Ising-type transitions in coupled map lattices

We study, by means of computer simulations, some models of coupled map lattices (CML) with symmetry, subject to diffusive nearest neighbor coupling, with the purpose of providing, a better understanding of the occurrence of Isingtype transitions of the type found by Miller and Huse. We argue, on the basis of numerical evidence, that such transitions are connected to the appearance of a minimum in the Lyapunov dimension of the system as a function of the coupling parameter. Two-dimensional CMLs similar to the one in Miller and Huse, but with no minimum in the Lyapunov dimension plot, have no Ising transition. The condition seems to be necessary, though by no means sufficient. We also argue, relying on the analysis of Bunimovich and Sinai, that coupled map lattices should behave differently, with respect to dimension, than Ising models.Dedicated to Yakov Grigorievich Sinai on his 60th birthday.     

基于多重耦合映像格子的信号初值恢复研究

利用耦合映像格子恢复信号初值是信号处理研究中一个重要的问题.耦合映像格子具有混沌系统的初值敏感性，当初值受到噪声污染时将会影响到系统对其的恢复.提出了一种由多个一维耦合映像格子系统并列耦合而成的多重耦合映像格子系统，通过将多个一维系统耦合，使因受到噪声干扰而趋向于指数分离的混沌轨道相互靠近，以达到抑制噪声的目的.数值仿真表明，该系统具有较强的抗噪声能力和较高的鲁棒性.在耦合系数选取适当的情况下，即使初始信号受到噪声干扰，该多重耦合系统仍然能够很好地恢复信号初值的统计特性，且对单个初值的恢复情况及与初始信号 关键词： 耦合映像格子 恢复信号的统计特性 多重耦合     

Experimental evidence for non-linear growth in compressible mixing layer

An experimental study of compressible mixing layers(CMLs)was conducted using planar laser Mie scattering(PLMS)visualizations from condensed ethanol droplets in the flow.Large ensembles of digital images were collected for two flow conditions at convective Mach numbers Mc=0.11 and 0.47.The coherent vortices,braids and eruptions in the mixing zone were observed,interpreted as evidence of multi-scale,three-dimensional structures at a high Reynolds number.The mixing layers with a large visualized range present two stages along the streamwise direction,corresponding to the initial mixing and the well-developed stage.A new method,the gray level ensemble average method(GLEAM),by virtue of the similarity of the mixing layer,was applied to measure the growth rate of the CML thickness.New evidence for a nonlinear growth of CML is reported,providing an interpretation of previous observations of the scattering of the growth rate.     

A self-learning coupled map lattice for vortex shedding in cable and cylinder wakes

A coupled map lattice (CML) with self-learning features is developed to model flow over freely vibrating cables and stationary cylinders at low Reynolds numbers. Coupled map lattices that combine a series of low-dimensional circle maps with a diffusion model have been used previously to predict qualitative features of these flows. However, the simple nature of these CML models implies that there will be unmodeled wake features if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is first trained to precisely estimate wake patterns from a target numerical simulation. A new convective-diffusive map that includes additional wake dynamics is developed. The new self-learning CML uses an adaptive estimation scheme (multivariable least-squares algorithm). Studies of this approach are conducted using wake patterns from a Navier-Stokes solution (spectral element-based NEKTAR simulation) of freely vibrating cable wakes at Reynolds numbers Re=100. It is shown that the self-learning model accurately and efficiently estimates the simulated wake patterns. The self-learning scheme is then successfully applied to vortex shedding patterns obtained from experiments on stationary cylinders. This constitutes a first step toward the use of the self-learning CML as a wake model in flow control studies of laboratory wake flows.     

Existence and stability of steady fronts in bistable coupled map lattices

We prove the existence and we study the stability of the kinklike fixed points in a simple coupled map lattice (CML) for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CMLs in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.     

Stability analysis of coupled map lattices at locally unstable fixed points

Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for exploring fundamental features of CMLs, such as their stability properties. Since CMLs can be considered as graphs, we apply methods of spectral graph theory to analyze their stability at locally unstable fixed points for different updating rules, different coupling scenarios, and different types of neighborhoods. Numerical studies are found to be in excellent agreement with our theoretical results.     

A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics

Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices (CMLs). It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence (CD). Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to-noise ratios (SNRs) are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors using symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.     

An improved algorithm and its parallel implementation for solving a general blood-tissue transport and metabolism model

Fast algorithms for simulating mathematical models of coupled blood-tissue transport and metabolism are critical for the analysis of data on transport and reaction in tissues. Here, by combining the method of characteristics with the standard grid discretization technique, a novel algorithm is introduced for solving a general blood-tissue transport and metabolism model governed by a large system of one-dimensional semilinear first order partial differential equations. The key part of the algorithm is to approximate the model as a group of independent ordinary differential equation (ODE) systems such that each ODE system has the same size as the model and can be integrated independently. Thus the method can be easily implemented in parallel on a large-scale multiprocessor computer. The accuracy of the algorithm is demonstrated for solving a simple blood-tissue exchange model introduced by Sangren and Sheppard [W.C. Sangren, C.W. Sheppard, A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment, Bull. Math. Biophys. 15 (1953) 387–394], which has an analytical solution. Numerical experiments made on a distributed-memory parallel computer (an HP Linux cluster) and a shared-memory parallel computer (a SGI Origin 2000) demonstrate the parallel efficiency of the algorithm.     

Developments in geothermal energy in Mexico—part thirty-four. Numerical steady-state simulation of the steam supply system of the cerro prieto geothermal plant

The philosophy used in the mathematical modelling of the steam supply network of Cerro Prieto geothermal power stations is described. In order to form the simulation model of this system, mathematical models were developed for: the surface equipment such as separators, pressure control stations, steam turbines, low and high pressure interconnections, purges and wells. With the above mentioned models a computer programme was produced which operating conditions in the steam supply system.     

从耦合映象格子中粗略恢复初值的统计特性

耦合映象格子用于信号处理研究时，从中恢复出初始条件是一个非常重要的问题.提出一种粗略恢复格点初值的方法，数值实验表明，动力学函数使用Logistic映射时，在映象过程不存在噪声的情况下，恢复的整个格子初始信号平均值等于给定信号分布的真实平均值，而恢复信号的方差小于给定信号的真实方差.将耦合看作是对独立映射的一种变换，对此作了初步解释，同时发现Logistic映射不同参数下的符号序列排序存在一些有趣的规律.对耦合格子映射研究、非线性耦合则量等是非常有启发意义的. 关键词： 耦合映射格子 信号恢复的统计特性     

Computer simulation of a shock-absorbing pneumatic cylinder

A mathematical simulation model of a double-acting pneumatic cushioning cylinder, designed to absorb periodic shock loads, is presented, which is based on the following assumptions: ideal equation of state, isentropic flow through a port-bleed orifice, isentropic compression process, single degree of freedom piston-cylinder dynamics, and the energy-equivalent linear damping. Because of the non-linear differential equation and a requirement for simultaneous iterative solution, a computer simulation model is employed to predict pressure and motion time histories, and cylinder performance indices. Predictions for both untuned and tuned cylinder example cases are compared with measurements. Good correlations between simulation and experiment are evident even though empirical models for discharge coefficients and damping have been used. The computer simulation has been successful in evaluating a number of products, and thus can be used as a design tool. However, more experimental work must be done to improve its prediction capabilities.     

Predicting Fiber Contact in a Three-Dimensional Model of Paper

We present a new methodology for the mathematical analysis of 3D paper structure and apply it to a model that can be simulated on a computer. We rigorously derive upper and lower bounds for fiber contact areas, and derive an approximation that is very close to values calculated from the simulations. The method involves the stochastic geometry and combinatorics of large numbers of randomly located sets, which quantify the interactions between fibers. The main calculation involves a sum resembling a partition function with many-body interactions of all orders.     

蚀刻表面面形的分析

采用一个有效的数学模型,分析了在蚀刻工艺中基底自身面形轮廓的曲线形状对基底局部区域的蚀刻速率产生的影响,并通过对数学模型的理论分析和计算机模拟得出受此影响而产生的面形形状,并将结果与实验进行对比.利用这个数学模型对使用离子束蚀刻制作单台阶光栅的台阶与沟槽部分的表面面形随时间的演变过程进行了计算机模拟分析,并通过把理论结果与在实验中得到的蚀刻表面在原子力显微镜(AFM)下拍摄的照片进行比较,结果说明这种模拟分析能够保证对该问题分析所要求的精度,从而也证明了理论模型的合理性和正确性.     

An Introduction to Digital Philosophy

Digital Philosophy (DP) is a new way of thinking about how things work. This paper can be viewed as a continuation of the author's work of 1990[3]; it is based on the general concept of replacing normal mathematical models, such as partial differential equations, with Digital Mechanics (DM). DP is based on two concepts: bits, like the binary digits in a computer, correspond to the most microscopic representation of state information; and the temporal evolution of state is a digital informational process similar to what goes on in the circuitry of a computer processor. We are motivated in this endeavor by the remarkable clarification that DP seems able to provide with regard to many of the most fundamental questions about processes we observe in our world.     

Fundamental comparison of time-domain experimental modal analysis methods based on high- and first-order matrix models

All time-domain methods for experimental modal analysis (EMA) begin with a mathematical model. Based on either a high-order matrix polynomial model or a first-order state-space model, this paper emphasizes the comparison of numerical conditioning and stability, as well as the modal parameter estimation, among EMA methods. Numerical conditioning pertains to the perturbation behavior of a mathematical problem (model) itself and stability pertains to the perturbation behavior of an algorithm used to solve that problem on a computer. As various EMA methods are modeled differently with distinct solution algorithms, implementing these methods would have different conditioning and stability. In this paper, both deterministic and stochastic EMA methods are covered. Three different scenarios for the response signal are considered: (1) clean response from impulse loading, (2) noisy response from impulse loading, and (3) noisy response from ambient noise excitation. Comparing the numerical conditioning of various EMA methods, this paper theoretically illustrates that methods based on first-order state-space models are more likely to be well-conditioned (with a smaller conditioning number) than those based on high-order polynomial models. Furthermore, the numerical observation of a case study for a 6 degree-of-freedom system also suggests that first-order state-space model methods are more robust and accurate for the estimation of modal frequency and damping.     

A tailored solver for bifurcation analysis of ocean-climate models

In this paper, we present a new linear system solver for use in a fully-implicit ocean model. The new solver allows to perform bifurcation analysis of relatively high-resolution primitive-equation ocean-climate models. It is based on a block-ILU approach and takes special advantage of the mathematical structure of the governing equations. In implicit models Jacobian matrices have to be constructed. Analytical construction is hard for complicated but more realistic representations of mixing. This is overcome by evaluating the Jacobian in part numerically. The performance of the new implicit ocean model is demonstrated using (i) a high-resolution model of the wind-forced double-gyre flow problem in a (relatively small) midlatitude spherical basin, and (ii) a medium-resolution model of thermohaline and wind-driven flows in an Atlantic size single-hemispheric basin.     

Critical area computation for real defects and arbitrary conductor shapes

In current critical area models, it is generally assumed the defect outlines are circular and the conductors to be rectangle or the merger of rectangles. However, real defects and conductors associated with optimal layout design exhibit a great variety of shapes. Based on mathematical morphology, a new critical area model is presented, which can be used to estimate the critical area of short circuit, open circuit and pinhole. Based on the new model, the efficient validity check algorithms are explored to extract critical areas of short circuit, open circuit and pinhole from layouts. The results of experiment on an approximate layout of ${4\times 4}$ shifts register show that the new model predicts the critical areas accurately. These results suggest that the proposed model and algorithm could provide new approaches for yield prediction.     

透明管径及管厚的CCD成像在线测量方法

应用光线透过透明管径的折射规律,提出线阵CCD成像在线测量透明管状外径及壁厚的新方法。该方法用计算机进行模拟导出了数理模型。实验证明了这一方法的可行性,为透明管状产品的批量生产、高速、动态、非接触实时在线测量提供了一条新的技术途径。     

HL—IM装置等离子体MHD平衡问题分析

本文论述了用二维轴对称平衡模型计算和分析带铁芯变压器的HL-1M装置等离子体MHD自洽平衡问题。对固定边界和自由边界的等离子体平衡分别作了计算,给出了等离子体平衡的计算结果和磁通量图的研究结果,为HL-1M装置极向场系统设计和建造提供了可靠的数据,也为将来装置的运行提供了很好的数值编码。