Characterization of multiple reflections and phase space properties for a periodically corrugated waveguide

Dynamical properties for a beam light inside a sinusoidally corrugated waveguide are discussed in this paper. The beam is confined inside two-mirrors: one is flat and the other one is sinusoidally corrugated. The evolution of the system is described by the use of a two-dimensional and nonlinear mapping. The phase space of the system is of mixed type therefore exhibiting a large chaotic sea, periodic islands and invariant KAM curves. A careful discussion of the numerical method to solve the transcendental equations of the mapping is given. We characterize the probability of observing successive reflections of the light by the corrugated mirror and show that it is scaling invariant with respect to the amplitude of the corrugation. Average properties of the chaotic sea are also described by the use of scaling arguments.

A Phase Space Box-counting based Method for Arrhythmia Prediction from Electrocardiogram Time Series

Arrhythmia is one kind of cardiovascular diseases that give rise to the number of deaths and potentially yields immedicable danger. Arrhythmia is a life threatening condition originating from disorganized propagation of electrical signals in heart resulting in desynchronization among different chambers of the heart. Fundamentally, the synchronization process means that the phase relationship of electrical activities between the chambers remains coherent, maintaining a constant phase difference over time. If desynchronization occurs due to arrhythmia, the coherent phase relationship breaks down resulting in chaotic rhythm affecting the regular pumping mechanism of heart. This phenomenon was explored by using the phase space reconstruction technique which is a standard analysis technique of time series data generated from nonlinear dynamical system. In this project a novel index is presented for predicting the onset of ventricular arrhythmias. Analysis of continuously captured long-term ECG data recordings was conducted up to the onset of arrhythmia by the phase space reconstruction method, obtaining 2-dimensional images, analysed by the box counting method. The method was tested using the ECG data set of three different kinds including normal (NR), Ventricular Tachycardia (VT), Ventricular Fibrillation (VF), extracted from the Physionet ECG database. Statistical measures like mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) for the box-counting in phase space diagrams are derived for a sliding window of 10 beats of ECG signal. From the results of these statistical analyses, a threshold was derived as an upper bound of Coefficient of Variation (CV) for box-counting of ECG phase portraits which is capable of reliably predicting the impeding arrhythmia long before its actual occurrence. As future work of research, it was planned to validate this prediction tool over a wider population of patients affected by different kind of arrhythmia, like atrial fibrillation, bundle and brunch block, and set different thresholds for them, in order to confirm its clinical applicability.

Four-window technique for measuring optical-phase-space-time-frequency tomography

A new approach, the four-window technique, was developed to measure optical phase-space-time-frequency tomography (OPSTFT). The four-window technique is based on balanced heterodyne detection with two local oscillator (LO) fields. This technique can provide independent control of position, momentum, time and frequency resolution. The OPSTFT is a Wigner distribution function of two independent Fourier transform pairs, phase-space and time-frequency. The OPSTFT can be applied for early disease detection.

Iterative determination of clinical beam phase space from dose measurements

Monte Carlo (MC) method can accurately compute the dose produced by medical linear accelerators. However, these calculations require a reliable description of the electron and/or photon beams delivering the dose, the phase space (PHSP), which is not usually available. A method to derive a phase space model from reference measurements that does not heavily rely on a detailed model of the accelerator head is presented. The iterative optimization process extracts the characteristics of the particle beams which best explains the reference dose measurements in water and air, given a set of constrains

The Phase Space as a New Representation of the Dynamical Behaviour of Temperature and Enthalpy in a Reefer monitored with a Multidistributed Sensors Network

The study of temperature gradients in cold stores and containers is a critical issue in the food industry for the quality assurance of products during transport, as well as forminimizing losses. The objective of this work is to develop a new methodology of data analysis based on phase space graphs of temperature and enthalpy, collected by means of multidistributed, low cost and autonomous wireless sensors and loggers. A transoceanic refrigerated transport of lemons in a reefer container ship from Montevideo (Uruguay) to Cartagena (Spain) was monitored with a network of 39 semi-passive TurboTag RFID loggers and 13 i-button loggers. Transport included intermodal transit from transoceanic to short shipping vessels and a truck trip. Data analysis is carried out using qualitative phase diagrams computed on the basis of Takens?Ruelle reconstruction of attractors. Fruit stress is quantified in terms of the phase diagram area which characterizes the cyclic behaviour of temperature. Areas within the enthalpy phase diagram computed for the short sea shipping transport were 5 times higher than those computed for the long sea shipping, with coefficients of variation above 100% for both periods. This new methodology for data analysis highlights the significant heterogeneity of thermohygrometric conditions at different locations in the container.

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Representing microstates of static granular matter in a stress phase space

A stress phase space is proposed to compare the static packings of a granular system (microstates) that are compatible to a macrostate described by external stresses. The equivalent stress of each particle of a static packing can be obtained from the mechanical interaction forces, and the associated volume is given by the respective Voronoi cell. Therefore, particles can be located at different stress levels and grouped into categories or configurations, which are defined in base of the geometrical features of the local arrangement (in particular, of the number of forces that keep them force-balanced). They can be represented as points in a stress phase space. The nature of this space is analyzed in detail. The integration limits of the stress variables that avoid or limit tensile states and the capability of each configuration to represent specific stress states establish its main features. Furthermore, if some stress variables are used, instead of the usual components of the Cauchy stress tensor, then some symmetries can be found. Results obtained from molecular dynamics simulations are used to check this nature. Finally, some statistical ensembles are written in terms of the coordinates of this phase space. These require some assumptions that are made in base on continuum mechanics principles.

Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

Validation of a phase space determination algorithm for intraoperative radiation therapy

Monte-Carlo (MC) methods are a valuable tool for dosimetry in radiotherapy, including Intra-Operative Electron Radiotherapy (IOERT), since effects such as inhomogeneities or beam hardening may be realistically reproduced.

Advanced Characterisation of a Coffee Fermenting Tank by Multi-distributed Wireless Sensors: Spatial Interpolation and Phase Space Graphs

The fermentation stage is considered to be one of the critical steps in coffee processing due to its impact on the final quality of the product. The objective of this work is to characterise the temperature gradients in a fermentation tank by multi-distributed, low-cost and autonomous wireless sensors (23 semi-passive TurboTag® radio-frequency identifier (RFID) temperature loggers). Spatial interpolation in polar coordinates and an innovative methodology based on phase space diagrams are used. A real coffee fermentation process was supervised in the Cauca region (Colombia) with sensors submerged directly in the fermenting mass, leading to a 4.6 °C temperature range within the fermentation process. Spatial interpolation shows a maximum instant radial temperature gradient of 0.1 °C/cm from the centre to the perimeter of the tank and a vertical temperature gradient of 0.25 °C/cm for sensors with equal polar coordinates. The combination of spatial interpolation and phase space graphs consistently enables the identification of five local behaviours during fermentation (hot and cold spots).

Teleonomic entropy: measuring the phase-space of end-directed systems

We introduce a novel way of measuring the entropy of a set of values undergoing changes. Such a measure becomes useful when analyzing the temporal development of an algorithm designed to numerically update a collection of values such as artificial neural network weights undergoing adjustments during learning. We measure the entropy as a function of the phase-space of the values, i.e. their magnitude and velocity of change, using a method based on the abstract measure of entropy introduced by the philosopher Rudolf Carnap. By constructing a time-dynamic two-dimensional Voronoi diagram using Voronoi cell generators with coordinates of value- and value-velocity (change of magnitude), the entropy becomes a function of the cell areas. We term this measure teleonomic entropy since it can be used to describe changes in any end-directed (teleonomic) system. The usefulness of the method is illustrated when comparing the different approaches of two search algorithms, a learning artificial neural network and a population of discovering agents. (C) 2004 Elsevier Inc. All rights reserved.

Phase-space analysis of bosonic spontaneous emission

We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description within the limits of our model. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck equation and still fails to agree with the full quantum results of the positive-P representation. We show that quantum statistics and correlations between the ground and excited states affect the dynamics of the emission process, so that it is in general non-exponential. (c) 2005 Elsevier B.V. All rights reserved.

Quantum phase-space simulations of fermions and bosons

We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations of the dynamics and thermal equilibrium states of many-body quantum systems from first principles. As an example, we numerically calculate finite-temperature correlation functions for the Fermi Hubbard model, with no evidence of the Fermi sign problem. (c) 2005 Elsevier B.V. All rights reserved.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behavior in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.