By Christos H Skiadas, Ioannis Dimotikalis, Charilaos Skiadas

This quantity comprises the simplest papers provided on the CHAOS 2008 overseas convention on Chaotic Modeling, Simulation and purposes. It presents a worthy choice of new principles, tools, and strategies within the box of nonlinear dynamics, chaos, fractals and their purposes more often than not technological know-how and in engineering sciences. It touches on many fields similar to chaos, dynamical structures, nonlinear platforms, fractals and chaotic attractors. It additionally covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic regulate, and chaos in economic system and markets, and chaotic simulations; therefore, containing state of the art interdisciplinary study with high-interest purposes. those contributions current new options by way of examining the suitable info and during using contemporary advances in several fields, particularly in chaotic simulation equipment and methods.

Show description

Read or Download Topics on Chaotic Systems: Selected Papers from Chaos 2008 International Conference PDF

Best hydraulics books

Topological Methods in Hydrodynamics

This e-book develops the differential geometrical and topological issues of view in hydrodynamics. It discusses interactions of hydrodynamics with a large choice of mathematical domain names reminiscent of concept of lie teams, differential geometry, topology of knots, magnetic dynamo concept, calculus of adaptations and hamiltonian mechanics.

Design and Installation of Marine Pipelines

This entire guide on submarine pipeline platforms covers a vast spectrum of subject matters from making plans and placement investigations, procurement and layout, to set up and commissioning. It considers instructions for the alternative of layout parameters, calculation equipment and building methods. it really is in line with restrict kingdom layout with partial safeguard coefficients.

Environmental Impacts of Hydraulic Fracturing

There's a powerful want for innovation and the advance of conceivable renewable power resources. fresh technological advances permit traditional gasoline offers -- formerly believed inaccessible or nonexistent -- to be stumbled on, mined, and processed for either commercial and buyer use. The expertise, a arguable procedure that's however known as hydraulic fracturing, fracking, fracing, or hydrofracking, has enormously increased traditional fuel creation within the usa.

Applied Groundwater Modeling

This moment version is greatly revised all through with multiplied dialogue of modeling basics and assurance of advances in version calibration and uncertainty research which are revolutionizing the technology of groundwater modeling. The textual content is meant for undergraduate and graduate point classes in utilized groundwater modeling and as a complete reference for environmental experts and scientists/engineers in and governmental corporations.

Extra info for Topics on Chaotic Systems: Selected Papers from Chaos 2008 International Conference

Example text

A. Cornell, Phys. Rev. Lett. 77, 4984 (1996) 11. A. S. Rokhsar, Phys. Rev. A 55, 4346 (1997) 12. F. London, Nature 141, 643 (1938) Chapter 3 Gross-Pitaevskii Model of the Condensate Abstract The Gross-Pitaevskii equation (GPE) is a successful and well-established model for describing an atomic Bose-Einstein condensate. Here we introduce this model, along with its assumptions. Throughout the rest of this chapter we explore its properties and key time-independent solutions. 1 The Gross-Pitaevskii Equation We assume that the gas is at zero temperature, such that the thermal gas and thermallydriven excitations of the condensate are non-existent.

13) The continuity equation expresses conservation of the number of atoms (or, when written in terms of ρ(r, t), conservation of mass). By integrating the equation over a given volume, we see that, if the number of atoms changes in that volume, it is because fluid has moved in or out of it. The second equation is, ∂v = −∇ m ∂t √ 2 1 2 ∇2 n mv + V + gn − √ 2 2m n . 14) √ √ The ∇ 2 n/ n term is termed the quantum pressure term (see below). 15) where P and P are respectively the pressure and the quantum pressure, P= gn 2 , 2 P =− 2 4m n∇ 2 (ln n).

23) V (r) = ωr2 r 2 , 2 where r 2 = x 2 + y 2 + z 2 . The characteristic length scale of this potential is the harmonic oscillator length, /mωr . 24) r = There is no general analytic solution for the ground state (lowest energy) solution of the BEC in a harmonic trap; usually the ground state is found by numerically solving Eq. 9). However, there exist useful analytic results for certain regimes which we describe below. It is useful to work in terms of the interaction parameter,2 N as / r . Below we distinguish the following cases: no interactions, strong repulsive 1) and weak interactions (|N as / r | 1).

Download PDF sample

Rated 4.76 of 5 – based on 46 votes