Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems

The authors generalize notions of transport in phase space associated with the classical Poincare map reduction of a periodically forced two-dimensional system to apply to a sequence of nonautonomous maps derived from a quasiperiodically forced two-dimensional system. They obtain a global picture of the dynamics in homoclinic and heteroclinic tangles using a sequence of time-dependent two-dimensional lobe structures derived from the invariant global stable and unstable manifolds of one or more normally hyperbolic invariant sets in a Poincare section of an associated autonomous system phase space. The invariant manifold geometry is studied via a generalized Melnikov function. Transport in phase space is specified in terms of two-dimensional lobes mapping from one to another within the sequence of lobe structures, which provides the framework for studying several features of the dynamics associated with chaotic tangles

The Anticipated Economic Effect of a North American Free Trade Area on Business in the North American Context

North American free trade area and commerc

The United States\u27 Potential Contribution to Canada\u27s Technological Policy Goals

Canada-United States Economic Ties: The Technology Contex

The United States\u27 Potential Contribution to Canada\u27s Technological Policy Goals

Canada-United States Economic Ties: The Technology Contex

Dynamics associated with a quasiperiodically forced Morse oscillator: Application to molecular dissociation

The dynamics associated with a quasiperiodically forced Morse oscillator is studied as a classical model for molecular dissociation under external quasiperiodic electromagnetic forcing. The forcing entails destruction of phase-space barriers, allowing escape from bounded to unbounded motion. In contrast to the ubiquitous Poincaré map reduction of a periodically forced system, we derive a sequence of nonautonomous maps from the quasiperiodically forced system. We obtain a global picture of the dynamics, i.e., of transport in phase space, using a sequence of time-dependent two-dimensional lobe structures derived from the invariant homoclinic tangle of a persisting invariant saddle-type torus in a Poincaré section of an associated autonomous system phase space. Transport is specified in terms of two-dimensional lobes mapping from one to another within the sequence of lobe structures, and this provides the framework for studying basic features of molecular dissociation in the context of classical phase-space trajectories. We obtain a precise criterion for discerning between bounded and unbounded motion in the context of the forced problem. We identify and measure analytically the flux associated with the transition between bounded and unbounded motion, and study dissociation rates for a variety of initial phase-space ensembles, such as an even or weighted distribution of points in phase space, or a distribution on a particular level set of the unperturbed Hamiltonian (corresponding to a quantum state). A double-phase-slice sampling method allows exact numerical computation of dissociation rates. We compare single- and two-frequency forcing. Infinite-time average flux is maximal in a particular single-frequency limit; however, lobe penetration of the level sets of the unperturbed Hamiltonian can be maximal in the two-frequency case. The variation of lobe areas in the two-frequency problem gives one added freedom to enhance or diminish aspects of phase-space transport on finite time scales for a fixed infinite-time average flux, and for both types of forcing the geometry of lobes is relevant. The chaotic nature of the dynamics is understood in terms of a traveling horseshoe map sequence

Statistical relaxation under nonturbulent chaotic flows: Non-Gaussian high-stretch tails of finite-time Lyapunov exponent distributions

We observe that high-stretch tails of finite-time Lyapunov exponent distributions associated with interfaces evolving under a class of nonturbulent chaotic flows can range from essentially Gaussian tails to nearly exponential tails, and show that the non-Gaussian deviations can have a significant effect on interfacial evolution. This observation motivates new insight into stretch processes under chaotic flows

Developing soil cation exchange capacity pedotransfer functions using regression and neural networks and the effect of soil partitioning on the accuracy and precision of estimation

Soil fertility measures such as cation exchange capacity (CEC) may be used in upgrading soil maps and improving their quality. Direct measurement of CEC is costly and laborious. Therefore, indirect estimation of CEC via pedotransfer functions may be appropriate and effective. Several delineations of two consociation map units consisting of two soil families (Shahrak series and Chaharmahal series), located in Shahrekord plain, Iran were identified. Soil samples were taken from two depths of 0-20 and 30-50 cm and were analyzed in lab for several physico-chemical properties. Clay and organic matter percentages as well as moisture content at -1500 kpa best correlated with CEC. Pedotransfer functions were successfully developed using regression and neural networks. Soil partitioning increased the accuracy and precision of functions. Compared to regression, neural network technique resulted in pedotransfer functions with higher R2 and lower RMSE