky

No abstract provided.

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Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman Jan 2012

Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman

Mikhail Khenner

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.

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Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz Jan 2012

Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz

Chad M. Topaz

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem’s block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer …

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The Generalised Zakharov-Shabat System And The Gauge Group Action, Georgi Grahovski Jan 2012

The Generalised Zakharov-Shabat System And The Gauge Group Action, Georgi Grahovski

Articles

The generalized Zakharov–Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the example of the multi-component nonlinear Schr¨odinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type …

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Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, Stergios Mentesidis Jan 2012

Welfare Versus Stability In "Stabilizing An Unstable Economy": A Minskyan Growth Model, Stergios Mentesidis

Senior Projects Spring 2012

The paper focuses on Minsky's financial fragility hypothesis incorporated in a growth model and investigates whether an inherently unstable economy can be stabilized by a big and proactive government. Using dynamical systems theory and expanding a supply-driven growth model developed by Lin, Day and Tse (1992), the paper explores how different government spending programs and financing paths can affect the growth, as well as the stability of a capitalist economy. The results and implications of the new frameworks are analyzed, using analytical and numerical methods of bifurcation, to examine the dependence of optimal government intervention on the economic environment. The …

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Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman Jan 2012

Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman

Mathematics Faculty Publications

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.

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Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman Jan 2012

Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A and are not ordered. If the systems fail the criterion, it does not follow they are ordered. Thus the theory only serves to avoid some a priori useless comparisons: when neither A nor can be said to be better than the other. The power of the theory lies in its wide potential applicability: the assumptions involve very weak estimates on the asymptotic behavior (as t→0 and as t→∞) of the constituent survival probabilities. We include examples.

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Singular Solutions Of Coss-Coupled Epdiff Equations: Waltzing Peakons And Compacton Pairs, Colin Cotter, Darryl Holm, Rossen Ivanov, James Percival Jan 2012

Singular Solutions Of Coss-Coupled Epdiff Equations: Waltzing Peakons And Compacton Pairs, Colin Cotter, Darryl Holm, Rossen Ivanov, James Percival

Conference papers

We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rn). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.

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