Quantum entanglement and fixed-point bifurcations

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.

Dynamics of gene expression in an artificial genome

Complex systems techniques provide a powerful tool to study the emergent properties of networks of interacting genes. In this study we extract models of genetic regulatory networks from an artificial genome, represented by a sequence of nucleotides, and analyse how variations in the connectivity and degree of inhibition of the extracted networks affects the resulting classes of behaviours. For low connectivity systems were found to be very stable. Only with higher connectivity was a significant occurrence of chaos found. Most interestingly, the peak in occurrence of chaos occurs perched on the edge of a phase transition in the occurrence of attractors.

QUANDO OS ESPÍRITOS SAEM DO ABISMO: O ESTABELECIMENTO NARRATIVO DO TERROR ESCATOLÓGICO EM APOCALIPSE 9,1-21

O Apocalipse de João é uma obra instigante. Sua linguagem cheia de violência, com monstros aterrorizantes, pessoas clamando por justiça, anúncios de mortes e desespero, em um quadro de espetáculos celestes, fascina os que gostam de ficção e alimenta a esperança dos que esperam um dia entrar na Nova Jerusalém, onde não haverá mar nem morte, quando as lágrimas serão enxugadas. Contudo, o livro do Apocalipse será lido como uma narração da realidade. Nesse sentido, o texto não é visto como reflexo de qualquer opressão, mas construção discursiva a respeito do sistema que, para o visionário, é a negação da ordem. Neste trabalho, a partir dos conceitos de texto e memória cultural, à luz das pesquisas de I. Lótman, da escola russa de semiótica da cultura e das pesquisas dos Assmann, observar-se-á como as memórias de seres celestes caídos e aprisionados da tradição enoquita estão presentes na literatura judaico-cristã e servem para a construção narrativa do cenário de terror escatológico na quinta e sexta trombetas de Ap 9,1-21. Assim sendo, a tese defende o terror como instrumento de persuasão, o qual serviu, na estratégia do visionário, para descrever o seu contexto como realidade caótica. Por meio de estratégias narrativas, o narrador deseja que sua visão seja levada a sério e que seus interlocutores aceitem a sua interpretação da realidade, deixando a associação com a vida e sistema romanos, pois se assim procederem serão comparados aos selados e receberão as mesmas recompensas. Dessa maneira, sua descrição com linguagem escatológica joga com o futuro e com o presente; prevê o caos, mas o vive em nível narrativo. Por isso o livro do Apocalipse, com um dualismo extremamente radical, não dá espaços para dúvidas. A tese defende, portanto, que essa obra pode ser lida como instrumento retórico de terror e medo que leva seus leitores implícitos a não flertarem com Roma, a não aceitarem seus discursos ou os que com ela se associam.

CRIAÇÃO E RECRIAÇÕES COSMOGÔNICAS EM ISAÍAS 51, 9-11: Um estudo do uso do mito cosmogônico pelo Dêutero-Isaías para o entendimento da comunidade dos cativos judaítas em Babilônia

Como estudar uma cultura ou uma comunidade perdida nos tempos bíblicos? Esta é um questão motriz para o autor. Foi dessa maneira que surgiu o seu interesse em discutir a possibilidade do uso do mito cosmogônico para o entendimento da comunidade dos cativos judaítas em Babilônia. É uma iniciativa, que precisava ser trilhada pelos pesquisadores que se dispusessem ao estudo das culturas do mundo bíblico. Assim se elegeu o tema Mito Cosmogônico no Primeiro Testamento como instrumento de aprofundamento da pesquisa bíblica. O mito é uma escolha mais ou menos óbvia, pela sua capacidade de funcionar como paradigma, pragmática e traditiva contra-hegemônica dentro de um contexto social interétnico. Estas eram ponderações vindas de matrizes como a do fenomenólogo Mircea Eliade, do Antropólogo Roger Bastide e do teólogo e fenomenólogo José Severino Croatto. É por isto que um paralelo é traçado entre o mito de Marduk e o texto de Isaías 51, 9-11, que fala de Javé como sendo criador do mundo e que luta contra as forças do caos. Isto é feito, com vistas à percepção da profecia do Isaías do exílio, como parentesco e sua justaposição com a mitologia babilônica, e ambos se aproximam bastante de forma sintagmática e histórico-social. Coube ainda saber se a profecia do Dêutero-Isaías atuava da mesma maneira que o poema Enuma elish funcionava para os babilônicos. Ou seja, fazia-se surgir modelos sociais às comunidades de escravos dentro do Império Neobabilônico; se com base nestes cânticos, os cativos conseguiam construir um ordenamento para as suas comunidades, que gozavam de uma relativa autonomia, tais como colônias e guetos ; se de posse dessa ousada profecia, os judeus da golah eram capazes de elaborar uma desobediência cívil nos termos de um nutrir nos corações, uma utopia que rompesse com o status quo do passado, comprometendo-os com a esperança no Javé criador.(AU)

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

Challenging the predictive ability of accounting techniques in modelling organizational futures

This article considers the role of accounting in organisational decision making. It challenges the rational nature of decisions made in organisations through the use of accounting models and the problems of predicting the future through the use of such models. The use of accounting in this manner is evaluated from an epochal postmodern stance. Issues raised by chaos theory and the uncertainty principle are used to demonstrate problems with the predictive ability of accounting models. The authors argue that any consideration of the predictive value of accounting needs to change to incorporate a recognition of the turbulent external environment, if it is to be of use for organisational decision making. Thus it is argued that the role of accounting as a mechanism for knowledge creation regarding the future is fundamentally flawed. We take this as a starting-point to argue for the real purpose of the use of the predictive techniques of accounting, using its ritualistic role in the context of myth creation to argue for the cultural benefits of the use of such flawed techniques.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

On models for magnetic field line diffusion

In this contribution, certain aspects of the nonlinear dynamics of magnetic field lines are reviewed. First, the basic facts (known from literature) concerning the Hamiltonian structure are briefly summarized. The paper then concentrates on the following subjects: (i) Transition from the continuous description to discrete maps; (ii) Characteristics of incomplete chaos; (iii) Control of chaos. The presentation is concluded by some remarks on the motion of particles in stochastic magnetic fields.

Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time. © 2008 Springer Science+Business Media, LLC.

Investigation of chaotic mixing in laminar fluid systems by the use of computational fluid dynamics

This work presents significant development into chaotic mixing induced through periodic boundaries and twisting flows. Three-dimensional closed and throughput domains are shown to exhibit chaotic motion under both time periodic and time independent boundary motions, A property is developed originating from a signature of chaos, sensitive dependence to initial conditions, which successfully quantifies the degree of disorder withjn the mixing systems presented and enables comparisons of the disorder throughout ranges of operating parameters, This work omits physical experimental results but presents significant computational investigation into chaotic systems using commercial computational fluid dynamics techniques. Physical experiments with chaotic mixing systems are, by their very nature, difficult to extract information beyond the recognition that disorder does, does not of partially occurs. The initial aim of this work is to observe whether it is possible to accurately simulate previously published physical experimental results through using commercial CFD techniques. This is shown to be possible for simple two-dimensional systems with time periodic wall movements. From this, and subsequent macro and microscopic observations of flow regimes, a simple explanation is developed for how boundary operating parameters affect the system disorder. Consider the classic two-dimensional rectangular cavity with time periodic velocity of the upper and lower walls, causing two opposing streamline motions. The degree of disorder within the system is related to the magnitude of displacement of individual particles within these opposing streamlines. The rationale is then employed in this work to develop and investigate more complex three-dimensional mixing systems that exhibit throughputs and time independence and are therefore more realistic and a significant advance towards designing chaotic mixers for process industries. Domains inducing chaotic motion through twisting flows are also briefly considered. This work concludes by offering possible advancements to the property developed to quantify disorder and suggestions of domains and associated boundary conditions that are expected to produce chaotic mixing.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.