One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, 2014 Dublin Institute of Technology

#### One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

*Articles*

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

Study Of Nonlinear Vibration Of Euler-Bernoulli Beams By Using Analytical Approximate Techniques, 2014 SelectedWorks

#### Study Of Nonlinear Vibration Of Euler-Bernoulli Beams By Using Analytical Approximate Techniques, Saman Bagheri, Ali Nikkar

*Ali Nikkar*

In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated. Two efficient and easy mathematical techniques called He’s Variational Approach and Laplace Iteration Method are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

A Cellular Automaton Model For Traffic Flow - Investigating The Effect Of Turning, 2014 Indiana University – Purdue University Fort Wayne

#### A Cellular Automaton Model For Traffic Flow - Investigating The Effect Of Turning, Tracy Finner, Matthew A. Beauregard

*American Journal of Undergraduate Research*

A cellular automaton model is proposed, modeling vehicular traffic flow on a two dimensional lattice in which the vehicles turn at an intersection with a given probability. It is shown that the introduction of turning reduces the long-term average velocity, and can be predicted by a power law depending on the probability of a vehicle turning and the density of cars. The reduction in speed decreases rapidly once the light cycle length surpasses a certain threshold, the value of which can be predicted from the observed power law.

Leslie Matrices And Women Population In The United States Of America, 2014 Indiana University – Purdue University Fort Wayne

#### Leslie Matrices And Women Population In The United States Of America, Brittney Nelson, Denise T. Reid, Antonija Tangar, Jos´E V´Elez-Marulanda

*American Journal of Undergraduate Research*

This research tests the accuracy of the Leslie matrix, which is a discrete age-structured method that uses fertility and survival rates, as a tool for predicting women population. Based on available data for the year 2000, we have constructed a Leslie matrix that predicts female population in the United States for every five years from the years 2000 to 2020. To test the accuracy of this method, we compare the aforementioned obtained projected data for the year 2010 with the actual data for women population in the United States obtained by the 2010 U.S. Census.

Euler-Poincar´E Equations For G-Strands, 2014 Dublin Institute of Technology

#### Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

*Conference papers*

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g^{∗} with respect to the pairing provided by the variational derivatives of the Lagrangian ...

Dynamic Model Of Large Amplitude Vibration Of A Uniform Cantilever Beam Carrying An Intermediate Lumped Mass And Rotary Inertia, 2014 SelectedWorks

#### Dynamic Model Of Large Amplitude Vibration Of A Uniform Cantilever Beam Carrying An Intermediate Lumped Mass And Rotary Inertia, Ali Nikkar, Saman Bagheri, Masoud Saravi

*Ali Nikkar*

In this paper, a mathematical model of large amplitude vibration of a uniform cantilever beam arising in the structural engineering is proposed. Two efficient and easy mathematical techniques called variational iteration method and He’s variational approach are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. An excellent agreement of the approximate frequencies and periodic solutions with the numerical results and published results has been demonstrated. The results show that both methods can be easily extended to other nonlinear oscillations and it can be ...

Coleman-Gurtin Equations With Dynamic Boundary Conditions With Memory, 2014 Providence College

#### Coleman-Gurtin Equations With Dynamic Boundary Conditions With Memory, Joseph L. Shomberg, Ciprian G. Gal

*Joseph L. Shomberg*

No abstract provided.

Ogden College News, 2014 Western Kentucky University

#### Ogden College News, Cheryl Stevens, Dean

*Ogden College of Science & Engineering Publications*

No abstract provided.

Assesment Of New Analytical Method For Solving The Foam Drainage Equation, 2014 SelectedWorks

#### Assesment Of New Analytical Method For Solving The Foam Drainage Equation, Ali Nikkar

*Ali Nikkar*

No abstract provided.

On A Nonlocal Nonlinear Schrodinger Equation, 2014 Dublin Institute of Technology

#### On A Nonlocal Nonlinear Schrodinger Equation, Tihomir I. Valchev

*Conference papers*

We consider a nonlocal nonlinear Schr\"odinger equation recently proposed by Ablowitz and Musslimani as a theoretical model for wave propagation in {\it PT}-symmetric coupled wave-guides and photonic crystals. This new equation is integrable by means of inverse scattering method, i. e. it possesses a Lax pair, infinite number of integrals of motion and exact solutions. We aim to describe here some of the basic properties of the nonlocal Schr\"odinger equation and its scattering operator. In doing this we shall make use of methods alternative to those applied by Ablowitz and Musslimani which seem to be better suited ...

Arnold Diffusion, 2014 Claremont Colleges

#### Arnold Diffusion, Florin Diacu

*Journal of Humanistic Mathematics*

Poem about Arnold diffusion

An Introduction To Fourier Analysis With Applications To Music, 2014 Claremont Colleges

#### An Introduction To Fourier Analysis With Applications To Music, Nathan Lenssen, Deanna Needell

*Journal of Humanistic Mathematics*

In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for ...

A Molecular Simulation Study On Micelle Fragmentation And Wetting In Nano-Confined Channels, 2014 Western University

#### A Molecular Simulation Study On Micelle Fragmentation And Wetting In Nano-Confined Channels, Mona Habibi

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

We performed coarse-grained molecular-dynamics (MD) simulations to study the structural and dynamical properties of surfactant micelles in equilibrium and under Poiseuille-like flow in a nano-confined geometry. We used the MARTINI force-field to model the interactions between water molecules, counter-ions, and sodium dodecyl sulfate (SDS) surfactants. SDS surfactant was chosen as the standard model because of its potential application in drug delivery systems. First, we focused on the self-assembly of SDS in equilibrium. To form stable spherical mi- celles, we ran simulations in the isothermal-isobaric ensemble (NPT) on a system of free SDS surfactants, counter-ions and water molecules. We studied the ...

Image Fusion And Axial Labeling Of The Spine, 2014 Western University

#### Image Fusion And Axial Labeling Of The Spine, Brandon Miles

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

In order to improve radiological diagnosis of back pain and spine disease, two new algorithms have been developed to aid the 75% of Canadians who will suffer from back pain in a given year. With the associated medical imaging required for many of these patients, there is a potential for improvement in both patient care and healthcare economics by increasing the accuracy and efficiency of spine diagnosis. A real-time spine image fusion system and an automatic vertebra/disc labeling system have been developed to address this. Both magnetic resonance (MR) images and computed tomography (CT) images are often acquired for ...

Citations Of Articles Authored By Wojciech M. Budzianowski, 2014 SelectedWorks

#### Citations Of Articles Authored By Wojciech M. Budzianowski, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

A Mathematical Model Of Redox/Methylation Metabolism In Human Neuronal Cells, 2014 Northeastern University

#### A Mathematical Model Of Redox/Methylation Metabolism In Human Neuronal Cells, Mustafa Kesir

*Mathematics Dissertations*

It is vital for cells to control their state of reduction and oxidation (redox), and the metabolic pathways providing this crucial function intersect with pathways controlling hundreds of methylation reactions. It has been hypothesized that abnormal redox and methylation status contributes to a number of brain disorders, including autism or Alzheimer's disease (AD). Following in the footsteps of Reed et al., who created a mathematical model of these pathways in liver cells, I built a mathematical model of redox and methylation metabolism for human neuronal cells, in order to explore the predictions of this hypothesis and to see if ...

Homotopy Perturbation Method With Two Expanding Parameters, 2014 SelectedWorks

#### Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He

*Ji-Huan He*

A homotopy perturbation method with two expanding parameters is suggested. The method is especially effective for a nonlinear equation with two nonlinear terms, which might have different effects on the solution. A nonlinear oscillator is used as an example to elucidate the solution procedure.

Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, 2014 SelectedWorks

#### Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong

*Chongyang Liu*

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently ...

Mechanika Płynów Lab., 2014 SelectedWorks

#### Mechanika Płynów Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Tematyka Prac Doktorskich, 2014 SelectedWorks

#### Tematyka Prac Doktorskich, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.