Decoherence and coherent population transfer between two coupled systems

We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled fi om the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can he completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. in particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases. in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and Lambda-type three-level atoms and two nonidentical tao-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in Lambda-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.

Coupled experimental and thermodynamic modeling studies for metallurgical smelting and coal combustion slag systems

An extensive research program focused on the characterization of various metallurgical complex smelting and coal combustion slags is being undertaken. The research combines both experimental and thermodynamic modeling studies. The approach is illustrated by work on the PbO-ZnO-Al2O3-FeO-Fe2O3-CaO-SiO2 system. Experimental measurements of the liquidus and solidus have been undertaken under oxidizing and reducing conditions using equilibration, quenching, and electron probe X-ray microanalysis. The experimental program has been planned so as to obtain data for thermodynamic model development as well as for pseudo-ternary Liquidus diagrams that can be used directly by process operators. Thermodynamic modeling has been carried out using the computer system FACT, which contains thermodynamic databases with over 5000 compounds and evaluated solution models. The FACT package is used for the calculation of multiphase equilibria in multicomponent systems of industrial interest. A modified quasi-chemical solution model is used for the liquid slag phase. New optimizations have been carried out, which significantly improve the accuracy of the thermodynamic models for lead/zinc smelting and coal combustion processes. Examples of experimentally determined and calculated liquidus diagrams are presented. These examples provide information of direct relevance to various metallurgical smelting and coal combustion processes.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Synchronization properties of multi-oscillator circadian systems

Dissertation presented to obtain the Ph.D degree in Computational Biology

Quantum phase transitions in magnetic systems: application of coupled cluster method

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2009

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

Studies on the effect of randoniness on the synchronization of coupled systems and on the dynamics of intermittently driven systems

It has been shown recently that systems driven with random pulses show the signature of chaos ,even without non linear dynamics.This shows that the relation between randomness and chaos is much closer than it was understood earlier .The effect of random perturbations on synchronization can be also different. In some cases identical random perturbations acting on two different chaotic systems induce synchronizations. However most commonly ,the effect of random fluctuations on the synchronizations of chaotic system is to destroy synchronization. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. The author tries to unearth yet another manifestation of randomness on chaos and sychroniztion. This thesis is organized into six chapters.

Closely coupled behaviour in networked robot systems

Multiple cooperating robot systems may be required to take up a closely coupled configuration in order to perform a task. An example is extended baseline stereo (EBS), requiring that two robots must establish and maintain for a certain period of time a constrained kinematic relationship to each other. In this paper we report on the development of a networked robotics framework for modular, distributed robot systems that supports the creation of such configurations. The framework incorporates a query mechanism to locate modules distributed across the two robot systems. The work presented in this paper introduces special mechanisms to model the kinematic constraint and its instantiation. The EBS configuration is used as a case study and experimental implementation to demonstrate the approach.

Local oscillator phase lock under multipath for video deghoster systems

Under multipath conditions, standard Video Intermediate Frequency (VIF) detectors generate a local oscillator phase error and consequently produce a dispersed non-ideal detected video signal due to the presence of additional IF carriers. The dispersed video causes problems when attempting to identify and remove the multipath interference, or ghosts, by the use of Digital Signal Processing and digital filtering. A digital phase lock system is presented which derives the correct phase for synchronous detection in the presence of multipath by using correlation information that has already been calculated as part of the deghosting process. As a result, the video deghoster system is made simpler, faster and more economical.