A general method for exploring three-dimensional chaotic attractors with complicated topological structure based on the two-dimensional local vector field around equilibriums

2015 ◽  
Vol 83 (1-2) ◽  
pp. 1069-1078 ◽  
Author(s):  
Shijian Cang ◽  
Aiguo Wu ◽  
Zhonglin Wang ◽  
Zenghui Wang ◽  
Zengqiang Chen
Keyword(s):  
Vector Field ◽  
Topological Structure ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Local Vector ◽  
General Method

scholarly journals Estimating oxygen distribution from vasculature in three-dimensional tumour tissue

2016 ◽  
Vol 13 (116) ◽  
pp. 20160070 ◽  
Author(s):  
David Robert Grimes ◽  
Pavitra Kannan ◽  
Daniel R. Warren ◽  
Bostjan Markelc ◽  
Russell Bates ◽  
...  
Keyword(s):  
Kernel Method ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Oxygen Distribution ◽  
Two Dimensional ◽  
Dose Painting ◽  
Positron Emission ◽  
Boost Dose ◽  
Tumour Oxygenation ◽  
General Method

Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18 F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution.

scholarly journals NONORIENTABLE MANIFOLDS IN THREE-DIMENSIONAL VECTOR FIELDS

2003 ◽  
Vol 13 (03) ◽  
pp. 553-570 ◽  
Author(s):  
HINKE M. OSINGA
Keyword(s):  
Vector Field ◽  
Periodic Orbit ◽  
Vector Fields ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Period Doubling ◽  
Building Blocks ◽  
Two Dimensional ◽  
Dimensional Vector ◽  
Three Dimensional Vector Field

It is well known that a nonorientable manifold in a three-dimensional vector field is topologically equivalent to a Möbius strip. The most frequently used example is the unstable manifold of a periodic orbit that just lost its stability in a period-doubling bifurcation. However, there are not many explicit studies in the literature in the context of dynamical systems, and so far only qualitative sketches could be given as illustrations. We give an overview of the possible bifurcations in three-dimensional vector fields that create nonorientable manifolds. We mainly focus on nonorientable manifolds of periodic orbits, because they are the key building blocks. This is illustrated with invariant manifolds of three-dimensional vector fields that arise from applications. These manifolds were computed with a new algorithm for computing two-dimensional manifolds.

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

2021 ◽  
pp. 107754632110264
Author(s):  
Cun-Fang Feng ◽  
Hai-Jun Yang ◽  
Cai Zhou
Keyword(s):  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Lag Synchronization ◽  
Different Dimensions ◽  
Projective Lag Synchronization ◽  
General Method

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

The purine–carboxylate-containing coordination polymer poly[[μ4-1-(2-carboxylatoethyl)-6-oxo-6,9-dihydro-1H-purin-9-ido]zinc(II)]

2013 ◽  
Vol 69 (11) ◽  
pp. 1314-1316
Author(s):  
Wen-Juan Ma ◽  
Guo-Ting Li
Keyword(s):  
Thermal Stability ◽  
Coordination Polymer ◽  
Title Compound ◽  
Topological Structure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Metal Organic ◽  
Very High ◽  
Thermal Stability Of

The title compound, [Zn(C8H6N4O3)]nor [Zn(L)]n[H2Lis 3-(6-oxo-6,9-dihydro-1H-purin-1-yl)propionic acid], crystallized as a nonmerohedral twin. The ZnIIcation is four-coordinated, ligated by two carboxylate O atoms from twoLligands and two N atoms from another two ligands. Each ligand bridges four ZnIIcentres, extending the structure into a three-dimensional polymer with a 4-connected (65,41) topological structure containing two-dimensional homochiral layers constructed from one-dimensional metal–organic helices. Investigation of the thermal stability of the compound shows that the network has very high thermostability and is stable up to 720 K.

scholarly journals Total Dielectric Function Approach to the Electron Boltzmann Equation for Scattering from a Two-Dimensional Coupled Mode System

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 69-72
Author(s):  
B. A. Sanborn
Keyword(s):  
Boltzmann Equation ◽  
Dielectric Function ◽  
Three Dimensional ◽  
Collision Term ◽  
Two Dimensional ◽  
Coupled Mode ◽  
Low Field ◽  
Electron Boltzmann Equation ◽  
General Method ◽  
Dynamical Screening

The nonequilibrium total dielectric function lends itself to a simple and general method for calculating the inelastic collision term in the electron Boltzmann equation for scattering from a coupled mode system. Useful applications include scattering from plasmon-polar phonon hybrid modes in modulation doped semiconductor structures. This paper presents numerical methods for including inelastic scattering at momentum-dependent hybrid phonon frequencies in the low-field Boltzmann equation for two-dimensional electrons coupled to bulk phonons. Results for electron mobility in GaAs show that the influence of mode coupling and dynamical screening on electron scattering from polar optical phonons is stronger for two dimensional electrons than was previously found for the three dimensional case.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

Computer Assisted Image Reconstruction of Oligomer Structure

1976 ◽  
Vol 34 ◽  
pp. 472-473
Author(s):  
A.M. Jones ◽  
A. Max Fiskin
Keyword(s):  
Three Dimensional ◽  
Depth Of Field ◽  
Computer Assisted ◽  
Projection Data ◽  
Two Dimensional ◽  
Single Particles ◽  
Dimensional Reconstruction ◽  
Computer Assisted Image ◽  
The Fourier Transform ◽  
Space Approach

If the tilt of a specimen can be varied either by the strategy of observing identical particles orientated randomly or by use of a eucentric goniometer stage, three dimensional reconstruction procedures are available (l). If the specimens, such as small protein aggregates, lack periodicity, direct space methods compete favorably in ease of implementation with reconstruction by the Fourier (transform) space approach (2). Regardless of method, reconstruction is possible because useful specimen thicknesses are always much less than the depth of field in an electron microscope. Thus electron images record the amount of stain in columns of the object normal to the recording plates. For single particles, practical considerations dictate that the specimen be tilted precisely about a single axis. In so doing a reconstructed image is achieved serially from two-dimensional sections which in turn are generated by a series of back-to-front lines of projection data.

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