热处理对GeSb2Te4薄膜微观结构及其摩擦性能的影响

利用射频溅射法制备了GeSb2Te4薄膜并对其进行热处理,分析热处理前后样品的结晶情况,用纳米硬度计测定硬度,利用静电力显微镜表征样品的表面电势,采用原子力显微镜观察薄膜表面形貌,利用侧向力显微镜对比考察了在考虑相对湿度的情况下,热处理前后GeSb2Te4薄膜的粘附力和摩擦性能.结果表明:经过退火的沉积态GeSb2Te4薄膜发生从非晶相到fcc亚稳相再到hex稳定相转变;粘附力与表面粗糙度之间没有明显的对应关系,但与样品表面自由能和表面电势有一定关系;在低载荷下GeSb2Te4薄膜的摩擦力很大程度上受粘附力支配,而在高载荷下的摩擦力受犁沟影响显著;经过340 ℃退火GeSb2Te4薄膜由于具有层状结构,呈现出一定的润滑作用.     

纳米GeSb2Te4薄膜在大气环境中的摩擦性能研究

采用摩擦力显微镜考察了磁控溅射纳米GeSb2Te4薄膜在大气环境中的微观摩擦性能,利用JKRS理论分析了针尖同GeSb2Te4薄膜接触时的粘附力和表面能之间的关系.结果表明:当湿度较大时,粘附力较大;而当湿度较小时,粘附力较小;当针尖表面能一定时,粘附力的微小变化可以导致GeSb2Te4薄膜的表面能产生较明显变化;随着扫描范围逐渐减小,摩擦力变化趋于稳定;不同扫描速度下法向力和摩擦力保持较好线性关系,但不同扫描速度下的平均摩擦力随扫描速率变化而呈现非线性变化;为了更好地分析探针和样品表面的微观摩擦机制,宜选择扫描范围为0.1～0.5μm或更小.     

磨损表面形貌的三维分形维数计算

基于分形理论和磨损表面扫描电子显微分析，采用盒子维方法计算了磨损表面的三维分形维数．结果表明，在计算尺度范围内，采用与尺度无关的分形维数表征磨损表面形貌特征是可行的；实际磨损表面的三维分形维数同其表面粗糙度密切相关，表面粗糙度越大，分形维数越大；同表面粗糙度相比，分形维数计算值较稳定.     

磨合过程摩擦力单重分形和多重分形的研究

分别在CD40润滑油和加入添加剂的CD40润滑油润滑条件下,通过销-盘摩擦磨损试验机对船用柴油机活塞环和缸套进行磨合磨损试验,提取摩擦力的时间序列信号,应用分形维数和多重分形谱研究了摩擦力的分形行为.结果表明:摩擦力信号具有分形特征;随着磨合磨损过程的进行,信号的分形维数和多重分形谱出现规律性的变化;不同阶段信号的分形维数趋于减小,与磨损表面粗糙度的变化规律一致;不同阶段信号的多重分形谱呈现出递增或递减趋势,反映了磨损表面的动态变化过程.因此,摩擦力信号的分形维数和多重分形谱可以对磨合磨损过程进行定量分析.     

表面轮廓分形维数计算方法的研究

阐述了表面轮廓分形和分形曲线的基本概念，对目前常用于表面轮廓分形维数的４种计算方法的基本思路作了评介，指出这些方法的计算结果都存在一定的偏差，对选择不同计算尺度得到的分形维数表现出较大的不稳定性，致使分形维数难以准确地反映表面轮廓的真实复杂特征．根据表面轮廓的均方差与区间尺度成比例的性质，提出了表面轮廓分形维数计算的协方差加权法．通过与Ｗｅｉｅｒｓｔｒａｓｓ－Ｍａｎｄｅｌｂｒｏｔ分形函数曲线的分形维数计算的比较，协方差加权法所得表面轮廓分形维数的稳定性良好，计算结果的准确性也明显提高，可以简化表面形貌的识别过程，为摩擦学研究中更准确地描述粗糙表面的复杂特征提供了一种简便适用的新方法．     

用侧向力显微镜对不同非晶态GeSbTe薄膜的摩擦性能研究

采用侧向力显微镜研究了磁控溅射方法制备的GeSbTe薄膜在大气环境中的纳米级摩擦性能,考虑了相对湿度、扫描速度及表面粗糙度对其摩擦性能的影响,对比不同成分的GeSbTe薄膜的摩擦特性.结果表明:在相对湿度较大时,扫描速度对针尖和GeSbTe薄膜之间的摩擦力影响很大;在其它条件相同、外加载荷较大时,同一载荷下的摩擦力与表面粗糙度呈线性关系,但在外加载荷较小的情况下,二者呈现非线性变化规律;相对湿度对Ge2Sb2Te5薄膜和针尖的粘附力影响较GeSb2Te4薄膜弱,且粘附力使得摩擦系数减小;在同一相对湿度下,由于薄膜成分的变化导致硬度不同,其对薄膜的摩擦性能也有一定影响.     

砂轮约束磨粒喷射加工表面的分形及摩擦特性研究

对砂轮约束磨粒喷射精密光整加工(Abrasive Jet Precision Finishing,AJF)表面进行分形维数和摩擦磨损特性研究.试验在MB1332A外圆磨床上完成,加工式样为Ra为0.6μm左右的45#钢.加工表面形貌和微观几何参数用MICROMESVRE2表面轮廓仪测量;应用分形维数和功率谱密度函数评价磨削加工和光整加工表面的微观形貌特征;利用MG-2000型销盘式高速高温摩擦磨损试验机研究表面形貌和分形维数对摩擦系数和磨损性能的影响.试验结果表明:磨粒喷射精密光整加工使工件表面高度特性参数大幅度降低,轮廓波动平均间距减小,波纹细密性提高.随着加工循环的增加,Ra值由0.6μm下降到0.2μm左右.光整加工表面摩擦系数和磨损量与磨削加工表面相比明显降低,摩擦磨损试验结果和分形维数变化相吻合.     

基于基底长度的粗糙表面分形接触模型的构建与分析

为建立更为精确的粗糙表面接触模型,根据微凸体变形特征、分形理论以及摩擦的作用,从微观角度基于基底长度建立了粗糙表面分形接触模型.通过与其他粗糙表面接触模型和实验数据的比较,验证了本文模型的正确与合理,并由数值仿真分析了分形维数、接触载荷与真实接触面积之间的相互关系.分析结果表明:特征尺度一定时,要维持一定的真实接触面积,分形维数越大,所需要的力也越大;分形维数与特征尺度一定时,随着载荷的增加,接触面积也在增加;特征尺度与接触力一定时,随着分形维数的增大,真实接触面积在减小.该模型的建立为进一步研究粗糙表面的摩擦、磨损与润滑提供了理论依据.     

球形磨粒和切削磨粒轮廓分形维数研究

选取 FAENA法作为计算磨粒分形维数方法 ,用试验法、现场收集和磨粒相片 3种方法收集了球形磨粒和切削磨粒各 5 0 0个样本 ,并进行了轮廓分形维数计算 .结果表明 ,这 2种磨粒在 80 0倍放大倍数时具有最好的统计分形 ,轮廓分形维数分布为正态分布 ,球形磨粒分形维数为 D(μD,σ2 )～ D(1.0 2 5 ,0 .36 89× 10 - 4) ,切削磨粒分形维数为 D(μD,σ2 )～ D(1.10 2 ,3.5 79× 10 - 4) ,这 2种典型磨粒轮廓分形维数分布参数的确定对磨粒的自动识别有借鉴作用     

摩擦力和摩擦振动的分形行为研究

在不同的摩擦磨损试验机上提取了摩擦磨损过程中摩擦力和摩擦振动的时间序列信号,采用关联维数方法研究了摩擦力和摩擦振动的分形行为．结果表明：摩擦力和摩擦振动信号具有分形特征;随着摩擦磨损过程的进行,信号分形维数的变化出现规律性的递增或递减;对于“收敛”或磨合磨损过程,不同阶段摩擦信号的分形维数趋于增大;对于“发散”的摩擦磨损过程,不同阶段的摩擦信号的关联维数趋于减小．摩擦力和摩擦振动的分形维数的变化规律同摩擦磨损过程中表面形貌分形维数的变化规律相似。     

粗糙表面的分形特征与分形表达研究

得用触针轮廓仪和数据采集系统对磨削和车削表面的粗糙轮廓曲线进行了测量，并就粗糙表面的分形特征作了分析与讨论，同时还提出了粗糙表面的特征粗糙度概念及其定义，并将其用表面粗糙度水平的表述。     

Fractal porous media

The transport properties of continuous deterministic fractals are reviewed. The method of construction, the fractal dimension, and the major features of transport are summarized. Then the major single-phase transports are addressed; attention is focused on the numerical results and on the analytical arguments which may be used to derive these results in a simple way, whenever it is possible.     

磨粒积聚与磨损表面之间的分形维数关联性研究

在环端面接触磨损试验机上，采用45^#钢—铜配副进行磨损试验，收集不同磨损阶段的磨屑，用光学显微镜进行统计，分析磨粒积聚与磨损表面之间的分形维数关联性．结果表明，磨粒积聚数与其粒径之间存在显著的分段分形特征，第二分形维数同试验时间具有反抛物线函数关系．对磨损表面轮廓的分形测量表明，磨损表面的分形维数变化也具有相似的反抛物线函数关系．此外，磨损表面分形维数同磨粒积聚分形维数具有很好的相关性，但二者之间在磨合前后的对应关系稍有差别；磨粒积聚第二分形维数同磨损率变化成反比．     

Analysis on Fractal Objects

Irregular objects are often modeled by fractals sets. In order to formulate partial differential equations on these nowhere differentiable sets the development of a “new analysis” is necessary. With the help of the model case of the Sierpinski gasket the definition of energy forms and Laplacians on self-similar finitely ramified fractals is explained. Moreover, some results for certain classes of non-self-similar fractals are presented. 2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05     

Waves in Fractal Media

The term fractal was coined by Benoît Mandelbrot to denote an object that is broken or fractured in space or time. Fractals provide appropriate models for many media for some finite range of length scales with lower and upper cutoffs. Fractal geometric structures with cutoffs are called pre-fractals. By fractal media, we mean media with pre-fractal geometric structures. The basis of this study is the recently formulated extension of continuum thermomechanics to such media. The continuum theory is based on dimensional regularization, in which we employ fractional integrals to state global balance laws. The global forms of governing equations are cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order. Using Hamilton??s principle, we derive the equations of motion of a fractal elastic solid under finite strains. Next, we consider one-dimensional models and obtain equations governing nonlinear waves in such a solid. Finally, we study shock fronts in linear viscoelastic solids under small strains. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions and reduce to conventional forms for continuous media with Euclidean geometries upon setting the dimensions to integers.     

On Modeling Flow in Fractal Media form Fractional Continuum Mechanics and Fractal Geometry

In this work we present a model for radial flow in highly heterogenous porous media. Heterogeneity is modeled by means of fractal geometry, a heterogeneous medium is regarded as fractal if its Hausdorff dimension is non-integral. Our purpose is to present a derivation of the model consistent with continuum mechanics, capable to describe anomalous diffusion as observed in some naturally fractured reservoirs. Consequently, we introduce fractional mass and a generalized Gauss theorem to obtain a continuity equation in fractal media. A generalized Darcy law for flux completes the model. Then we develop the basic equation for Well test analysis as is applied in petroleum engineering. Finally, the equation is solved by Laplace transform and inverted numerically to illustrate anomalous diffusion. In this case by showing that the flow rate from fractal systems is smaller than that from the Euclidean system.     

Fractal First-Order Partial Differential Equations

The present paper is concerned with semi-linear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local Hamilton–Jacobi equations. The idea is to combine an integral representation of the operator and Duhamel's formula to prove, on the one hand, the key a priori estimates for the scalar conservation law and the Hamilton–Jacobi equation and, on the other hand, the smoothing effect of the operator. As far as Hamilton–Jacobi equations are concerned, a non-local vanishing viscosity method is used to construct a (viscosity) solution when existence of regular solutions fails, and a rate of convergence is provided. Turning to conservation laws, global-in-time existence and uniqueness are established. We also show that our formula allows us to obtain entropy inequalities for the non-local conservation law, and thus to prove the convergence of the solution, as the non-local term vanishes, toward the entropy solution of the pure conservation law.     

Fractal analysis of Mesoamerican pyramids

A myth of ancient cultural roots was integrated into Mesoamerican cult, and the reference to architecture denoted a depth religious symbolism. The pyramids form a functional part of this cosmovision that is centered on sacralization. The space architecture works was an expression of the ideological necessities into their conception of harmony. The symbolism of the temple structures seems to reflect the mathematical order of the Universe. We contemplate two models of fractal analysis. The first one includes 16 pyramids. We studied a data set that was treated as a fractal profile to estimate the Df through variography (Dv). The estimated Fractal Dimension Dv = 1.383 +/- 0.211. In the second one we studied a data set to estimate the Dv of 19 pyramids and the estimated Fractal Dimension Dv = 1.229 +/- 0.165.     

Fractal sets in control systems

In this paper the Hausdorff measure of sets of integral and fractional dimensions is introduced and applied to control systems.A new concept,namely,pseudo-self-similar set is also introduced.The existence and uniqueness of such sets are then proved,and the formula for calculating the dimension of self-similar sets is extended to the psuedo-self-similar case.Using the previous theorem,we show that the reachable set of a control system may have fractional dimensions.We hope that as a new approach the geometry of fractal sets will be a proper tool to analyze the controllability and observability of nonlinear systems.     

Fractal dimensionality in Rayleigh-Taylor instability

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 162–163, March–April, 1993.