Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Interference in hyperbolic space

The interference in a phase space algorithm of Schleich and Wheeler [Nature 326, 574 (1987)] is extended to the hyperbolic space underlying the group SU(1,1). The extension involves introducing the notion of weighted areas. Analytic expressions for the asymptotic forms for overlaps between the eigenstates of the generators of su(1,1) thus obtained are found to be in excellent agreement with the numerical results.[S1050-2947(98)08602-8].

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Pulsed quadrature-phase squeezing of solitary waves in chi((2)) parametric waveguides

It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive chi((2)) waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched chi((2)) waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.

On the origin of the MR image phase contrast: an in vivo MR microscopy study of the rat brain at 14.1 T.

Recent studies at high magnetic fields using the phase of gradient-echo MR images have shown the ability to unveil cortical substructure in the human brain. To investigate the contrast mechanisms in phase imaging, this study extends, for the first time, phase imaging to the rodent brain. Using a 14.1 T horizontal bore animal MRI scanner for in vivo micro-imaging, images with an in-plane resolution of 33 microm were acquired. Phase images revealed, often more clearly than the corresponding magnitude images, hippocampal fields, cortical layers (e.g. layer 4), cerebellar layers (molecular and granule cell layers) and small white matter structures present in the striatum and septal nucleus. The contrast of the phase images depended in part on the orientation of anatomical structures relative to the magnetic field, consistent with bulk susceptibility variations between tissues. This was found not only for vessels, but also for white matter structures, such as the anterior commissure, and cortical layers in the cerebellum. Such susceptibility changes could result from variable blood volume. However, when the deoxyhemoglobin content was reduced by increasing cerebral blood flow (CBF) with a carbogen breathing challenge, contrast between white and gray matter and cortical layers was not affected, suggesting that tissue cerebral blood volume (and therefore deoxyhemoglobin) is not a major source of the tissue phase contrast. We conclude that phase variations in gradient-echo images are likely due to susceptibility shifts of non-vascular origin.

Fluorodeoxyuridine mediated cell cycle synchronization in S-phase increases the Auger radiation cell killing with 125I-iododeoxyuridine.

Aim: 125I-iododeoxyuridine is a potential Auger radiation therapy agent. Its incorporation in DNA of proliferating cells is enhanced by fluorodeoxyuridine. Here, we evaluated therapeutic activities of 125I-iododeoxyuridine in an optimized fluorodeoxyuridine pre-treatment inducing S-phase synchronization. Methods: After S-phase synchronization by fluorodeoxyuridine, cells were treated with 125I-iododeoxyuridine. Apoptosis analysis and S-phase synchronization were studied by flow cytometry. Cell survival was determined by colony-forming assay. Based on measured growth parameters, the number of decays per cell that induced killing was extrapolated. Results: Treatment experiments showed that 72 to 91% of synchronized cells were killed after 0.8 and 8 kBq/ml 125I-iododeoxyuridine incubation, respectively. In controls, only 8 to 38% of cells were killed by corresponding 125I-iododeoxyuridine activities alone and even increasing the activity to 80 kBq/ml gave only 42 % killing. Duplicated treatment cycles or repeated fluorodeoxyuridine pre-treatment allowed enhancing cell killing to >95 % at 8 kBq/ml 125I-iododeoxyuridine. About 50 and 160 decays per S-phase cells in controls and S-phase synchronization, respectively, were responsible for the observed cell killing at 0.8 kBq/ml radio-iododeoxyuridine. Conclusion: These data show the successful application of fluorodeoxyuridine that provided increased 125I-iododeoxyuridine Auger radiation cell killing efficacy through S-phase synchronization and high DNA incorporation of radio-iododeoxyuridine.

Mathematical modeling of level of anaesthesia from EEG measurements

Problem of modeling of anaesthesia depth level is studied in this Master Thesis. It applies analysis of EEG signals with nonlinear dynamics theory and further classification of obtained values. The main stages of this study are the following: data preprocessing; calculation of optimal embedding parameters for phase space reconstruction; obtaining reconstructed phase portraits of each EEG signal; formation of the feature set to characterise obtained phase portraits; classification of four different anaesthesia levels basing on previously estimated features. Classification was performed with: Linear and quadratic Discriminant Analysis, k Nearest Neighbours method and online clustering. In addition, this work provides overview of existing approaches to anaesthesia depth monitoring, description of basic concepts of nonlinear dynamics theory used in this Master Thesis and comparative analysis of several different classification methods.

The development of automated methods for the determination of trace concentrations of carbomate pesticides in water using solid sorbent pre-concentration methods and high performance liquid chromatography /

Several automated reversed-phase HPLC methods have been developed to determine trace concentrations of carbamate pesticides (which are of concern in Ontario environmental samples) in water by utilizing two solid sorbent extraction techniques. One of the methods is known as on-line pre-concentration'. This technique involves passing 100 milliliters of sample water through a 3 cm pre-column, packed with 5 micron ODS sorbent, at flow rates varying from 5-10 mUmin. By the use of a valve apparatus, the HPLC system is then switched to a gradient mobile phase program consisting of acetonitrile and water. The analytes, Propoxur, Carbofuran, Carbaryl, Propham, Captan, Chloropropham, Barban, and Butylate, which are pre-concentrated on the pre-column, are eluted and separated on a 25 cm C-8 analytical column and determined by UV absorption at 220 nm. The total analytical time is 60 minutes, and the pre-column can be used repeatedly for the analysis of as many as thirty samples. The method is highly sensitive as 100 percent of the analytes present in the sample can be injected into the HPLC. No breakthrough of any of the analytes was observed and the minimum detectable concentrations range from 10 to 480 ng/L. The developed method is totally automated for the analysis of one sample. When the above mobile phase is modified with a buffer solution, Aminocarb, Benomyl, and its degradation product, MBC, can also be detected along with the above pesticides with baseline resolution for all of the analytes. The method can also be easily modified to determine Benomyl and MBC both as solute and as particulate matter. By using a commercially available solid phase extraction cartridge, in lieu of a pre-column, for the extraction and concentration of analytes, a completely automated method has been developed with the aid of the Waters Millilab Workstation. Sample water is loaded at 10 mL/min through a cartridge and the concentrated analytes are eluted from the sorbent with acetonitrile. The resulting eluate is blown-down under nitrogen, made up to volume with water, and injected into the HPLC. The total analytical time is 90 minutes. Fifty percent of the analytes present in the sample can be injected into the HPLC, and recoveries for the above eight pesticides ranged from 84 to 93 percent. The minimum detectable concentrations range from 20 to 960 ng/L. The developed method is totally automated for the analysis of up to thirty consecutive samples. The method has proven to be applicable to both purer water samples as well as untreated lake water samples.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Relative entropy measures applied to healthy and pathological voice characterization

Nowadays, noninvasive methods of diagnosis have increased due to demands of the population that requires fast, simple and painless exams. These methods have become possible because of the growth of technology that provides the necessary means of collecting and processing signals. New methods of analysis have been developed to understand the complexity of voice signals, such as nonlinear dynamics aiming at the exploration of voice signals dynamic nature. The purpose of this paper is to characterize healthy and pathological voice signals with the aid of relative entropy measures. Phase space reconstruction technique is also used as a way to select interesting regions of the signals. Three groups of samples were used, one from healthy individuals and the other two from people with nodule in the vocal fold and Reinke`s edema. All of them are recordings of sustained vowel /a/ from Brazilian Portuguese. The paper shows that nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic component of the human voice. Relative entropy is well suited due to its sensibility to uncertainties, since the pathologies are characterized by an increase in the signal complexity and unpredictability. The results showed that the pathological groups had higher entropy values in accordance with other vocal acoustic parameters presented. This suggests that these techniques may improve and complement the recent voice analysis methods available for clinicians. (C) 2008 Elsevier Inc. All rights reserved.