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Ordinary Differential Equations and Applied Dynamics Commons™

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2011

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Articles 1 - 12 of 12

Full-Text Articles in Ordinary Differential Equations and Applied Dynamics

Modelling Β2ar Regulation, Sharat J. Vayttaden Dec 2011

Modelling Β2ar Regulation, Sharat J. Vayttaden

Dissertations and Theses (Open Access)

The β2 adrenergic receptor (β2AR) regulates smooth muscle relaxation in the vasculature and airways. Long- and Short-acting β-agonists (LABAs/SABAs) are widely used in treatment of chronic obstructive pulmonary disorder (COPD) and asthma. Despite their widespread clinical use we do not understand well the dominant β2AR regulatory pathways that are stimulated during therapy and bring about tachyphylaxis, which is the loss of drug effects. Thus, an understanding of how the β2AR responds to various β-agonists is crucial to their rational use. Towards that end we have developed deterministic models that explore the mechanism of drug- induced β2AR regulation. These mathematical models …

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A New Hermite Collocation Method For Solving Differential Difference Equations, Mustafa Gülsu, Hatice Yalman, Mehmet Sezer Jun 2011

A New Hermite Collocation Method For Solving Differential Difference Equations, Mustafa Gülsu, Hatice Yalman, Mehmet Sezer

Applications and Applied Mathematics: An International Journal (AAM)

The purpose of this study is to give a Hermite polynomial approximation for the solution of mth order linear differential-difference equations with variable coefficients under mixed conditions. For this purpose, a new Hermite collocation method is introduced. This method is based on the truncated Hermite expansion of the function in the differential-difference equations. Hence, the resulting matrix equation can be solved and the unknown Hermite coefficients can be found approximately. In addition, examples that illustrate the pertinent features of the method are presented and the results of the study discussed

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Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid Jun 2011

Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid

Applications and Applied Mathematics: An International Journal (AAM)

A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is …

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Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed Jun 2011

Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed

Applications and Applied Mathematics: An International Journal (AAM)

The nonlinear propagation of small but finite amplitude dust-acoustic solitary waves (DAWs) in magnetized collision less dusty plasma has been investigated. The fluid model is a four component magnetized dusty plasma, consisting of positive and negative dust species, isothermal electrons and ions in the presence of an external magnetic field. A reductive perturbation method was employed to obtain the Zakharov Kuznetsov (ZK) equation for the first-order potential. The effects of the presence of positively charged dust fluid, the external magnetic field, and the obliqueness are obtained. The results of the present investigation may be applicable to some plasma environments, such …

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Positive Solutions For Nth Order Differential Equations Under Some Conditions, S. N. Odda Jun 2011

Positive Solutions For Nth Order Differential Equations Under Some Conditions, S. N. Odda

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents an existence and nonexistence of positive solutions for the nonlinear boundary value problems. We prove that the nth order nonlinear differential equation has at least one positive solution by using appropriate fixed point theorems.

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Exact Soliton Solutions For Second-Order Benjamin-Ono Equation, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz Jun 2011

Exact Soliton Solutions For Second-Order Benjamin-Ono Equation, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

The homogeneous balance method is proposed for seeking the travelling wave solutions of the second-order Benjamin-Ono equation. Many exact traveling wave solutions of second-order Benjamin-Ono equation, which contain soliton like and periodic-like solutions are successfully obtained. This method is straightforward and concise, and it may also be applied to other nonlinear evolution equations.

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Inverse Heat Conduction Problem In A Semi-Infinite Cylinder And Its Thermal Stresses By Quasi-Static Approach, K. C. Deshmukh, S. D. Warbhe, G. D. Kedar, V. S. Kulkarni Jun 2011

Inverse Heat Conduction Problem In A Semi-Infinite Cylinder And Its Thermal Stresses By Quasi-Static Approach, K. C. Deshmukh, S. D. Warbhe, G. D. Kedar, V. S. Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the determination of unknown temperature and thermal stresses on the curved surface of a semi-infinite circular cylinder defined as 0 ≤ r ≤ a , 0 ≤ z ≤ ∞. The circular cylinder is subjected to an arbitrary known temperature under unsteady state condition. Initially, the cylinder is at zero temperature and temperature at the lower surface is held fixed at zero. The governing heat conduction equation has been solved by using the integral transform method. The results are obtained in series form in terms of Bessel’s functions. A mathematical model has been constructed for …

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Algorithms To Solve Singularly Perturbed Volterra Integral Equations, Marwan T. Alquran, Bilal Khair Jun 2011

Algorithms To Solve Singularly Perturbed Volterra Integral Equations, Marwan T. Alquran, Bilal Khair

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the Differential Transform Method (DTM) and Variational Iterative Method (VIM) to develop algorithms for solving singularly perturbed volterra integral equations (SPVIEs). The study outlines the significant features of the two methods. A comparison between the two methods for the solution of SPVIs is given for three examples. The results show that both methods are very efficient, convenient and applicable to a large class of problems.

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Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan May 2011

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

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Mathematical Analysis And Applications Of Logistic Differential Equation, Eva Arnold, Monika Neda Apr 2011

Mathematical Analysis And Applications Of Logistic Differential Equation, Eva Arnold, Monika Neda

Festival of Communities: UG Symposium (Posters)

Logistic differential equation has a way to measure the proportionality of various resources with respect to time. This equation has been used in many research areas, such as, biology, medicine, psychology, economics, etc. A mathematical description, analysis and solution of the logistic type differential equation is studied. Besides the mathematical part, the poster will contain biological examples, graphs of the direction fields for different parameter settings and logistic plots for specific species population. The logistic growth function will also be applied to learning curves in area of psychology, as a rate at which performance improves.

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Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng Jan 2011

Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng

Department of Mathematics: Faculty Publications

For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum’s constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.

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Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng Jan 2011

Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng

Department of Mathematics: Faculty Publications

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

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