Logistic Map耦合格子模型模拟环带

本论文采用Logistic Map耦合格子模型对高聚物中特有的环带球晶进行了模拟，所得到的模拟结果与实验结果吻合较好。同时，研究结果能够对实验制备环带球晶样品提供可靠的理论指导。 首先，我们对Logistic Map耦合格子模型及模型中的两个模拟参量μ和ε进行分析，同时结合实验中各种实验条件对聚合物结晶行为的影响，认为Logistic Map的动力学特征与聚合物结晶行为非常相似，并且参量μ与实验中的结晶温度相关，即随温度的升高而减小，而参量ε与实验中影响扩散的因素有关，即随温度的升高而增大、随分子量的增大而减小，并且随样品厚度的增大而增大。我们对模型的整个参数空间进行计算，得到了可以形成环带球晶形貌的参数范围，通过进一步研究发现环带图案的带宽随参量μ的增大而变窄，随参量ε的增大而变宽。上述研究结果与实验中带宽随实验条件的变化规律是一致的。 在得到环带图案的基础上，我们又进一步计算得到了靶状和螺旋状形貌的参量μ和ε的具体取值范围。通过改变μ和ε的参数取值，模拟了环带球晶形貌由靶状过渡到螺旋状的过程，即靶状图案的环带由外层向内层逐渐断裂成较短的条带结构，所有的条带结构呈现出以空间某处为中心团聚在一起的形貌；随后，这种“团聚”的形貌逐渐消失了，空间中小的条带结构的排列呈无序状态。随着参数的进一步变化，短的条带结构变成较长的带状结构，并且这些带状结构的边缘逐渐发生卷曲，最终形成了螺旋状图案。我们还考察了系统初值和耦合方式对上述图案的影响，结果发现，形成环带球晶的参数范围对系统初值没有明显的依赖性，然而靶状和螺旋状图案的分布受初值的影响较大。此外，发现只有采用交替耦合、并考虑长程耦合作用的Logistic Map耦合格子模型才可以得到环带球晶图案。 为了更好地与实验结果进行对比，我们利用Logistic Map耦合格子模型对二维空间中的几种受限体系进行了模拟。（一）对温度梯度场中的环带球晶进行模拟，发现环带球晶在低温处较易成核，向高温处生长，并且，高温处环带的带宽比低温处宽。（二）对格子宽度受限情况进行了模拟，发现随着受限方向的宽度越来越窄，球晶尺寸逐渐变小，相邻两个环带球晶碰撞产生的界线变短，三个相邻环带球晶所形成的界线的交汇点减少。（三）研究了受限边界上的成核作用对狭长格子中环带球晶的影响，结果发现，随着受限边界上成核点密度的不断增加，其形貌转变分为三个不同阶段：①当成核密度稍有增大时，环带球晶数量增加，直径变小；②继续增大边界成核密度，使得大量晶层从受限边界向格子内生长，导致环带球晶的数量减少，直径也减小；③当成核点增加到一定程度时，整个空间中只有极少数由格子内部成核生长且直径非常小的环带球晶，而占主导地位的是由成核点垂直于受限边界生长出的穿透晶层。这些模拟结果均与实验结果相符合。 我们将Logistic Map耦合映象格子模型发展到三维空间格子中，得到了与环带球晶形貌一致的图案，并且其带宽随模拟参量μ的增大而变窄，随ε的增大而变宽。这一规律性结果与二维正方格子的模拟结果是一致的。这一部分的研究结果还表明，边界条件和格子尺寸对模拟结果有显著的影响，周期性边界条件导致在小体积立方格子中只能得到靶状图案；而当格子尺寸很大时，可以得到螺旋状环带球晶的图案。最后，通过调节垂直于薄膜平面方向上的格子数来研究薄膜厚度对环带图案带宽的影响，发现环带的带宽随厚度的增加而变宽，这与实验中环带球晶的带宽随样品厚度的增加而变大的结论是一致的。

The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter mu in the logistic map and increased with the increase of the coupling parameter epsilon, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

Banded spherulite patterns are simulated in three dimensions by means of a Coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the hand spacing is decreased with the increase of parameter mu in the Logistic map and increased with the increase of the coupling parameter e for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.

植物群落复杂性与群落结构组建的描述与分析

时间、空间格局的保持和发展及其对种群、群落和生态系统动态的影响是生态学中两个相互关联的基本课题。围绕这个中心议题作者在植物个体、种群、群落各个层次上开展了研究。 1)研究了克隆植物构型及其对资源异质性的响应，给出了描述该连续体的一个指数v：In1/ln刀．（士Logistic方程表述每个斑块内的局部种群动态，用扩散系数e表示斑块间的扩散，建立了描述Meta-种群动态的耦合映象格子模型。并单峰映象Xn+l =1-ax2给出了耦合映象格子的时空行为，对这些模式的深入研究，将无疑会帮助我们理解Mcta种群时空复杂行为的本质。 3)在更广的意义上考虑群落复杂性的概念，将群落总复杂性分为基于无序的复杂性和结构复杂性。并用描述群落的最小剩余码的平均码长L(S)测度群落总复杂性，用Shannon-Wiener熵H(S)和Renyi熵H12 (S)测度基于无序的复杂性，并将总复杂性和基于无序的复杂性之差△(S)=L(S)一H(S)和 A，：=/(S) - H12 (S)作为组织复杂性或群落结构复杂性的测度。研究了中国东北样带(NECT)典型植物群落的结构复杂性和多样性。以群落结构组建的理论为基础提出了一个描述群落内种间相互作用强度的指标，利用约束典型排序和偏典型排序技术：典型对应分析CCA和剩余分析RA为基础，发展一种包括环境，空间格局和物种相互作用三方面因素的植物群落数量分析方法，并在种多度数据的变化中分离出这几个方面的变化。 4)以适宜度理论和草原类型理论为基础，利用草原湿润度指标k作为生境综合生态因子的一个测度，构造出草原生物的适宜度模型;给出了草原生境对草原生物适宜度的评价指标：提出了草原生境指数，生境适宜度，生境适宜度过程等新的概念。(公式从略)

Synchronous chaos in the coupled system of two logistic maps

Synchronous chaos is investigated in the coupled system of two Logistic maps. Although the diffusive coupling admits all synchronized motions, the stabilities of their configurations are dependent on the transverse Lyapunov exponents while independent of the longitudinal Lyapunov exponents. It is shown that synchronous chaos is structurally stable with respect to the system parameters. The mean motion is the pseudo-orbit of an individual local map so that its dynamics can be described by the local map. (C) 2004 Elsevier Ltd. All rights reserved.

Wavelike patterns in one-dimensional coupled map lattices

We investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two-dimensional mapping. The existence of such wavelike solutions is proved by the implicit function theorem with constraints. We also examine the stabilities of these wave solutions under perturbations of uniform small deformation type. We show that in some specific cases these perturbations are completely general. The technique used in this paper is also applicable to investigate other space-time regular patterns.

Sensitivity map of laser tweezers Raman spectroscopy for single-cell analysis of colorectal cancer

Raman spectroscopy on single, living epithelial cells captured in a laser trap is shown to have diagnostic power over colorectal cancer. This new single-cell technology comprises three major components: primary culture processing of human tissue samples to produce single-cell suspensions, Raman detection on singly trapped cells, and diagnoses of the cells by artificial neural network classifications. it is compared with DNA flow cytometry for similarities and differences. Its advantages over tissue Raman spectroscopy are also discussed. In the actual construction of a diagnostic model for colorectal cancer, real patient data were taken to generate a training set of 320 Raman spectra and, a test set of 80. By incorporating outlier corrections to a conventional binary neural classifier, our network accomplished significantly better predictions than logistic regressions, with sensitivity improved from 77.5% to 86.3% and specificity improved from 81.3% to 86.3% for the training set and moderate improvements for the test set. Most important, the network approach enables a sensitivity map analysis to quantitate the relevance of each Raman band to the normal-to-cancer transform at the cell level. Our technique has direct clinic applications for diagnosing cancers and basic science potential in the study of cell dynamics of carcinogenesis. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Sensitivity map of laser tweezers Raman spectroscopy for single-cell analysis of colorectal cancer

Raman spectroscopy on single, living epithelial cells captured in a laser trap is shown to have diagnostic power over colorectal cancer. This new single-cell technology comprises three major components: primary culture processing of human tissue samples to produce single-cell suspensions, Raman detection on singly trapped cells, and diagnoses of the cells by artificial neural network classifications. it is compared with DNA flow cytometry for similarities and differences. Its advantages over tissue Raman spectroscopy are also discussed. In the actual construction of a diagnostic model for colorectal cancer, real patient data were taken to generate a training set of 320 Raman spectra and, a test set of 80. By incorporating outlier corrections to a conventional binary neural classifier, our network accomplished significantly better predictions than logistic regressions, with sensitivity improved from 77.5% to 86.3% and specificity improved from 81.3% to 86.3% for the training set and moderate improvements for the test set. Most important, the network approach enables a sensitivity map analysis to quantitate the relevance of each Raman band to the normal-to-cancer transform at the cell level. Our technique has direct clinic applications for diagnosing cancers and basic science potential in the study of cell dynamics of carcinogenesis. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Convective coupled map for simulating spatiotemporal chaos in flows

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.

The mechanism of pattern selection in coupled map lattices

The pattern selection of one-dimensional coupled map lattices is studied in this paper. It is shown by spatiotemporal variable separation that there exists a threshold wavelength in pattern selection which possesses wave-like structures in space and periodic chaotic motion in time.

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.