Non-linear Dynamics Commons^™

Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov

Book chapter/book

This volume contains selected papers based on the talks,presentedat the Conference Integrability, Recursion Operators and Soliton Interactions, held in Sofia, Bulgaria (29-31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. …

Examples Of G-Strand Equations, Darryl Holm, Rossen Ivanov

Conference papers

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincare´ reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of G-strand constructions, including …

Neutrosophic Theory And Its Applications : Collected Papers - Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every entity tends to be …

Collected Papers, Vol. V, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Hamiltonian Approach To The Modeling Of Internal Geophysical Waves With Vorticity, Alan Compelli

Articles

We examine a simplified model of internal geophysical waves in a rotational 2-dimensional water-wave system, under the influence of Coriolis forces and with gravitationally induced waves. The system consists of a lower medium, bound underneath by an impermeable flat bed, and an upper lid. The 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of its conjugate variables and perform a variable transformation to show that it has canonical Hamiltonian structure. We then linearize the system, …

Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi

Articles

We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.

Hamiltonian Formulation Of 2 Bounded Immiscible Media With Constant Non-Zero Vorticities And A Common Interface, Alan Compelli

Articles

We examine a 2-dimensional water-wave system, with gravitationally induced waves, consisting of a lower medium bound underneath by an impermeable flat bed and an upper medium bound above by an impermeable lid such that the 2 media have a free common interface. Both media have constant density and constant (non-zero) vorticity. By examining the governing equations of the system we calculate the Hamiltonian of the system in terms of it's conjugate variables and per- form a variable transformation to show that it has canonical Hamiltonian structure.

Two-Source Energy Balance Model To Calculate E, T, And Et: Comparison Of Priestley-Taylor And Penman-Monteith Formulations And Two Time Scaling Methods, Paul D. Colaizzi, Nurit Agam, Judy A. Tolk, Steven R. Evett, Terry A. Howell, Prasanna H. Gowda, Susan A. O'Shaughnessy, William P. Kustas, Martha C. Anderson

United States Department of Agriculture-Agricultural Research Service / University of Nebraska-Lincoln: Faculty Publications

The two-source energy balance (TSEB) model calculates the energy balance of the soil-canopy-atmosphere continuum, where transpiration is initially determined by the Priestley-Taylor equation. The TSEB was revised recently using the Penman-Monteith equation to replace the Priestley-Taylor formulation, thus better accounting for the impact of large and varying vapor pressure deficits (VPD) typical of advective, semiarid climates. This study is a comparison of the Priestley- Taylor and Penman-Monteith versions of the TSEB (termed TSEB-PT and TSEB-PM, respectively). Evaporation (E), transpiration (T), and evapotranspiration (ET) calculated by the TSEB-PT and TSEB-PM versions were compared to measurements obtained with microlysimeters, sap flow gauges, …

Matrix G-Strands, Darryl Holm, Rossen Ivanov

Articles

We discuss three examples in which one may extend integrable Euler–Poincare ordinary differential equations to integrable Euler–Poincare partial differential
equations in the matrix G-Strand context. After describing matrix G-Strand examples for SO(3) and SO(4) we turn our attention to SE(3) where the matrix G-Strand equations recover the exact rod theory in the convective representation. We then find a zero curvature representation of these equations and establish the conditions under which they are completely integrable. Thus, the G-Strand equations turn out to be a rich source of integrable systems. The treatment is meant to be expository and most concepts are explained …

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …

Zakharov-Shabat System With Constant Boundary Conditions. Reflectionless Potentials And End Point Singularities, Tihomir Valchev, Rossen Ivanov, Vladimir Gerdjikov

Conference papers

We consider scalar defocusing nonlinear Schroedinger equation with constant boundary conditions. We aim here to provide a self contained pedagogical exposition of the most important facts regarding integrability of that classical evolution equation. It comprises the following topics: direct and inverse scattering problem and the dressing method.

Modelling And Analysis On Noisy Financial Time Series, Jinsong Leng

Research outputs 2014 to 2021

Building the prediction model(s) from the historical time series has attracted many researchers in last few decades. For example, the traders of hedge funds and experts in agriculture are demanding the precise models to make the prediction of the possible trends and cycles. Even though many statistical or machine learning (ML) models have been proposed, however, there are no universal solutions available to resolve such particular prob-lem. In this paper, the powerful forward-backward non-linear filter and wavelet-based denoising method are introduced to remove the high level of noise embedded in financial time series. With the filtered time series, the statistical …

Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa Michelle Slaughter

Physics

This experiment uses an electromagnetic shaker to produce standing wave patterns on the surface of a vertically oscillating sample of silicon liquid. These surface waves, known as Faraday waves, form shapes such as squares, lines, and hexagons. They are known to be dependent upon the frequency and amplitude of the forcing as well as on the viscosity and depth of the liquid in the dish. At a depth of 4mm and for various silicon liquids having kinematic viscosities of 10, 20, and 38 cSt, we determined the acceleration at which patterns form for frequencies between 10 and 60 Hz. For …

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mathematics Faculty Publications

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …

Universal Scaling And Intrinsic Classification Of Electro-Mechanical Actuators, Sambit Palit, Ankit Jain, Muhammad A. Alam

Birck and NCN Publications

Actuation characteristics of electromechanical (EM) actuators have traditionally been studied for a few specific regular electrode geometries and support (anchor) configurations. The ability to predict actuation characteristics of electrodes of arbitrary geometries and complex support configurations relevant for broad range of applications in switching, displays, and varactors, however, remains an open problem. In this article, we provide four universal scaling relationships for EM actuation characteristics that depend only on the mechanical support configuration and the corresponding electrode geometries, but are independent of the specific geometrical dimensions and material properties of these actuators. These scaling relationships offer an intrinsic classification for …

On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov

Articles

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.

Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons

Articles

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid being zero there.

Project Haiti 2012: Providing An Experiential Learning Experience Through The Design And Delivery Of A Water Purifier In Haiti, Yung Wong, Johnathon Camp, Shavin Pinto, Kyle Fennesy, Marc Compere, Yan Tang

Publications

In this paper, we share our experiences and lessons learned from Project Haiti 2012, a project to design and install a water purification system serving 20,000 people per day in the largest tent city in Haiti. Project Haiti 2012 was the third and largest system we have built for Haitians and represents a huge success for all participants and stakeholders. This paper discusses the unique experiential learning opportunity involved in the design and delivery of the water purifier in a foreign developing country. Multiple positive educational, social, and economic outcomes were achieved including students applying knowledge gained from coursework towards …

G-Strands And Peakon Collisions On Diff(R), Darryl Holm, Rossen Ivanov

Articles

A G-strand is a map g : R x R --> G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. Some G-strands on finite-dimensional groups satisfy 1+1 space-time evolutionary equations that admit soliton solutions as completely integrable Hamiltonian systems. For example, the SO(3)-strand equations may be regarded physically as integrable dynamics for solitons on a continuous spin chain. Previous work has shown that G-strands for diffeomorphisms on the real line possess solutions with singular support (e.g. peakons). This paper studies collisions of such singular solutions of G-strands when G = Diff( …