Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Non-linear Dynamics (5)
- Partial Differential Equations (4)
- Ordinary Differential Equations and Applied Dynamics (3)
- Engineering (2)
- Mathematics (2)
-
- Other Applied Mathematics (2)
- Physics (2)
- Aerodynamics and Fluid Mechanics (1)
- Aerospace Engineering (1)
- Atomic, Molecular and Optical Physics (1)
- Biological Psychology (1)
- Computational Neuroscience (1)
- Developmental Psychology (1)
- Dynamical Systems (1)
- Electrical and Computer Engineering (1)
- Electrical and Electronics (1)
- Fluid Dynamics (1)
- Life Sciences (1)
- Medicine and Health Sciences (1)
- Neuroscience and Neurobiology (1)
- Psychiatry and Psychology (1)
- Psychology (1)
- Quantitative Psychology (1)
- Social and Behavioral Sciences (1)
- Systems Neuroscience (1)
- Institution
- Keyword
-
- Integrable systems (2)
- Solitons (2)
- <p>Differential equations.</p> <p>Difference equations.</p> <p>Differentiable dynamical systems.</p> (1)
- Action potential (1)
- Boundary value problems (1)
-
- Camassa-Holm equation (1)
- Cerebral palsy (1)
- Computational fluid dynamics (1)
- Crank-Nicolson method (1)
- Delayed development (1)
- Diffusion based models (1)
- Eigenvalues (1)
- Electromagnetic fields and waves (1)
- Electronics (1)
- Exact inverse scattering theory (1)
- Excitable membrane (1)
- Fixed point theorem (1)
- Flow structures (1)
- Fluid equations (1)
- Fluid flow (1)
- Fractaional calculus (1)
- Fractional diffusion (1)
- Fractional-step theta scheme (1)
- Green's function (1)
- I-V characteristics (1)
- Infant (1)
- Intermediate scattering models (1)
- Inverse Scattering (1)
- Inverse Scattering Method (1)
- Inverse scattering solutions (1)
- Publication
- Publication Type
Articles 1 - 10 of 10
Full-Text Articles in Dynamic Systems
Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge
Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge
Other resources
Electromagnetic scattering theory is fundamental to understanding the interaction between electromagnetic waves and inhomogeneous dielectric materials. The theory unpins the engineering of electromagnetic imaging systems over a broad range of frequencies, from optics to radio and microwave imaging, for example. Developing accurate scattering models is particularly important in the field of image understanding and the interpretation of electromagnetic signals generated by scattering events. To this end there are a number of approaches that can be taken. For relatively simple geometric configurations, approximation methods are used to develop a transformation from the object plane (where scattering events take place) to the …
Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda
Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda
Undergraduate Research Opportunities Program (UROP)
We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop.
Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori
Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori
All HMC Faculty Publications and Research
Analysis of acoustic phonons modulated due to the surfaces of a free-standing semiconductor plate and their deformation-potential interaction with electrons are presented. The form factor for electron-modulated acoustic phonon interaction is formulated and analyzed in detail. The form factor at zero in-plane phonon wave vector satisfies sum rules regardless of electron wave function. The form factor is larger than that calculated using bulk phonons, leading to a higher scattering rate and lower electron mobility. When properly normalized, the form factors lie on a universal curve regardless of plate thickness and material.
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Theses, Dissertations and Capstones
This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …
Two Component Integrable Systems Modelling Shallow Water Waves, Rossen Ivanov
Two Component Integrable Systems Modelling Shallow Water Waves, Rossen Ivanov
Conference papers
Our aim is to describe the derivation of shallow water model equations for the constant vorticity case and to demonstrate how these equations can be related to two integrable systems: a two component integrable generalization of the Camassa-Holm equation and the Kaup - Boussinesq system.
Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy
Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy
All HMC Faculty Publications and Research
A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …
Nonlinear Dynamics Of Infant Sitting Postural Control, Joan E. Deffeyes
Nonlinear Dynamics Of Infant Sitting Postural Control, Joan E. Deffeyes
Department of Psychology: Dissertations, Theses, and Student Research
Sitting is one of the first developmental milestones that an infant achieves. Thus measurements of sitting posture present an opportunity to assess sensorimotor development at a young age, in order to identify infants who might benefit from therapeutic intervention, and to monitor the efficacy of the intervention. Sitting postural sway data was collected using a force plate from infants with typical development, and from infants with delayed development, where the delay in development was due to cerebral palsy in most of the infants in the study. The center of pressure time series from the infant sitting was subjected to a …
Generalised Fourier Transform And Perturbations To Soliton Equations, Georgi Grahovski, Rossen Ivanov
Generalised Fourier Transform And Perturbations To Soliton Equations, Georgi Grahovski, Rossen Ivanov
Articles
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton …
Equations Of The Camassa-Holm Hierarchy, Rossen Ivanov
Equations Of The Camassa-Holm Hierarchy, Rossen Ivanov
Articles
The squared eigenfunctions of the spectral problem associated with the CamassaHolm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized Fourier transform (GFT). All the fundamental properties of the CH equation, such as the integrals of motion, the description of the equations of the whole hierarchy, and their Hamiltonian structures, can be naturally expressed using the completeness relation and the recursion operator, whose eigenfunctions are the squared solutions. Using the GFT, we explicitly describe some members of the CH hierarchy, including integrable deformations for the CH …
Conceptual Circuit Models Of Neurons, Bo Deng
Conceptual Circuit Models Of Neurons, Bo Deng
Department of Mathematics: Faculty Publications
A systematic circuit approach tomodel neurons with ion pump is presented here by which the voltage-gated current channels are modeled as conductors, the diffusion-induced current channels are modeled as negative resistors, and the one-way ion pumps are modeled as one-way inductors. The newly synthesized models are different from the type of models based on Hodgkin-Huxley (HH) approach which aggregates the electro, the diffusive, and the pump channels of each ion into one conductance channel. We show that our new models not only recover many known properties of the HH type models but also exhibit some new that cannot be extracted …