Non-linear Dynamics Commons^™

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Experimental Analysis Of Nonlinear Wave Propagation In Bistable Mechanical Metamaterials With A Defect, Samuel R. Harre

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Mechanical metamaterials built up of compliant units can support the propagation of linear and nonlinear waves. A popular architecture consists of a one-dimensional chain of bistable elements connected by linear springs. This type of chain can support nonlinear transition waves that switch each element from one stable state to the other as they propagate along the chain. One way to manipulate the propagation of such waves is via introduction of a local inhomogeneity, i.e., a defect in the otherwise periodic chain. Recent analytical and numerical work has shown that based on its initial velocity, a transition wave may be reflected, …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

All Dissertations

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …

Dynamic Rotation Of Maxwellian Fluid With Fluctuating Thermal Conductivity, Yasir Iqbal, Iqra Batool, Zia Ur Rehman

International Journal of Emerging Multidisciplinaries: Mathematics

This investigation examined the behavior of an overhead-connected Maxwell (UCM) fluid within a rotating framework, with consideration for variations in thermal conductivity based on temperature. The heat deportation process was simulated by incorporating a non-Fourier heat flux term, accounting for thermal relaxation effects. The governing set of partial differential equations underwent decomposition through boundary layer approximations, followed by employing similarity transformations to convert them into self-similar forms. To investigate the effect of the rotation criterion ($\lambda$), Prandtl number (Pr), Deborah number ($\beta$), parameter ($\epsilon$), and dimensionless thermal relaxation time ($\gamma$), an advanced three-stage Lobatto IIIa numerical method was applied. The …

Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu

Doctoral Dissertations

In this thesis, we study the mathematical model of one-dimensional microscopic heat conduction of gas particles, applying both both analytical and numerical approaches. The macroscopic law of heat conduction is the renowned Fourier’s law J = −k∇T, where J is the local heat flux density, T(x, t) is the temperature gradient, and k is the thermal conductivity coefficient that characterizes the material’s ability to conduct heat. Though Fouriers’s law has been discovered since 1822, the thorough understanding of its microscopic mechanisms remains challenging [3] (2000). We assume that the microscopic model of heat conduction is a hard ball system. The …

Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using A Coupled Integral Projection Model To Investigate Interspecific Competition During An Invasion: An Application To Silver Carp (Hypophthalmichthys Molitrix) And Gizzard Shad (Dorosoma Cepedianum), James Peirce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Critical Transitions In Mental Health: Van Gogh Case Study, Anna Singley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Effects Of Seasonal Birth And Predation On Disease Spread, Leah Shaw, Allison Introne

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Epidemic Conditions With Temporary Link Deactivation On A Network Sir Disease Model, John Gemmer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kadelka: Modularizing The Control Search For Biological Systems, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kadelka: Canalization Reduces The Nonlinearity Of Regulation In Biological Networks, Claus Kadelka, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Communication Dynamics In Human-Autonomy Teams: Insights From Search And Rescue Scenarios, Carlos E. Bustamante Orellana, Lucero Rodriguez Rodriguez, Yun Kang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Study Of Behaviour Change And Impact On Infectious Disease Dynamics By Mathematical Models, Tianyu Cheng

Electronic Thesis and Dissertation Repository

This thesis uses mathematical models to study human behaviour changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behaviour response evolves during epidemics and the effects of adaptive precaution behaviour on epidemics. The second topic is how to build general framework models incorporating human behaviour response in epidemiological modelling.

In the first project, based on the fact that a fraction of the epidemiologically susceptible population is actually susceptible due to precautions, we present a novel perspective on understanding the infection force, incorporating human protection behaviours. This view explains many existing infection force …

Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann

Doctoral Dissertations and Master's Theses

Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …

Pathogen Emergence As Complex Biological Invasion: Lessons From Dynamical Systems Modeling, Sudam Surasinghe, Marisabel Rodriguez, Victor Meszaros, Jane Molofsky, Salvador Almagro-Moreno, Brandon Ogbunugafor

Northeast Journal of Complex Systems (NEJCS)

Infectious disease emergence has become the target of cross-disciplinary efforts
that aim to understand and predict the shape of outbreaks. The many challenges
involved with the prediction of disease emergence events is a characteristic that in-
fectious diseases share with biological invasions in many subfields of ecology (e.g.,
how certain plants are able to successfully invade a new niche). Like infectious
diseases, biological invasions by plants and animals involve interactions between
agents (pathogens and plants in their respective cases) and a recipient niche. In
this study, we examine the problem of pathogen emergence through the lens of a
framework first …

Temporality-Induced Chaos In The Kuramoto Model, Keanu Mason Rock, Hamza Dirie, Sean P. Cornelius

Northeast Journal of Complex Systems (NEJCS)

Switched dynamical systems have been extensively studied in engineering literature in the context of system control. In these systems, the dynamical laws change between different subsystems depending on the environment, a process that is known to produce emergent behaviors---notably chaos. These dynamics are analogous to those of temporal networks, in which the network topology changes over time, thereby altering the dynamics on the network. It stands to reason that temporal networks may therefore produce emergent chaos and other exotic behaviors unanticipated in static networks, yet concrete examples remain elusive. Here, we present a minimal example of a networked system in …

Deep Hybrid Modeling Of Neuronal Dynamics Using Generative Adversarial Networks, Soheil Saghafi

Dissertations

Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on …

Complex-Valued Approach To Kuramoto-Like Oscillators, Jacqueline Bao Ngoc Doan

Electronic Thesis and Dissertation Repository

The Kuramoto Model (KM) is a nonlinear model widely used to model synchrony in a network of oscillators – from the synchrony of the flashing fireflies to the hand clapping in an auditorium. Recently, a modification of the KM (complex-valued KM) was introduced with an analytical solution expressed in terms of a matrix exponential, and consequentially, its eigensystem. Remarkably, the analytical KM and the original KM bear significant similarities, even with phase lag introduced, despite being determined by distinct systems. We found that this approach gives a geometric perspective of synchronization phenomena in terms of complex eigenmodes, which in turn …

Computing Brain Networks With Complex Dynamics, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Modeling, Simulation And Control Of Microrobots For The Microfactory., Zhong Yang

Electronic Theses and Dissertations

Future assembly technologies will involve higher levels of automation in order to satisfy increased microscale or nanoscale precision requirements. Traditionally, assembly using a top-down robotic approach has been well-studied and applied to the microelectronics and MEMS industries, but less so in nanotechnology. With the boom of nanotechnology since the 1990s, newly designed products with new materials, coatings, and nanoparticles are gradually entering everyone’s lives, while the industry has grown into a billion-dollar volume worldwide. Traditionally, nanotechnology products are assembled using bottom-up methods, such as self-assembly, rather than top-down robotic assembly. This is due to considerations of volume handling of large …

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …

Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias

Doctoral Dissertations

In recent years, there has been an explosion of interest in media bearing quartic
dispersion. After the experimental realization of so-called pure-quartic solitons, a
significant number of studies followed both for bright and for dark solitonic struc-
tures exploring the properties of not only quartic, but also setic, octic, decic etc.
dispersion, but also examining the competition between, e.g., quadratic and quartic
dispersion among others.
In the first chapter of this Thesis, we consider the interaction of solitary waves in
a model involving the well-known φ⁴ Klein-Gordon theory, bearing both Laplacian and biharmonic terms with different prefactors. As a …

Continuum Model Of Faceted Ice Crystal Growth In Cirrus Clouds In 1 Dimension, Ella Slattery

Summer Research

Ice crystals in cirrus clouds exhibit stable faceted growth and roughening which affects reflectivity. A numerically stable modelling system of partial differential equations representing the thickness of ice surfaces over time may assist in describing these features. A sinusoidal relationship between total thickness and water vapor deposition on the surface of ice crystals was observed experimentally; the modelling equation for this relationship was applied to the system in order to develop a one variable model. The developed one variable models continue to exhibit numerical instabilities prior to a Fourier Transform. Stable limit cycles of ice growth were observed in the …

Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov

Conference papers

The article surveys the recent results on integrable systems arising from quadratic pencil of Lax operator L, with values in a Hermitian symmetric space. The counterpart operator M in the Lax pair defines positive, negative and rational flows. The results are illustrated with examples from the A.III symmetric space. The modeling aspect of the arising higher order nonlinear Schrödinger equations is briefly discussed.

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 …