Ordinary Differential Equations and Applied Dynamics Commons^™

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

G-Strands, Darryl Holm, Rossen Ivanov, James Percival

Articles

A G-strand is a map g(t,s): RxR --> G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. The SO(3)-strand is the G-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, SO(3)_K-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the SO(3) …

Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence, Rossen Ivanov, Emil Prodanov

Articles

Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction uid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing in ationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.

Latin Hypercube Sampling And Partial Rank Correlation Coefficient Analysis Applied To An Optimal Control Problem, Boloye Gomero

Masters Theses

Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis is an efficient tool often employed in uncertainty analysis to explore the entire parameter space of a model. Despite the usefulness of LHS/PRCC sensitivity analysis in studying the sensitivity of a model to the parameter values used in the model, no study has been done that fully integrates Latin Hypercube sampling with optimal control analysis.

In this thesis, we couple the optimal control numerical procedure to the LHS/PRCC procedure and perform a simultaneous examination of the effects of all the LHS parameter on the objective functional value. To test the effectiveness …

Synthesis Of Static And Dynamic Multiple-Input Translinear Element Networks, Bradley Minch

Bradley Minch

In this paper, we discuss the process of synthesizing static and dynamic multiple-input translinear element (MITE) networks systematically from high-level descriptions given in the time domain, in terms of static polynomial constraints and algebraic differential equations. We provide several examples, illustrating the process for both static and dynamic system constraints. Although our examples will all involve MITE networks, the early steps of the synthesis process are equally applicable to the synthesis of static and dynamic translinear-loop circuits.

Synthesis Of Dynamic Multiple-Input Translinear Element Networks, Bradley Minch

Bradley Minch

In this paper, the author discusses an approach to the synthesis of dynamic translinear circuits built from multiple-input translation elements (MITEs). In this method, we realize separately the basic static nonlinearities and dynamic signal-processing functions that when cascaded together, form the system that one wishes to construct. The circuit is then simplified systematically through local transformations that do not alter the behavior of the system. The author illustrates the method by synthesizing a simple nonlinear dynamical system, an RMS-DC converter.

Variational Iteration Method For Q-Difference Equations Of Second Order, Guo-Cheng Wu

G.C. Wu

Recently, Liu extended He's variational iteration method to strongly nonlinear q-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.

Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.

An Approximate Solution Of The Mathieu Fractional Equation By Using The Generalized Differential Transform Method (Gdtm), H. S. Najafi, S. R. Mirshafaei, E. A. Toroqi

Applications and Applied Mathematics: An International Journal (AAM)

The generalized differential transform method (GDTM) is a powerful tool for solving fractional equations. In this paper we solve the Mathieu fractional equation by this method. The approximate solutions obtained are compared with the exact solution. We also show that if both differential orders decrease, we can still have an approximate solution in the different interval of p.

Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.

Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …

Oscillation Of Neutral Partial Dynamic Equations, Deniz Uçar, Yaşar Bolat

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the oscillation of solutions of a certain more general neutral type dynamic equation. We establish within the necessary and sufficient conditions for the oscillation of its solutions.

Design Of Orbital Maneuvers With Aeroassisted Cubesatellites, Stephanie Clark

Graduate Theses and Dissertations

Recent advances within the field of cube satellite technology has allowed for the possible development of a maneuver that utilizes a satellite's Low Earth Orbit (LEO) and increased atmospheric density to effectively use lift and drag to implement a noncoplanar orbital maneuver. Noncoplanar maneuvers typically require large quantities of propellant due to the large delta-v that is required. However, similar maneuvers using perturbing forces require little or no propellant to create the delta-v required. This research reported here studied on the effects of lift on orbital changes, those of noncoplanar types in particular, for small satellites without orbital maneuvering thrusters. …

A Mathematical Model For Dengue Fever In A Virgin Environment, Jason K. Bowman

Senior Honors Projects

Dengue is a mosquito-borne viral infection found in tropical and subtropical regions around the world. The disease was named in 1779 and the first recorded epidemic of it occurred simultaneously on three continents within the following decade. Dengue is characterized by flu-like symptoms and, while its symptoms are generally reported as quite unpleasant, is rarely fatal. However, in some cases patients can contract a more serious form of the disease, known as Dengue Hemorrhagic Fever, which is far more dangerous. The World Health Organization estimates that today over 2.5 billion people are at risk for Dengue (over 40% of the …

Periodic Solutions And Positive Solutions Of First And Second Order Logistic Type Odes With Harvesting, Cody Alan Palmer

UNLV Theses, Dissertations, Professional Papers, and Capstones

It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:

u' = f (u) - ε h (t).

Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....

In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.

Additionally, we look at analagous steady states for the reaction-diusion …

The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

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, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.

Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.

R₀ Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, Jon T. Jacobsen, M. A. Lewis

All HMC Faculty Publications and Research

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R₀ for advection-diffusion-reaction equations and on related measures. We apply the measures to population persistence in rivers under various flow regimes. This work lays …

The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun

Xiao-Jun Yang

In the present paper, using the equation transform in fractal space, we point out the zero-mass renormalization group equations. Under limit cycles in the non-smooth initial value, we devote to the analytical technique of the local fractional Fourier series for treating zero-mass renormalization group equations, and investigate local fractional Fourier series solutions.

New Model For Preconditioning Techniques With Application To The Boundary Value Problems, Sa Edalatpanah, Hs Najafi

SA Edalatpanah

No abstract provided.