Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Automated Reasoning About Classical Mechanics

In recent years, researchers in artificial intelligence have become interested in replicating human physical reasoning talents in computers. One of the most important skills in this area is predicting how physical systems will behave. This thesis discusses an implemented program that generates algebraic descriptions of how systems of rigid bodies evolve over time. Discussion about the design of this program identifies a physical reasoning paradigm and knowledge representation approach based on mathematical model construction and algebraic reasoning. This paradigm offers several advantages over methods that have become popular in the field, and seems promising for reasoning about a wide variety of classical mechanics problems.

La incidencia de la complejidad en el ambiente organizacional

La realidad de la complejidad en las organizaciones actuales " Kellert: Hay que ver la teoría del caos como una nueva y revolucionaria ciencia que es discontinua radicalmente con la tradición occidental de objetivar y controlar la naturaleza pues falsifica tanto el carácter de la teoría del caos y la historia de la ciencia. ... cualquier expectativa de que la teoría del caos es el re-encantamiento del mundo se reunirá con la decepción“ La complejidad a lo largo de la segunda mitad del siglo XX, fue adquiriendo importancia a partir de los trabajos desarrollados desde diferentes disciplinas, como respuesta a los vertiginosos avances y a la aparición de nuevas tecnologías que están cambiando nuestra forma de vida y generando nuevo conocimiento. Estamos acostumbrados a ver el mundo de manera lineal, conforme a nuestras formación racionalista, y el ser humano desligado de la naturaleza y su proceso evolutivo, en ese sentido desde la aparición de las TCP, encontramos nuevas formas de entender, tanto los sistemas físicos, biológicos como los sociales humanos. El objetivo de este escrito e hipótesis es plantear la contradicción que se presenta al interior de las organizaciones desde el punto de vista de la realidad organizacional, realizando una mirada rápida al desarrollo las teorías que hoy en día componen lo que entendemos como complejidad, para terminar en el planteamiento de cómo ella se presenta en el interior de las organizaciones. En donde la toma de decisiones por la magnitud de información existe, se vuelven complejas y terminamos en la búsqueda de modelos que nos permitan un manejo adecuado de las organizaciones.

Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

A unified theory of balance in the extratropics

Many physical systems exhibit dynamics with vastly different time scales. Often the different motions interact only weakly and the slow dynamics is naturally constrained to a subspace of phase space, in the vicinity of a slow manifold. In geophysical fluid dynamics this reduction in phase space is called balance. Classically, balance is understood by way of the Rossby number R or the Froude number F; either R ≪ 1 or F ≪ 1. We examined the shallow-water equations and Boussinesq equations on an f -plane and determined a dimensionless parameter _, small values of which imply a time-scale separation. In terms of R and F, ∈= RF/√(R^2+R^2 ) We then developed a unified theory of (extratropical) balance based on _ that includes all cases of small R and/or small F. The leading-order systems are ensured to be Hamiltonian and turn out to be governed by the quasi-geostrophic potential-vorticity equation. However, the height field is not necessarily in geostrophic balance, so the leading-order dynamics are more general than in quasi-geostrophy. Thus the quasi-geostrophic potential-vorticity equation (as distinct from the quasi-geostrophic dynamics) is valid more generally than its traditional derivation would suggest. In the case of the Boussinesq equations, we have found that balanced dynamics generally implies hydrostatic balance without any assumption on the aspect ratio; only when the Froude number is not small and it is the Rossby number that guarantees a timescale separation must we impose the requirement of a small aspect ratio to ensure hydrostatic balance.

Hamiltonian geophysical fluid dynamics

Hamiltonian dynamics describes the evolution of conservative physical systems. Originally developed as a generalization of Newtonian mechanics, describing gravitationally driven motion from the simple pendulum to celestial mechanics, it also applies to such diverse areas of physics as quantum mechanics, quantum field theory, statistical mechanics, electromagnetism, and optics – in short, to any physical system for which dissipation is negligible. Dynamical meteorology consists of the fundamental laws of physics, including Newton’s second law. For many purposes, diabatic and viscous processes can be neglected and the equations are then conservative. (For example, in idealized modeling studies, dissipation is often only present for numerical reasons and is kept as small as possible.) In such cases dynamical meteorology obeys Hamiltonian dynamics. Even when nonconservative processes are not negligible, it often turns out that separate analysis of the conservative dynamics, which fully describes the nonlinear interactions, is essential for an understanding of the complete system, and the Hamiltonian description can play a useful role in this respect. Energy budgets and momentum transfer by waves are but two examples.

Abstract platforms of computation

Computational formalisms have been pushing the boundaries of the field of computing for the last 80 years and much debate has surrounded what computing entails; what it is, and what it is not. This paper seeks to explore the boundaries of the ideas of computation and provide a framework for enabling a constructive discussion of computational ideas. First, a review of computing is given, ranging from Turing Machines to interactive computing. Then, a variety of natural physical systems are considered for their computational qualities. From this exploration, a framework is presented under which all dynamical systems can be considered as instances of the class of abstract computational platforms. An abstract computational platform is defined by both its intrinsic dynamics and how it allows computation that is meaningful to an external agent through the configuration of constraints upon those dynamics. It is asserted that a platform’s computational expressiveness is directly related to the freedom with which constraints can be placed. Finally, the requirements for a formal constraint description language are considered and it is proposed that Abstract State Machines may provide a reasonable basis for such a language.

Exploration of a first year university multimedia module on field geology

As part of the teaching programme within a first year university unit on the earth’s physical systems, a ‘virtual reality’ field trip has been developed to support field studies relating to geological materials and landscape history. This module aims to increase student understanding of the use of geological features in the evaluation of geological / landscape history. The module has various applications in the curriculum. For students attending a weekend excursion, the module is available as an adjunct to actual field studies and can be used by students as either a digital pre-lab or as an excursion review tutorial. For students not attending a weekend excursion (i.e. off campus students), it is used as a digital ‘virtual reality’ substitute for field site inspection. The module has simple linked interactive and dynamic image base digital media that provide a framework in which the geology and landscape history of excursion sites can be explored. This module is delivered as a website via CD, but can also be integrated with the 'online interface' for this unit via a QuickTime reference movie loaded inside a relevant 'Deakin (University) Studies Online’ web page. The latter strategy enables assimilation of large multimedia files into online teaching formats

Quantum bioenergetics, mental boundaries and affective response : a randomized placebo-controlled pilot study

Previous research has demonstrated the effects of ostensible subtle energy on physical systems and subjective experience. However, one subtle energy technique that has been neglected by previous studies, despite anecdotal support for its efficacy, is Quantum BioEnergetics (QBE). Furthermore, personality traits that influence subtle energy effects remain unclear, and previous experimental studies have not investigated the constructs of Love and Joy, despite qualitative and anecdotal reports indicating that these variants of positive affect are essential elements of the subtle energy experience. The aim of the present study was to investigate experimentally the effects of QBE, and the personality trait Mental Boundaries, on positive and negative affect. Participants (N = 69) were administered the Boundary Questionnaire Short Form to quantify Boundaries, and then randomly assigned to one of three conditions: QBE, Placebo ("sham"), or Control. Affect was retrospectively assessed using the Positive and Negative Affect subdimensions of the Phenomenology of Consciousness Inventory (PCI). As predicted, a significant multivariate effect for condition was found with regards to the PCI subdimensions: Joy, Sexual Excitement, Love, Anger, Sadness, and Fear. In contrast to our expectations, a significant multivariate effect was not found for Boundaries with regards to the combined PCI-Affect variables. As hypothesized, significant interactions were found between condition and Boundaries with regards to Positive Affect, Love and Joy, with the QBE/Thin Boundaries factorial combination associated with the highest mean scores for these dependent variables. It will be prudent to ascertain whether these results are replicated in a larger sample and a placebo condition that improves on the standard randomized placebocontrolled protocols of previous subtle energy research.

An improved stochastic modeling of opportunistic routing in vehicular CPS

Vehicular Cyber-Physical System (VCPS) provides CPS services via exploring the sensing, computing and communication capabilities on vehicles. VCPS is deeply influenced by the performance of the underlying vehicular network with intermittent connections, which make existing routing solutions hardly to be applied directly. Epidemic routing, especially the one using random linear network coding, has been studied and proved as an efficient way in the consideration of delivery performance. Much pioneering work has tried to figure out how epidemic routing using network coding (ERNC) performs in VCPS, either by simulation or by analysis. However, none of them has been able to expose the potential of ERNC accurately. In this paper, we present a stochastic analytical framework to study the performance of ERNC in VCPS with intermittent connections. By novelly modeling ERNC in VCPS using a token-bucket model, our framework can provide a much more accurate results than any existing work on the unicast delivery performance analysis of ERNC in VCPS. The correctness of our analytical results has also been confirmed by our extensive simulations.