Non-linear Dynamics Commons^™

Geometrical Model For A Particle On A Rough Inclined Surface, Giovani L. Vasconcelos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which the dynamics is described by a one-dimensional map. This map is studied in detail and it is shown to exhibit several dynamical regimes (steady state, chaotic behavior, and accelerated motion) as the model parameters vary. A phase diagram showing the corresponding domain of existence for these regimes is presented. The model is also found to be in good qualitative agreement …

Contraction Of The Model For The Bray-Liebhafsky Oscillatory Reaction By Eliminating Intermediate I2o, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Spectral Features Of The Stimulated Raman Backscattering Of Modulated Laser Pulses In A Plasma, Nikolai E. Andreev, Serguei Y. Kalmykov

Serge Youri Kalmykov

The characteristic features of the stimulated Raman backscattering of short modulated (multi-frequency) laser pulses in an underdense plasma are investigated. A laser pulse consisting of a given pair of spectral components with the frequency difference close to the double plasma frequency is studied in the weak mode coupling approximation. The scattering of the component with the higher frequency is shown to be a five-wave resonant process, and the conditions under which this process is totally suppressed are found. The scattering of the component with the lower frequency is an ordinary three-wave decay process without any suppression. When the difference between …

Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu

Andrei Ludu

Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated. Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discussed. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one re-obtains the well-known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear …

Mass Transfer With Chemical Reaction In The Process Of Ammonia Desorption From Aqueous Solutions Containing Carbon Dioxide, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Backward Stimulated Raman Scattering Of A Modulated Laser Pulse In Plasmas, Nikolai E. Andreev, Serguei Y. Kalmykov

Serge Youri Kalmykov

The specific features of backward stimulated Raman scattering (BSRS) of a short modulated (multi-frequency) laser pulse in underdense plasmas are studied. The effect of resonant suppression of the BSRS of higher frequency pulse components is explored. For an arbitrary pair of pulse components, in the conditions of weak coupling, it is demonstrated that the backscattering of a higher frequency laser pulse component is a five-wave resonant process at a frequency difference between the components close to the double plasma frequency. In the conditions of strong coupling the backscattering of neither pulse component is suppressed and the spectrum of the instability …

Pseudo-Steady States In The Model Of The Bray-Liebhafsky Oscillatory Reaction, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upper- and and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the moduli of the eigenvalues of the underlying affine contraction are all equal (this includes Jordan blocks). The tiles we discuss play an important role in the theory of wavelets. We calculate the dimension for a …

Nonlinear Liquid Drop Model. Cnoidal Waves, Andrei Ludu

Andrei Ludu

No abstract provided.

Generalization Kdv Equation For Fluid Dynamics And Quantum Algebras, Andrei Ludu

Andrei Ludu

No abstract provided.

Alpha+28si Cluster Structure As Solitons On The Nuclear Surface, Andrei Ludu

Andrei Ludu

No abstract provided.

Quasimolecular Resonances In Alpha+20ne Systems, Andrei Ludu

Andrei Ludu

No abstract provided.

Dynamic Phase Steepening In Alfven Waves, Stephen R. Granade

Honors Theses

Our solar system contains more activity and complexity than can be seen through a telescope. One such "invisible" phenomenon is the solar wind, created by a steady stream of particles blasted away from the sun in all directions. The sun's donut-shaped magnetic field lines channel this stream. Particles moving along the field lines perform an intricate helical dance, with ions winding one way and electrons the other.

The solar wind shapes and is shaped by the magnetic fields of the planets and the sun. If left undisturbed by outside influences, the earth's magnetic field, like the sun's, would resemble a …

Transhipment Problem, Salt Exportation, Brian Hogben

Theses : Honours

In order to improve its shipping operations a major salt exporter needs to reduce costs, increase market share and improve customer service. This thesis examines the use of linear (LP) and nonlinear programming (NLP) as a means of solving a nonlinear transhipment problem associated with the export of salt. Tho feasibility of using a LP or NLP approach is explored, taking into consideration the computational time and useability of the models. To meet the demands of their customers the company currently uses heuristic methods to allocate varying size ships to different routes. To remain competitive the shipping options that are …

Sliding Mode Control Of The Systems With Uncertain Direction Of Control Vector, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.

Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic

Aviation Department Publications

In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is …

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

Sliding-Mode Observers Based On Equivalent Control Method, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.

Cluster As Solitons On The Nuclear Surface, Andrei Ludu

Andrei Ludu

No abstract provided.

On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from …

Monte Carlo Study Of Estimation For Nonlinear Models Subjected To Linearizing Transformations, Jeff Kennington, James E. Dunn

Journal of the Arkansas Academy of Science

No abstract provided.