Dynamics Of Quadratic Networks, 2018 SUNY New Paltz

#### Dynamics Of Quadratic Networks, Simone Evans

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Predicting Critical Transitions In Spatially Distributed Populations With Cubical Homology, 2018 College of William and Mary

#### Predicting Critical Transitions In Spatially Distributed Populations With Cubical Homology, Laura Storch, Sarah Day

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Axonal Transport With Attachment And Detachment To Parallel Microtubule Network, 2018 Rensselaer Polytechnic Institute

#### Axonal Transport With Attachment And Detachment To Parallel Microtubule Network, Abhishek Choudhary Mr.

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

The Computational Study Of Fly Swarms & Complexity, 2018 Linfield College

#### The Computational Study Of Fly Swarms & Complexity, Austin Bebee

*Senior Theses*

A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the ...

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, 2018 Michigan Technological University

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

*Ramy El-Ganainy*

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 ...

Analyzing Lagrangian Statistics Of Eddy-Permitting Models, 2018 University of Colorado, Boulder

#### Analyzing Lagrangian Statistics Of Eddy-Permitting Models, Amy Chen

*Applied Mathematics Graduate Theses & Dissertations*

Mesoscale eddies are the strongest currents in the world oceans and transport properties such as heat, dissolved nutrients, and carbon. The current inability to effectively diagnose and parameterize mesoscale eddy processes in oceanic turbulence is a critical limitation upon the ability to accurately model large-scale oceanic circulations. This investigation analyzes the Lagrangian statistics for four faster and less computationally expensive eddy-permitting models --- Biharmonic, Leith, Jansen & Held Deterministic, and Jansen & Held Stochastic --- and compares them against each other and an eddy-resolving quasigeostrophic Reference model. Results from single-particle climatology show that all models exhibit similar behaviour in large-scale movement over long times ...

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, 2018 University of North Florida

#### 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 ...

Darboux-Box Variables And The Existence Of A Complete Set Of Lagrangians For Given N-Dimensional Newtonian Equations Of Motion. The Isomorphism Of N-Dimensional Newtonian Dynamical Systems, 2018 University of North Georgia

#### Darboux-Box Variables And The Existence Of A Complete Set Of Lagrangians For Given N-Dimensional Newtonian Equations Of Motion. The Isomorphism Of N-Dimensional Newtonian Dynamical Systems, Piotr W. Hebda, Beata Hebda

*Faculty Publications*

For given time-independent Newtonian system of equations of motion and given Poisson Brackets allowed by these equations, it is proven that locally a Lagrangian exists that gives these equations of motion as its regular Euler-Lagrange equations, and gives these Poisson Brackets in a regular process of obtaining the Hamiltonian and its Poisson Brackets. However, this Lagrangian may be using generalized position-velocity variables instead of the original position-velocity variables from the original equations of motion. Also, Darboux Box variables are introduced to prove that all Newtonian dynamical systems are locally isomorphic, meaning that locally there exists a one-to-one function relating the ...

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, 2018 Michigan Technological University

#### 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 ...

Algebraic Methods For The Construction Of Algebraic-Difference Equations With Desired Behavior, 2018 Aristotle University of Thessaloniki

#### Algebraic Methods For The Construction Of Algebraic-Difference Equations With Desired Behavior, Lazaros Moysis, Nicholas Karampetakis

*Electronic Journal of Linear Algebra*

For a given system of algebraic and difference equations, written as an Auto-Regressive (AR) representation $A(\sigma)\beta(k)=0$, where $\sigma $ denotes the shift forward operator and $A\left( \sigma \right) $ a regular polynomial matrix, the forward-backward behavior of this system can be constructed by using the finite and infinite elementary divisor structure of $A\left( \sigma \right) $. This work studies the inverse problem: Given a specific forward-backward behavior, find a family of regular or non-regular polynomial matrices $A\left( \sigma \right) $, such that the constructed system $A\left( \sigma \right) \beta \left( k\right) =0$ has exactly the ...

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, 2018 Laboratoire des Signaux et Systèmes (L2S) CNRS-CentraleSupélec-Université Paris-Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France

#### 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, 2018 CUNY City College

#### 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 ...

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, 2018 Nanjing University of Science and Technology

#### 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 between local strong ...

Modelling Heterogeneous Effects In Network Contagion: Evidence From The Steam Community, 2018 University of Pennsylvania

#### Modelling Heterogeneous Effects In Network Contagion: Evidence From The Steam Community, Henrique Laurino Dos Santos

*Wharton Research Scholars*

This study considers heterogeneous effects of reviews and social interactions on diffusion or contagion of new products in a networked setting, using a sample of interconnected public user profiles from the Steam Community. Ownership and reviews of two cult hit independent games – The Binding of Isaac: Rebirth, and To the Moon – are analyzed over a period of four years. This data was fit with a Hawkes Process Hazard Regression Model with exponential decay kernels for each game, yielding estimates of scale and duration of incremental heterogeneous actions within the network. This analysis finds strong, short term, additive, and marginally decreasing ...

Fluid-Dynamic Models Of Geophysical Waves, 2018 Dublin Institute of Technology

#### 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 ...

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, 2018 University of Central Florida

#### Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

*Honors in the Major 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 ...

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, 2017 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Spectral Dynamics Of Graph Sequences Generated By Subdivision And Triangle Extension, 2017 Jimei University

#### Spectral Dynamics Of Graph Sequences Generated By Subdivision And Triangle Extension, Haiyan Chen, Fuji Zhang

*Electronic Journal of Linear Algebra*

For a graph G and a unary graph operation X, there is a graph sequence \G_k generated by G_0=G and G_{k+1}=X(G_k). Let Sp({G_k}) denote the set of normalized Laplacian eigenvalues of G_k. The set of limit points of \bigcup_{k=0}^\infty Sp(G_k)$, $\liminf_{k\rightarrow\infty}Sp(G_k) and $\limsup_{k\rightarrow \infty}Sp(G_k)$ are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained that the spectral dynamic of graph sequence generated by subdivision is determined by a quadratic function, which is ...

Social Balance And The Bernoulli Equation, 2017 Portland State University

#### Social Balance And The Bernoulli Equation, J. J. P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

Since the 1940s there has been an interest in the question of why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an introduction to the notion of social balance and a new (and simplified) analysis of that model. This new analysis allows us to choose general initial conditions, as opposed to the symmetric ones previously considered. We show that for general initial conditions, four factions will evolve instead of two. We characterize the four factions, and give an idea of their ...

Mathematical Studies Of Optimal Economic Growth Model With Monetary Policy, 2017 College of William and Mary

#### Mathematical Studies Of Optimal Economic Growth Model With Monetary Policy, Xiang Liu

*Undergraduate Honors Theses*

In this paper, efforts will be made to study an extended Neoclassic economic growth model derived from Solow-Swan Model and Ramsey-Cass-Koopsman Model. Some growth models (e.g. Solow-Swan Model) attempt to explain long-run economic growth by looking at capital accumulation, labor or population growth, and in- creases in productivity, while our derived model tends to look at growth from individual household and how their choice of saving, consumption and money holdings would affect the overall economic capital accumulation over a long period of time.

First an optimal control model is set up, and a system of differential equations and algebraic ...