Dynamic Systems Commons^™

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle

Master's Theses

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing …

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni

Mechanical Engineering Research Theses and Dissertations

Optimal control is a control method which provides inputs that minimize a performance index subject to state or input constraints [58]. The existing solutions for finding the exact optimal control solution such as Pontryagin’s minimum principle and dynamic programming suffer from curse of dimensionality in high order dynamical systems. One remedy for this problem is finding near optimal solution instead of the exact optimal solution to avoid curse of dimensionality [31]. A method for finding the approximate optimal solution is through Approximate Dynamic Programming (ADP) methods which are discussed in the subsequent chapters.

In this dissertation, optimal switching in switched …

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, Mahbubur Rahman 6203748

Showcase of Faculty Scholarly & Creative Activity

Approximation of stochastic differential equations (SDEs) with parametric noise plays an important role in a range of application areas, including engineering, mechanics, epidemiology, and neuroscience. A complete understanding of SDE theory with perturbed noise requires familiarity with advanced probability and stochastic processes. In this paper, we derive an asymptotic estimate of variance, and it is shown that numerical method gives a useful step toward solving SDEs with perturbed noise. Our goal is to diffuse the results to an audience not entirely familiar with functional notations or semi-group theory, but who might nonetheless be interested in the practical simulation of dynamical …

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

Department of Physics Publications

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other …

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …

Communication Based Control For Dc Microgrids, Mahmoud S. Saleh, Yusef Esa, Ahmed Mohamed

Publications and Research

Centralized communication-based control is one of the main methods that can be implemented to achieve autonomous advanced energy management capabilities in DC microgrids. However, its major limitation is the fact that communication bandwidth and computation resources are limited in practical applications. This can be often improved by avoiding redundant communications and complex computations. In this paper, an autonomous communication-based hybrid state/event driven control scheme is proposed. This control scheme is hierarchical and heuristic, such that on the primary control level, it encompasses state-driven local controllers, and on the secondary control level, an event-driven MG centralized controller (MGCC) is used. This …

The Study Of Non-Newtonian Nanofluid With Hall And Ion Slip Effects On Peristaltically Induced Motion In A Non-Uniform Channel, Sara I. Abdelsalam, M. M. Bhatti

Basic Science Engineering

In this study, we considered the unsteady peristaltic motion of a non-Newtonian nanofluid under the influence of a magnetic field and Hall currents. The simultaneous effects of ion slip and chemical reaction were also taken into consideration. The flow problem was suggested on the basis of the continuity, thermal energy, linear momentum, and nanoparticle concentration, which were further reduced with the help of Ohm's law. Mathematical modelling was executed using the lubrication approach. The resulting highly nonlinear partial differential equations were solved semi-analytically using the homotopy perturbation technique. The impacts of all the pertinent parameters were investigated mathematically and graphically. …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

Honors Undergraduate Theses

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …

Optimization And Control Of An Array Of Wave Energy Converters, Jianyang Lyu

Dissertations, Master's Theses and Master's Reports

This study explored optimal configuration of both the array layout and the dimension of each WEC in the array. The array contains heaving buoys with full interaction and exact hydrodynamics. Optimization of dimension was done on each WEC in the array with a given optimal layout, and a higher q-factor was achieved. Both impedance matching optimal control and derivative control were employed, which provides both theoretical maximum energy and a more realistic case. Then the work was expanded to optimization of both the array layout and the dimension of each WEC in the array. An average of 39.21% higher q-factor …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Delay Differential Equations And Their Application To Micro Electro Mechanical Systems, Asset Ospanov

Theses and Dissertations

Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is …

Fluid-Dynamic Models Of Geophysical Waves, Alan Compelli

Doctoral

Geophysical waves are waves that are found naturally in the Earth's atmosphere and oceans. Internal waves, that is waves that act as an interface between uids of dierent density, are examples of geophysical waves. A uid system with a at bottom, at surface and internal wave is initially considered. The system has a depth-dependent current which mimics a typical ocean set-up and, as it is based on the surface of the rotating Earth, incorporates Coriolis forces. Using well established uid dynamic techniques, the total energy is calculated and used to determine the dynamics of the system using a procedure called …

Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …

On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin

Graduate Theses/Dissertations

In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.

Nonspreading Solutions In Integro-Difference Models With Allee And Overcompensation Effects., Garrett Luther Otto

Electronic Theses and Dissertations

Previous work in Integro-Difference models have generally considered Allee effects and over-compensation separately, and have either focused on bounded domain problems or asymptotic spreading results. Some recent results by Sullivan et al. (2017 PNAS 114(19), 5053-5058) combining Allee and over-compensation in an Integro-Difference framework have shown chaotic fluctuating spreading speeds. In this thesis, using a tractable parameterized growth function, we analytically demonstrate that when Allee and over-compensation are present solutions which persist but essentially remain in a compact domain exist. We investigate the stability of these solutions numerically. We also numerically demonstrate the existence of such solutions for more general …

On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on L^P-spaces are used, defining the L^p_F F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented.

Applications Of Planar Newtonian Four-Body Problem To The Central Configurations, M. R. Hassan, M. S. Ullah, Md. Aminul Hassan, Umakant Prasad

Applications and Applied Mathematics: An International Journal (AAM)

The present study deals with the applications of the planar Newtonian four-body problem to
the different central configurations. The basic concept of central configuration is that the
vector force must be in the direction of the position vector so that the origin may be taken at
the centre of mass of the four bodies and the force towards the position vector multiplied by
corresponding inverse mass is directly proportional to the position vector relative to the
centre of mass. For applying the Newtonian four body problem to the central configuration,
the equations of motion of four bodies have been established …

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal

Publications

No abstract provided.

Model Selection And Permanence In A Stochastic Integrated Pest Management Model, Timothy Comar, Olcay Akman, Daniel Hrozencik

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar, Elizabeth Rodriguez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stochastic And Deterministic Multigroup Epidemiology, Jordan Hasler, Chris Chang, Ananya Yammanuru, Lewis Oh, Esther Matthew, Mounisha Kovour

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Yeast Cell Cycle And Metabolism Can Be Coupled In Nontrivial Ways., Todd Young

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Microtubule-Based Transport In The Frog Egg Cell, Maria-Veronica Ciocanel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model Of Dengue Transmission With Wolbachia-Free And Wolbachia-Infected Mosquitoes, Iftikhar Ahmed

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Voting Dynamics In A Two-Party System: Social Interaction And Media Consumption, Caleb Ignace

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

We have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of …

Stability Of Triangular Libration Points In The Sun - Jupiter System Under Szebehely’S Criterion, M. R. Hassan, Md. A. Hassan, M. Z. Ali

Applications and Applied Mathematics: An International Journal (AAM)

In the present study, the classical fourth-order Runge-Kutta method with seventh-order automatic step-size control has been carried out to examine the stability of triangular libration points in the Sun-Jupiter system. The Sun is a highly luminous body and Jupiter is a highly spinning body, so radiation pressure of the Sun and oblateness of the Jupiter cannot be neglected. These factors must have some effects on the motion of the infinitesimal mass (spacecraft) and consequent effects on the stability of the triangular libration points. It is to be noted that in our problem, infinitesimal mass exerts no influence of attraction on …