Non-linear Dynamics Commons^™

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

Theses and Dissertations

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Vibrations Reduction Of A Clamped- Clamped Micro-Beam Via Positive Position Feedback Controller, H. Mosaa, M. Kamel, H. El Gohry, L. S. Diab, H. M. Shawky

Al-Azhar Bulletin of Science

This manuscript displays the vibrations reduction of a clamped- clamped micro-beam subjected to an excitation external force via applying the positive position feedback (PPF) controller. The approximate solutions of the whole system are obtained up to the second order approximation with the help of the multiple scale perturbation technique (MSP). The Stability analysis is studied by utilizing the frequency response equations near the simultaneous condition .Time histories and response curves figures before and after control of the whole system are examined numerically using Rung-Kutta Fourth-order method (Maple(16) software and Matlab 7.7(R2014) software. Numerical results of the influences of different parameters …

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

The Nonlinearity Of Regulation In Biological Networks, Santosh Manicka, Kathleen Johnson, Michael Levin, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Kuramoto Model Approach To Predicting Chaotic Systems With Echo State Networks, Sophie Wu, Jackson Howe

Undergraduate Student Research Internships Conference

An Echo State Network (ESN) with an activation function based on the Kuramoto model (Kuramoto ESN) is implemented, which can successfully predict the logistic map for a non-trivial number of time steps. The reservoir in the prediction stage exhibits binary dynamics when a good prediction is made, but the oscillators in the reservoir display a larger variability in states as the ESN’s prediction becomes worse. Analytical approaches to quantify how the Kuramoto ESN’s dynamics relate to its prediction are explored, as well as how the dynamics of the Kuramoto ESN relate to another widely studied physical model, the Ising model.

Travelling Wave Solutions On A Cylindrical Geometry, Karnav R. Raval

Undergraduate Student Research Internships Conference

Fluid equations are generally quite difficult and computationally-expensive to solve. However, if one is primarily interested in how the surface of the fluid deforms, we can re-formulate the governing equations purely in terms of free surface variables. Reformulating equations in such a way drastically cuts down on computational cost, and may be useful in areas such as modelling blood flow. Here, we study one such free-boundary formulation on a cylindrical geometry.

Modeling Empirical Stock Market Behavior Using A Hybrid Agent-Based Dynamical Systems Model, Daniel A. Cline, Grant T. Aguinaldo, Christian Lemp

Northeast Journal of Complex Systems (NEJCS)

We describe the development and calibration of a hybrid agent-based dynamical systems model of the stock market that is capable of reproducing empirical market behavior. The model consists of two types of trader agents, fundamentalists and noise traders, as well as an opinion dynamic for the latter (optimistic vs. pessimistic). The trader agents switch types stochastically over time based on simple behavioral rules. A system of ordinary differential equations is used to model the stock price as a function of the states of the trader agents. We show that the model can reproduce key stylized facts (e.g., volatility clustering and …

Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans

Biology and Medicine Through Mathematics Conference

No abstract provided.

Effects Of Local Mutations In Quadratic Iterations, Anca R. Radulescu, Abraham Longbotham

Biology and Medicine Through Mathematics Conference

No abstract provided.

Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Laura Ellwein Fix

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker

Theses and Dissertations

The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …

The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang

Mathematics Faculty Research Publications

We study the asymptotic behavior as p → ∞ of the Gelfand problem

−Δ_pu = λe^u in Ω ⊂ Rⁿ, u = 0 on ∂Ω.

Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of

min{|∇_u|−Λe^u, −Δ_∞u} = 0 in Ω, u = 0 on ∂Ω.

We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.

Representing And Analyzing The Dynamics Of An Agent-Based Adaptive Social Network Model With Partial Integro-Differential Equations, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

We formulated and analyzed a set of partial integro-differential equations that capture the dynamics of our adaptive network model of social fragmentation involving behavioral diversity of agents. Previous results showed that, if the agents’ cultural tolerance levels were diversified, the social network could remain connected while maintaining cultural diversity. Here we converted the original agent-based model into a continuous equation-based one so we can gain more theoretical insight into the model dynamics. We restricted the node states to 1-D continuous values and assumed the network size was very large. As a result, we represented the whole system as a set …

Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode, Joshua Sonderegger

Doctoral Dissertations and Master's Theses

The landing and reusability of space vehicles is one of the driving forces into renewed interest in space utilization. For missions to planetary surfaces, this soft landing has been most commonly accomplished with parachutes. However, in spite of their simplicity, they are susceptible to parachute drift. This parachute drift makes it very difficult to predict where the vehicle will land, especially in a dense and windy atmosphere such as Earth. Instead, recent focus has been put into developing a powered landing through gimbaled thrust. This gimbaled thrust output is dependent on robust path planning and controls algorithms. Being able to …

Period Doubling Cascades From Data, Alexander Berliner

Undergraduate Honors Theses

Orbit diagrams of period doubling cascades represent systems going from periodicity to chaos. Here, we investigate whether a Gaussian process regression can be used to approximate a system from data and recover asymptotic dynamics in the orbit diagrams for period doubling cascades. To compare the orbits of a system to the approximation, we compute the Wasserstein metric between the point clouds of their obits for varying bifurcation parameter values. Visually comparing the period doubling cascades, we note that the exact bifurcation values may shift, which is confirmed in the plots of the Wasserstein distance. This has implications for studying dynamics …

Bistability And Switching Behavior In Moving Animal Groups, Daniel Strömbom, Stephanie Nickerson, Catherine Futterman, Alyssa Difazio, Cameron Costello, Kolbjørn Tunstrøm

Northeast Journal of Complex Systems (NEJCS)

Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching …

On The Coriolis Effect For Internal Ocean Waves, Rossen Ivanov

Conference papers

A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth's rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.

Smoothed Bounded-Confidence Opinion Dynamics On The Complete Graph, Solomon Valore-Caplan

HMC Senior Theses

We present and analyze a model for how opinions might spread throughout a network of people sharing information. Our model is called the smoothed bounded-confidence model and is inspired by the bounded-confidence model of opinion dynamics proposed by Hegselmann and Krause. In the Hegselmann–Krause model, agents move towards the average opinion of their neighbors. However, an agent only factors a neighbor into the average if their opinions are sufficiently similar. In our model, we replace this binary threshold with a logarithmic weighting function that rewards neighbors with similar opinions and minimizes the effect of dissimilar ones. This weighting function can …

An Adaptive Hegselmann–Krause Model Of Opinion Dynamics, Phousawanh Peaungvongpakdy

HMC Senior Theses

Models of opinion dynamics have been used to understand how the spread
of information in a population evolves, such as the classical Hegselmann–
Krause model (Hegselmann and Krause, 2002). One extension of the model
has been used to study the impact of media ideology on social media
networks (Brooks and Porter, 2020). In this thesis, we explore various
models of opinions and propose our own model, which is an adaptive
version of the Hegselmann–Krause model. The adaptive version implements
the social phenomenon of homophily—the tendency for like-minded agents to
associate together. This is done by having agents dissolve connections …

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Convergence Properties Of Solutions Of A Length-Structured Density-Dependent Model For Fish, Geigh Zollicoffer

Rose-Hulman Undergraduate Mathematics Journal

We numerically study solutions to a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We make conjectures about the convergence properties of solutions to this equation, and give numerical simulations which support these conjectures. We also study the distribution of biomass in the different age classes as a function of the total biomass.

Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Neural Network Controller Vs Pulse Control To Achieve Complete Eradication Of Cancer Cells In A Mathematical Model, Joel A. Quevedo, Sergio A. Puga, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Reconstructing Mathematical Models With Chaotic Attractors Via Genetic Algorithms, Luis A. Ramirez Islas, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Improved Ships Course-Keeping Robust Control Algorithm Based On Backstepping And Nonlinear Feedback, Sirui Wang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

Symphas: A Modular Api For Phase-Field Modeling Using Compile-Time Symbolic Algebra, Steven A. Silber

Electronic Thesis and Dissertation Repository

The phase-field method is a common approach to qualitative analysis of phase transitions. It allows visualizing the time evolution of a phase transition, providing valuable insight into the underlying microstructure and the dynamical processes that take place. Although the approach is applied in a diverse range of fields, from metal-forming to cardiac modelling, there are a limited number of software tools available that allow simulating any phase-field problem and that are highly accessible. To address this, a new open source API and software package called SymPhas is developed for simulating phase-field and phase-field crystal in 1-, 2- and 3-dimensions. Phase-field …

Using An Analytical Approach Of The Kuramoto Model To Stimulate 3d Neural Activity Of The Stomach, Morteza Al Rabya

Undergraduate Student Research Internships Conference

No abstract provided.

Representation Of Nonlinear Pseudo-Random Generators Using State-Space Equations, Raghad K. Salih

Emirates Journal for Engineering Research

The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.

Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen

Faculty Research, Scholarly, and Creative Activity

In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c∗0 , which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗ = c∗0 , which …

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.