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

Applied Mathematics Commons™

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

Dynamic Systems

Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 451 - 480 of 508

Full-Text Articles in Applied Mathematics

Effect Of Network Structure On The Stability Margin Of Large Vehicle With Distributed Control, He Hao, Prabir Barooah, J. J. P. Veerman Dec 2010

Effect Of Network Structure On The Stability Margin Of Large Vehicle With Distributed Control, He Hao, Prabir Barooah, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We study the problem of distributed control of a large network of double-integrator agents to maintain a rigid formation. A few lead vehicles are given information on the desired trajectory of the formation; while every other vehicle uses linear controller which only depends on relative position and velocity from a few other vehicles, which are called its neighbors. A predetermined information graph defines the neighbor relationships. We limit our attention to information graphs that are D-dimensional lattices, and examine the stability margin of the closed loop, which is measured by the real part of the least stable eigenvalue of …

Go to article

Bound For The Complex Growth Rate In Thermosolutal Convection Coupled With Cross-Diffusions, Hari Mohan Sharma Dec 2010

Bound For The Complex Growth Rate In Thermosolutal Convection Coupled With Cross-Diffusions, Hari Mohan Sharma

Applications and Applied Mathematics: An International Journal (AAM)

Thermosolutal convection problem of the Veronis’ type coupled with cross–diffusion is considered in the present paper. A semi -circle theorem that prescribes upper limit for the complex growth rate of oscillatory motions of neutral or growing amplitude in such a manner that it naturally culminates in sufficient conditions precluding the non- existence of such motions is derived. Further, results for thermosolutal convection problems with or without the individual consideration of Dufour and Soret effects follow as a consequence.

Go to article

Engineering Flow States With Localized Forcing In A Thin, Marangoni-Driven Inclined Film, Rachel Levy, Stephen Rosenthal '09, Jeffrey Wong '11 Nov 2010

Engineering Flow States With Localized Forcing In A Thin, Marangoni-Driven Inclined Film, Rachel Levy, Stephen Rosenthal '09, Jeffrey Wong '11

All HMC Faculty Publications and Research

Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections to theory for hyperbolic conservation laws predicting wave fronts from Marangoni-driven thin films without forcing. We demonstrate how a variety of forcing profiles, such as Gaussian, rectangular, and triangular, affect the formation of downstream transient structures, including an N wave not commonly discussed in …

Go to article

Conservation Based Uncertainty Propagation In Dynamic Systems, Lillian J. Ratliff Aug 2010

Conservation Based Uncertainty Propagation In Dynamic Systems, Lillian J. Ratliff

UNLV Theses, Dissertations, Professional Papers, and Capstones

Uncertainty is present in our everyday decision making process as well as our understanding of the structure of the universe. As a result an intense and mathematically rigorous study of how uncertainty propagates in the dynamic systems present in our lives is warranted and arguably necessary. In this thesis we examine existing methods for uncertainty propagation in dynamic systems and present the results of a literature survey that justifies the development of a conservation based method of uncertainty propagation. Conservation methods are physics based and physics drives our understanding of the physical world. Thus, it makes perfect sense to formulate …

Go to article

The Generation Of Domestic Electricity Load Profiles Through Markov Chain Modelling, Aidan Duffy, Fintan Mcloughlin, Michael Conlon Jul 2010

The Generation Of Domestic Electricity Load Profiles Through Markov Chain Modelling, Aidan Duffy, Fintan Mcloughlin, Michael Conlon

Conference Papers

Micro-generation technologies such as photovoltaics and micro-wind power are becoming increasing popular among homeowners, mainly a result of policy support mechanisms helping to improve cost competiveness as compared to traditional fossil fuel generation. National government strategies to reduce electricity demand generated from fossil fuels and to meet European Union 20/20 targets is driving this change. However, the real performance of these technologies in a domestic setting is not often known as high time resolution models for domestic electricity load profiles are not readily available. As a result, projections in terms of reducing electricity demand and financial paybacks for these micro-generation …

Go to article

Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper May 2010

Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper

Mathematical Sciences Technical Reports (MSTR)

We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …

Go to article

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge Mar 2010

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

Go to article

The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov Jan 2010

The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov

Conference papers

The theory of soliton perturbations is considered. 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 solution one can ’modify’ …

Go to article

Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., Jared Hanson Jan 2010

Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., Jared Hanson

MA TESOL Collection

There are foundational errors in the mathematical frameworks currently used in Economic and Decision Theories. Recent systemic failures in the interdependent business and educational sectors also show that many practices based on these theories are unsustainable in the changing dynamics of the global economy. A new approach is needed in social science research and systems engineering. This paper examines how the new understandings of complex systems, the role of emotion in cognition, and the core dynamics of decision making can help us correct these errors and to create a general framework for systemic innovation. It argues for the development of …

Go to article

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng Jan 2010

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …

Go to article

From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng Jan 2010

From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng

Department of Mathematics: Faculty Publications

The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …

Go to article

Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, Vladimir Gerdjikov, Georgi Grahovski Jan 2010

Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, Vladimir Gerdjikov, Georgi Grahovski

Articles

The algebraic structure and the spectral properties of a special class of multicomponent NLS equations, related to the symmetric spaces of BD.I-type are analyzed. The focus of the study is on the spectral theory of the associated Lax operator to these nonlinear evolutionary equations for different fundamental representations of the underlying simple Lie algebra g. Special attention is paid to the spinor representation of the orthogonal Lie algebras of B type.

Go to article

Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge Nov 2009

Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge

Other resources

Electromagnetic scattering theory is fundamental to understanding the interaction between electromagnetic waves and inhomogeneous dielectric materials. The theory unpins the engineering of electromagnetic imaging systems over a broad range of frequencies, from optics to radio and microwave imaging, for example. Developing accurate scattering models is particularly important in the field of image understanding and the interpretation of electromagnetic signals generated by scattering events. To this end there are a number of approaches that can be taken. For relatively simple geometric configurations, approximation methods are used to develop a transformation from the object plane (where scattering events take place) to the …

Go to article

Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda Aug 2009

Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda

Undergraduate Research Opportunities Program (UROP)

We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop.

Go to article

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori Jun 2009

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori

All HMC Faculty Publications and Research

Analysis of acoustic phonons modulated due to the surfaces of a free-standing semiconductor plate and their deformation-potential interaction with electrons are presented. The form factor for electron-modulated acoustic phonon interaction is formulated and analyzed in detail. The form factor at zero in-plane phonon wave vector satisfies sum rules regardless of electron wave function. The form factor is larger than that calculated using bulk phonons, leading to a higher scattering rate and lower electron mobility. When properly normalized, the form factors lie on a universal curve regardless of plate thickness and material.

Go to article

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga Jan 2009

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

Theses, Dissertations and Capstones

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …

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

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy Jan 2009

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

All HMC Faculty Publications and Research

A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …

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

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

Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek Jan 2008

Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek

Theses, Dissertations and Capstones

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in …

Go to article

Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov Jan 2008

Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov

Articles

The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and H.1 right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left-invariant metric on SO(3). The CH and HS equations are integrable bi-hamiltonian equations and one of their Hamiltonian structures is associated to the …

Go to article

Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg Jun 2007

Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg

WM Keck Science Faculty Papers

We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …

Go to article

Mathematical Methods In Composing Melodies, Thomas Brown Apr 2007

Mathematical Methods In Composing Melodies, Thomas Brown

Undergraduate Theses and Capstone Projects

This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …

Go to article

Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov Jan 2007

Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov

Articles

Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this ontribution. The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some members of the CH hierarchy, including integrable deformations for the CH equation. Also we show that solutions …

Go to article

Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu Jan 2007

Hamiltonian Formulation, Nonintegrability And Local Bifurcations For The Ostrovsky Equation, S. Roy Choudhury, Rossen Ivanov, Yue Liu

Articles

The Ostrovsky equation is a model for gravity waves propagating down a channel under the influence of Coriolis force. This equation is a modification of the famous Korteweg-de Vries equation and is also Hamiltonian. However the Ostrovsky equation is not integrable and in this contribution we prove its nonintegrability. We also study local bifurcations of its solitary waves.

Go to article

Water Waves And Integrability, Rossen Ivanov Jan 2007

Water Waves And Integrability, Rossen Ivanov

Articles

The Euler’s equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler’s equations is taken (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modeling the motion of shallow water waves are reviewed in this contribution.

Go to article

Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov Jan 2007

Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of motion, the description of the equations of the whole hierarchy and their Hamiltonian structures can be naturally expressed making use of the completeness relation and the recursion …

Go to article

First Prev Next Last