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Non-linear Dynamics Commons

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Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar 2020 Florida International University

Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar

FIU Electronic Theses and Dissertations

In 1922, Louis de Broglie proposed wave-particle duality and introduced the idea of matter waves. In 1925, Erwin Schrodinger, proposed a wave equation for de Broglie’s matter waves. The Schrodinger equation is described using the de Broglie’s matter wave, which takes the wave function, and describes its quantum state over time.

Herein, we study the generalized Hartree (gHartree) equation, which is a nonlinear Schrodinger type equation except now the nonlinearities are a nonlocal (convolution) type. In the gHartree equation, the influence on the behavior of the solutions is global as opposed to the case of local (power type ...


Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. DeWeese 2020 University of California Berkeley

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.


Mitigating Safety Concerns And Profit/Production Losses For Chemical Process Control Systems Under Cyberattacks Via Design/Control Methods, Helen Durand, Matthew Wegener 2020 Wayne State University

Mitigating Safety Concerns And Profit/Production Losses For Chemical Process Control Systems Under Cyberattacks Via Design/Control Methods, Helen Durand, Matthew Wegener

Chemical Engineering and Materials Science Faculty Research Publications

One of the challenges for chemical processes today, from a safety and profit standpoint, is the potential that cyberattacks could be performed on components of process control systems. Safety issues could be catastrophic; however, because the nonlinear systems definition of a cyberattack has similarities to a nonlinear systems definition of faults, many processes have already been instrumented to handle various problematic input conditions. Also challenging is the question of how to design a system that is resilient to attacks attempting to impact the production volumes or profits of a company. In this work, we explore a process/equipment design framework ...


Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman 2020 Air Force Institute of Technology

Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman

Theses and Dissertations

The objective of this research is to develop a numerical method to characterize heat transfer and wear rates for samples of Vascomax® 300, or Maraging 300, steel. A pin-on-disc experiment was conducted in which samples were exposed to a high-pressure, high-speed, sliding contact environment. This sliding contact generates frictional heating that influences the temperature distribution and wear characteristics of the test samples. A two-dimensional nonlinear heat transfer equation is discretized and solved via a second-order explicit finite difference scheme to predict the transient temperature distribution of the pin. This schematic is used to predict the removal of material from the ...


Finding Music In Chaos: Designing And Composing With Virtual Instruments Inspired By Chaotic Equations, Landon P. Viator 2020 Louisiana State University

Finding Music In Chaos: Designing And Composing With Virtual Instruments Inspired By Chaotic Equations, Landon P. Viator

LSU Doctoral Dissertations

Using chaos theory to design novel audio synthesis engines has been explored little in computer music. This could be because of the difficulty of obtaining harmonic tones or the likelihood of chaos-based synthesis engines to explode, which then requires re-instantiating of the engine to proceed with sound production. This process is not desirable when composing because of the time wasted fixing the synthesis engine instead of the composer being able to focus completely on the creative aspects of composition. One way to remedy these issues is to connect chaotic equations to individual parts of the synthesis engine instead of relying ...


Responsive Economic Model Predictive Control For Next-Generation Manufacturing, Helen Durand 2020 Wayne State University

Responsive Economic Model Predictive Control For Next-Generation Manufacturing, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types ...


The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling 2020 Virginia Commonwealth University

The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling

Theses and Dissertations

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.

Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network ...


Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze 2020 Technological University Dublin

Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze

Articles

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and ...


On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov 2020 Technological University Dublin

On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov

Articles

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are ...


Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr 2020 Technological University Dublin

Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr

Articles

A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa–Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.


A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons 2020 Portland State University

A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons

Mathematics and Statistics Faculty Publications and Presentations

We analyze the asymptotic behavior of general first order Laplacian processes on digraphs. The most important ones of these are diffusion and consensus with both continuous and discrete time. We treat diffusion and consensus as dual processes. This is the first complete exposition of this material in a single work.


Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, Gregory Allen Riggs 2020 West Virginia University

Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, Gregory Allen Riggs

Graduate Theses, Dissertations, and Problem Reports

The application of bicoherence analysis to plasma research, particularly in non-linear, coupled-wave regimes, has thus far been significantly belied by poor resolution in time, and/or outright destruction of frequency information. Though the typical power spectrum cloaks the phase-coherency between frequencies, Fourier transforms of higher-order convolutions provide an n-dimensional spectrum which is adept at elucidating n-wave phase coherence. As such, this investigation focuses on the utility of the normalized bispectrum for detection of wave-wave coupling in general, with emphasis on distinct implications within the scope of non-linear plasma physics. Interpretations of bicoherent features are given for time series ...


The Effect Of External Perturbations On Ecological Oscillators, Eli Goldwyn 2019 Illinois State University

The Effect Of External Perturbations On Ecological Oscillators, Eli Goldwyn

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Analog Implementation Of The Hodgkin-Huxley Model Neuron, Zachary D. Mobille, George H. Rutherford, Jordan Brandt-Trainer, Rosangela Follmann, Epaminondas Rosa 2019 Illinois State University

Analog Implementation Of The Hodgkin-Huxley Model Neuron, Zachary D. Mobille, George H. Rutherford, Jordan Brandt-Trainer, Rosangela Follmann, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Analysis Of An Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar 2019 Benedictine University

Analysis Of An Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Discrete-Time Disease Model With Population Motion Under The Kolmogorov Equation View And Application, Ye Li 2019 Illinois State University

Discrete-Time Disease Model With Population Motion Under The Kolmogorov Equation View And Application, Ye Li

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Academic Skill Learning And The Problem Of Complexity I: Creational Purposeful Integrated Capability At Skill (Cpics), Martin F. Gardiner 2019 Brown University

Academic Skill Learning And The Problem Of Complexity I: Creational Purposeful Integrated Capability At Skill (Cpics), Martin F. Gardiner

Northeast Journal of Complex Systems (NEJCS)

Physical and mental skills are intended to achieve success at acting purposefully. As capability at any skill increases, the need to adjust details of application to complexity of context and goals will increase as well. It will become more and more important to prepare mentally for what I now term Creational Purposeful Integrated Capability at Skill (CPICS). This paper develops what I mean by CPICS. Theory concerning Complex Dynamical Systems (CDS) such as the brain and other evidence points to the likelihood that the mental operations by which our brain produces any kind of skillful behavior cannot remain constant, but ...


A Patterning Approach To Complexity Thinking And Understanding For Students: A Case Study, Shae L. Brown 2019 Southern Cross University

A Patterning Approach To Complexity Thinking And Understanding For Students: A Case Study, Shae L. Brown

Northeast Journal of Complex Systems (NEJCS)

Complexity thinking and understanding are vital skills for young people in these times of uncertainty and change. Such skills contribute to resilience and capacities for adaptivity and innovation. Within my teaching practice I have found students to be aware of complex dynamics, uncertainty and change, both in their lives and in the world. However, the current curriculum lacks language and process to conceptualise, articulate and develop complexity understanding. To address this problem, I developed and introduced a patterns-based design and process to a cohort of Australian secondary students. Comprising flowform patterning together with ecological metaphors, the design forms a conceptual ...


Being In Uncertainties: An Inquiry-Based Model Leveraging Complexity In Teaching-Learning, Diane Rosen 2019 State University of New York, Suffern

Being In Uncertainties: An Inquiry-Based Model Leveraging Complexity In Teaching-Learning, Diane Rosen

Northeast Journal of Complex Systems (NEJCS)

Education is traditionally structured as a closed system, privileging result-driven methods that offer control and predictability. In recent decades this reductionist approach has been effectively challenged by interdisciplinary work in complex systems theory, revealing myriad levels of orderly disorder that make either-or, linear instruction an inadequate norm. Narrowing the broad implications of a complexity lens on education, this paper focuses on generative uncertainty in teaching-learning, a paradoxical state of epistemological and creative growth described by English poet John Keats as "the negative capability of being in uncertainties, mysteries, doubts." Opportunities to advance this potentiating capacity are especially abundant in constructivist ...


Creativity As An Emergent Property Of Complex Educational System, Ceire Monahan, Mika Munakata, Ashwin Vaidya 2019 Montclair State University

Creativity As An Emergent Property Of Complex Educational System, Ceire Monahan, Mika Munakata, Ashwin Vaidya

Northeast Journal of Complex Systems (NEJCS)

The importance of creativity in education has been discussed often in the literature. While there remains no agreed-upon definition of creativity, the psychological literature points to traits of a creative person. These include the ability to think outside the box, make connections between seemingly disparate ideas, and question norms. The literature provides several examples of classroom experiments to help foster creativity in the classroom. In science and mathematics, we can start by getting students to recognize mathematics and the sciences as being creative endeavors. While these attempts are noteworthy, they are not necessarily aligned with instructional practices. In this article ...


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