On a Comprehensive Topological Analysis of Moore Spiegel Attractor

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Anirban Ray ◽  
A. RoyChowdhury
Keyword(s):  
Chaotic Dynamics ◽  
Topological Analysis ◽  
Chaotic Orbit ◽  
New Approach ◽  
Rotation Rates ◽  
Linking Numbers ◽  
Point Analysis ◽  
Flow Curvature ◽  
Pertinent Information ◽  
Explicit Realization

A topological analysis of the attractor associated with the Moore–Spiegel nonlinear system is performed, following the basic idea laid down by Gilmore and Lefranc (2002, The Topology of Chaos, Wiley, Hoboken, NJ). Starting with the usual fixed point analysis and their stability, we proceed to study in detail the process of chaotic orbit extraction with the help of close return map. This is then used to construct the symbolic dynamics associated with it, which is helpful in understanding the sequential change taking place inside the attractor. In the next part, we show how to characterize the evolution of the attractor from its birth to the crisis by finding out the homoclinic orbit and the corresponding unstable manifold. In the concluding part of the paper, we show how all the pertinent information of the attractor can be encoded in the template, leading to the explicit realization of linking numbers and the relative rotation rates. In the concluding section, we have touched upon a new approach to chaotic dynamics, using the flow curvature manifold to display the relative positioning of the attractor in relation to the fixed points and the null lines.

Exhibition Pavilions Car Showrooms Based on Translucent Structures: Providing Microclimatic Comfort for Clients

2014 ◽  
Vol 680 ◽  
pp. 467-473
Author(s):  
Viktor Pukhkal ◽  
Darko Stanojevic ◽  
Vera Murgul ◽  
Nikolay Vatin
Keyword(s):  
Additional Analysis ◽  
Human Comfort ◽  
New Approach ◽  
Winter Maintenance ◽  
Temperature Conditions ◽  
Pertinent Information ◽  
General Data

Transition to a new approach related to use of facades and roofs entirely made of glass in pavilions car showrooms construction called for an additional analysis to evaluate an issue of how to ensure an interior climate. There was a need to have solutions generalized and systematized with the aim to ensure human comfort in pavilions with large glazed areas in facades and roofs. Exhibition pavilions car showrooms based on translucent structures were taken for consideration. General data concerning temperature conditions for the rooms and internal glazing surfaces of pavilions car showrooms based on translucent structures are stated herein. Pertinent information for glazing design is given with due account for winter maintenance conditions in regard to the pavilions car showrooms having significant areas of façade or roof glazing.

TOPOLOGICAL ANALYSIS OF CHAOS IN EQUIVARIANT ELECTRONIC CIRCUITS

1996 ◽  
Vol 06 (12b) ◽  
pp. 2531-2555 ◽  
Author(s):  
C. LETELLIER ◽  
G. GOUESBET ◽  
N.F. RULKOV
Keyword(s):  
Time Series ◽  
Chaotic Dynamics ◽  
Electronic Circuit ◽  
Topological Analysis ◽  
Experimental System ◽  
Electronic Circuits ◽  
Chaotic Oscillations ◽  
Symmetry Properties

Chaotic oscillations in an electronic circuit are studied by recording two time series simultaneously. The chaotic dynamics is characterized by using topological analysis. A comparison with two models is also discussed. Some prescriptions are given in order to take into account the symmetry properties of the experimental system to perform the topological analysis.

DIMENSION REDUCTION FOR ANALYSIS OF UNSTABLE PERIODIC ORBITS USING LOCALLY LINEAR EMBEDDING

2012 ◽  
Vol 22 (01) ◽  
pp. 1230001
Author(s):  
BENJAMIN COY
Keyword(s):  
Learning Community ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Topological Analysis ◽  
Three Dimensions ◽  
Locally Linear Embedding ◽  
Unstable Periodic Orbits ◽  
Linking Numbers ◽  
Linear Embedding ◽  
Locally Linear

An autonomous four-dimensional dynamical system is investigated through a topological analysis. This system generates a chaotic attractor for the range of control parameters studied and we determine the organization of the unstable periodic orbits (UPOs) associated with the chaotic attractor. Surrogate UPOs were found in the four-dimensional phase space and pairs of these orbits were embedded in three-dimensions using Locally Linear Embedding. This is a dimensionality reduction technique recently developed in the machine learning community. Embedding pairs of orbits allows the computation of their linking numbers, a topological invariant. A table of linking numbers was computed for a range of control parameter values which shows that the organization of the UPOs is consistent with that of a Lorenz-type branched manifold with rotation symmetry.

scholarly journals Bioinformatics Analysis for the Antirheumatic Effects of Huang-Lian-Jie-Du-Tang from a Network Perspective

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyang Fang ◽  
Yichuan Wang ◽  
Tinghong Yang ◽  
Yang Ga ◽  
Yi Zhang ◽  
...  
Keyword(s):  
Therapeutic Effect ◽  
Bioinformatics Analysis ◽  
Topological Analysis ◽  
Ppi Network ◽  
New Approach ◽  
Target Proteins ◽  
Multiple Components ◽  
Main Pathway ◽  
Tcm Theory ◽  
Therapeutic Mechanisms

Huang-Lian-Jie-Du-Tang (HLJDT) is a classic TCM formula to clear “heat” and “poison” that exhibits antirheumatic activity. Here we investigated the therapeutic mechanisms of HLJDT at protein network level using bioinformatics approach. It was found that HLJDT shares 5 target proteins with 3 types of anti-RA drugs, and several pathways in immune system and bone formation are significantly regulated by HLJDT’s components, suggesting the therapeutic effect of HLJDT on RA. By defining an antirheumatic effect score to quantitatively measure the therapeutic effect, we found that the score of each HLJDT’s component is very low, while the whole HLJDT achieves a much higher effect score, suggesting a synergistic effect of HLJDT achieved by its multiple components acting on multiple targets. At last, topological analysis on the RA-associated PPI network was conducted to illustrate key roles of HLJDT’s target proteins on this network. Integrating our findings with TCM theory suggests that HLJDT targets on hub nodes and main pathway in the Hot ZENG network, and thus it could be applied as adjuvant treatment for Hot-ZENG-related RA. This study may facilitate our understanding of antirheumatic effect of HLJDT and it may suggest new approach for the study of TCM pharmacology.

Micro X-ray fluorescence in materials characterization

2004 ◽  
Vol 19 (2) ◽  
pp. 119-126 ◽  
Author(s):  
George J. Havrilla ◽  
Thomasin Miller
Keyword(s):  
Single Point ◽  
Three Dimensional ◽  
Chemical Imaging ◽  
Materials Characterization ◽  
New Approach ◽  
X Ray ◽  
Elemental Imaging ◽  
X Ray Imaging ◽  
Point Analysis ◽  
Comprehensive Characterization

Micro X-ray fluorescence (MXRF) offers the analyst a new approach to materials characterization. The range of applications is expanding rapidly. Single point analysis has been demonstrated for nanoliter volumes with detection limits at the 0.5 ng level. MXRF can be used as an element specific detector for capillary electrophoresis. Elemental imaging applications include analysis of sample corrosion and polymers, use as a combinatorial chemistry screening tool, and integration with molecular spectroscopic imaging methods to provide a more comprehensive characterization. Three-dimensional elemental imaging is a reality with the development of a confocal X-ray fluorescence microscope. Stereoview elemental X-ray imaging can provide unique views of materials that flat two-dimensional images cannot achieve. Spectral imaging offers chemical imaging capability, moving MXRF into a higher level of information content. The future is bright for MXRF as a materials characterization tool.

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation

1996 ◽  
Vol 118 (3) ◽  
pp. 313-317 ◽  
Author(s):  
D. J. Segalman ◽  
C. R. Dohrmann
Keyword(s):  
Natural Frequency ◽  
Configuration Space ◽  
Flexible Structures ◽  
Second Order ◽  
General Linear ◽  
New Approach ◽  
Kinematic Constraints ◽  
Rotation Rates ◽  
Deformation Modes

The problem of calculating the vibrations of rotating structures has challenged analysts since it was observed that the use of traditional modal approaches may incorrectly lead to the prediction of infinite deformation when rotation rates exceed the first natural frequency. Much recently published work on beams has shown that such predictions are artifacts of incorporating incomplete kinematics into the analysis, but only simple structures such as individual beams and plates are addressed. The authors present a new approach to analyzing rotating flexible structures that applies to the rotation of general linear (unjointed) structures, using a system of nonlinearly coupled deformation modes. This technique, tentatively named a Method of Quadratic Components, utilizes a nonlinear configuration space in which all kinematic constraints are satisfied up to second order.

Subcritical transition and spiral turbulence in circular Couette flow

2012 ◽  
Vol 709 ◽  
pp. 106-122 ◽  
Author(s):  
M. J. Burin ◽  
C. J. Czarnocki
Keyword(s):  
Velocity Profile ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Azimuthal Velocity ◽  
Transition To Turbulence ◽  
Coupling Mechanism ◽  
Rotation Rates ◽  
Circular Couette Flow ◽  
Flow Curvature ◽  
Gap Width

AbstractWe present new observations of a controlled transition to turbulence in a fundamental but little-studied regime: circular Couette flow with only the outer cylinder rotating. Our apparatus consists of an outer cylinder of fixed radius and three inner cylinders having different radii that are used interchangeably to study the effect of flow curvature. With the smallest inner cylinder the end-cap configuration (vertical boundary conditions) may also be varied. The turbulent transition is found to be sensitive to both gap width and end-cap configuration, with wider gaps transitioning at higher rotation rates. All configurations are observed to transition with hysteresis and intermittency. A laser Doppler velocimetry (LDV)-based study of the azimuthal velocity profile as a function of gap width and rotation rate reveals that turbulence, once initiated, is confined to regions of significant shear. For wider gap widths, the radial location of these shear layers is determined by the chosen end-cap configuration. This, in turn, affects the transition Reynolds number, which we posit to be radially dependent. The narrow-gap case in particular features spiral turbulence, whose properties are found to be similar to observations of the phenomenon in related shear flows. The velocity profile in this case is correlated with overlapping boundary layers, suggesting a coupling mechanism for the origin of laminar-turbulent banding phenomena.

scholarly journals The Development of an Information Criterion for Change-Point Analysis

2016 ◽  
Vol 28 (3) ◽  
pp. 594-612 ◽  
Author(s):  
Colin H. LaMont ◽  
Paul A. Wiggins
Keyword(s):  
Change Point ◽  
Information Criterion ◽  
Change Points ◽  
Change Point Analysis ◽  
Series Data ◽  
New Approach ◽  
Times Series ◽  
Point Analysis ◽  
Wide Range ◽  
Discrete States

Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change point algorithm is used to identify the time indices (change points) at which the system transitions between these discrete states. We present a unified information-based approach to testing for the existence of change points. This new approach reconciles two previously disparate approaches to change-point analysis (frequentist and information based) for testing transitions between states. The resulting method is statistically principled, parameter and prior free, and widely applicable to a wide range of change-point problems.

scholarly journals Dynamical Behavior of a New Chaotic System with One Stable Equilibrium

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3217
Author(s):  
Vijayakumar M.D. ◽  
Anitha Karthikeyan ◽  
Jozef Zivcak ◽  
Ondrej Krejcar ◽  
Hamidreza Namazi
Keyword(s):  
Chaotic Dynamics ◽  
Stable Equilibrium ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Stable Node ◽  
Point Analysis ◽  
New Chaotic System ◽  
Periodic Attractors ◽  
Flow Evolution

This paper reports a simple three-dimensional autonomous system with a single stable node equilibrium. The system has a constant controller which adjusts the dynamic of the system. It is revealed that the system exhibits both chaotic and non-chaotic dynamics. Moreover, chaotic or periodic attractors coexist with a single stable equilibrium for some control parameter based on initial conditions. The system dynamics are studied by analyzing bifurcation diagrams, Lyapunov exponents, and basins of attractions. Beyond a fixed-point analysis, a new analysis known as connecting curves is provided. These curves are one-dimensional sets of the points that are more informative than fixed points. These curves are the skeleton of the system, which shows the direction of flow evolution.

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

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