Dynamical Systems Commons^™

Discrete Breathers At The Interface Between A Diatomic And A Monoatomic Granular Chain, C. Hoogeboom, G. Theocharis, Panos Kevrekidis

Panos Kevrekidis

In the present work, we develop a systematic examination of the existence, stability, and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an “interface breather” is more robust than its bulk diatomic counterpart throughout the gap of the linear spectrum. The latter linear spectral gap needs to exist for the breather state to arise and the relevant spectral conditions are discussed. We illustrate the minimal excitation conditions under which such an interface breather can be “nucleated” and analyze its apparently weak interaction with regular highly nonlinear …

Compactons In Nonlinear Schrödinger Lattices With Strong Nonlinearity Management, F. Kh. Abdullaev, Panos Kevrekidis, M. Salerno

Panos Kevrekidis

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling depends on modulation parameters {\it and} on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multi-site stable discrete compactons in nonlinear optical waveguide and BEC arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.

Energetyka Niskoemisyjna, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells

Articles

We develop the Inverse Scattering Transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an sl(3) Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.

Spatiotemporal Dynamics In A Lower Montane Tropical Rainforest, Robert Michael Lawton

Doctoral Dissertations

Disturbance in a forest’s canopy, whether caused by treefall, limbfall, landslide, or fire determines not only the distribution of well-lit patches at any given time, but also the ways in which the forest changes over time. In this dissertation, I use a 25 year record of treefall gap formation find a novel and highly patterned process of forest disturbance and regeneration, providing a local mechanism by examining the factors that influence the likelihood of treefall. I then develop a stochastic cellular automaton for disturbance and regeneration based on the analysis of this long term data set and illustrate the potential …

Reconstructability Analysis Of Elementary Cellular Automata, Martin Zwick, Hui Shi

Systems Science Friday Noon Seminar Series

Reconstructability analysis is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss (reduction in constraint) into lower ordinality relations. Set-theoretic reconstructability analysis (SRA) is used to characterize the mappings of elementary cellular automata. The degree of lossless decomposition possible for each mapping is more effective than the λ parameter (Walker & Ashby, Langton) as a predictor of chaotic dynamics.

Complete SRA yields not only the simplest lossless structure but also a vector of losses of all decomposed structures, indexed by parameter, τ. This vector subsumes λ, Wuensche’s Z parameter, and Walker …

Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher

Theses and Dissertations

This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, T Kapitula, Kjh Law, Pg Kevrekidis

Panos Kevrekidis

In this paper we consider the existence and spectral stability of excited states in two-species Bose–Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov–Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.

Grafika Inżynierska Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Projektowanie Procesów Biotechnologicznych Proj., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Projektowanie I Optymalizacja Procesów Proj., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Metody Numeryczne Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Odnawialne Źródła Energii W., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger

CMC Senior Theses

Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.

Exponential Growth Rate Of Paths And Its Connection With Dynamics, Pengfei Zhang

Pengfei Zhang

No abstract provided.