Surfaces of Bounded Mean Curvature In Riemannian Manifolds

Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.

Chaotic dynamic analysis of viscoelastic plates

The dynamic buckling of viscoelastic plates with large deflection is investigated in this paper by using chaotic and fractal theory. The material behavior is given in terms of the Boltzmann superposition principle. in order to obtain accurate computation results, the nonlinear integro-differential dynamic equation is changed into an autonomic four-dimensional dynamical system. The numerical time integrations of equations are performed by using the fourth-order Runge-Kutta method. And the Lyapunov exponent spectrum, the fractal dimension of strange attractors and the time evolution of deflection are obtained. The influence of geometry nonlinearity and viscoelastic parameter on the dynamic buckling of viscoelastic plates is discussed.

Detection and Characterization of Long-Pulse Low-Velocity Impact Damage in Plastic Bonded Explosives

Damage not only degrades the mechanical properties of explosives, but also influences the shock sensitivity, combustion and even detonation behavior of explosives. The study of impact damage is crucial in the vulnerability evaluation of explosives. A long-pulse low-velocity gas gun with a gas buffer was developed and used to induce impact damage in a hot pressed plastic bonded explosive. Various methods were used to detect and characterize the impact damage of the explosive. The microstructure was examined by use of polarized light microscopy. Fractal analysis of the micrographs was conducted by use of box counting method. The correlation between the fractal dimensions and microstructures was analyzed. Ultrasonic testing was conducted using a pulse through-transmission method to obtain the ultrasonic velocity and ultrasonic attenuation. Spectra analyses were carried out for recorded ultrasonic signals using fast Fourier transform. The correlations between the impact damage and ultrasonic parameters including ultrasonic velocities and attenuation coefficients were also analyzed. To quantitatively assess the impact induced explosive crystal fractures, particle size distribution analyses of explosive crystals were conducted by using a thorough etching technique, in which the explosives samples were soaked in a solution for enough time that the binder was totally removed. Impact induces a large extent of explosive crystal fractures and a large number of microcracks. The ultrasonic velocity decreases and attenuation coefficients increase with the presence of impact damage. Both ultrasonic parameters and fractal dimension can be used to quantitatively assess the impact damage of plastic bonded explosives.

Avalanche behavior and statistical properties in a microcrack coalescence process

Fracture owing to the coalescence of numerous microcracks can be described by a simple statistical model, where a coalescence event stochastically occurs as the number density of nucleated microcracks increases. Both numerical simulation and statistical analysis reveal that a microcrack coalescence process may display avalanche behavior and that the final failure is catastrophic. The cumulative distribution of coalescence events in the vicinity of critical fracture follows a power law and the fracture profile has self-affine fractal characteristic. Some macromechanical quantities may be traced back and extracted from the mesoscopic process based on the statistical analysis of coalescence events.

Collective evolution characteristics and computer simulation of short fatigue cracks

Fatigue testing was conducted using a kind of triangular isostress specimen to obtain the short-fatigue-crack behaviour of a weld low-carbon steel. The experimental results show that short cracks continuously initiate at slip bands within ferrite grain domains and the crack number per unit area gradually increases with increasing number of fatigue cycles. The dispersed short cracks possess an orientation preference, which is associated with the crystalline orientation of the relevant slip system. Based on the observed collective characteristics, computer modelling was carried out to simulate the evolution process of initiation, propagation and coalescence of short cracks. The simulation provides progressive displays which imitate the appearance of experimental observations. The results of simulation indicate that the crack path possesses a stable value of fractal dimension whereas the critical value of percolation covers a wide datum band, suggesting that the collective evolution process of short cracks is sensitive to the pattern of crack site distribution.

Numerical simulation of evolution-induced catastrophe

A numerical simulation of damage evolution in a two-dimensional system of micocracks is presented. It reveals that the failure is induced by a cascade of coalescences of microcracks, and the fracture surface appears fractal. A model of evolution-induced catastrophe is introduced. The fractal dimension is found to be a function of evolution rule only. This result could qualitatively explain the correlation of fractal dimension and fracture toughness discovered in experiments.

Evolution induced catastrophe

Fracture due to coalescence of microcracks seems to be catalogued in a new model of evolution induced catastrophe (EIC). The key underlying mechanism of the EIC is its automatically enlarging interaction of microcracks. This leads to an explosively evolving catastrophe. Most importantly, the EIC presents a fractal dimension spectrum which appears to be dependent on the interaction.

On the Selection of Non-Invasive Methods Based on Speech Analysis Oriented to Automatic Alzheimer Disease Diagnosis

The work presented here is part of a larger study to identify novel technologies and biomarkers for early Alzheimer disease (AD) detection and it focuses on evaluating the suitability of a new approach for early AD diagnosis by non-invasive methods. The purpose is to examine in a pilot study the potential of applying intelligent algorithms to speech features obtained from suspected patients in order to contribute to the improvement of diagnosis of AD and its degree of severity. In this sense, Artificial Neural Networks (ANN) have been used for the automatic classification of the two classes (AD and control subjects). Two human issues have been analyzed for feature selection: Spontaneous Speech and Emotional Response. Not only linear features but also non-linear ones, such as Fractal Dimension, have been explored. The approach is non invasive, low cost and without any side effects. Obtained experimental results were very satisfactory and promising for early diagnosis and classification of AD patients.

Effect of surface roughness on rarefied-gas heat transfer in microbearings

In this Letter, the rarefaction and roughness effects on the heat transfer process in gas microbearings are investigated. A heat transfer model is developed by introducing two-variable Weierstrass-Mandelbrot (W-M) function with fractal geometry. The heat transfer problem in the multiscale self-affine rough microbearings at slip flow regime is analyzed and discussed. The results show that rarefaction has more significant effect on heat transfer in rough microbearings with lower fractal dimension. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. The heat transfer performance can be optimized with increasing fractal dimension of the rough surface. © 2012 Elsevier B.V. All rights reserved.

A priori assessment of algebraic flame surface density models in the context of large eddy simulation for nonunity lewis number flames in the thin reaction zones regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimension D and inner cut-off scale η i have been studied in detail. It has been found that D is strongly affected by Lewis number and increases significantly with decreasing Le. By contrast, η i remains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation of D is proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD. © 2012 Mohit Katragadda et al.

Effects of turbulent reynolds number on the performance of algebraic flame surface density models for large eddy simulation in the thin reaction zones regime: A direct numerical simulation analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an asymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel'dovich flame thickness ηi/δz does not exhibit any significant dependence on Ret for the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width. © 2012 Mohit Katragadda et al.

安达市碱性草地土壤颗粒的分维特征

运用土壤颗粒质量分形模型计算松嫩平原低平地安达试区植被分布区和碱斑区样点土壤颗粒的分形维数,并建立分形维数与土壤颗粒不同粒级间的回归关系,以探讨土地碱化后土壤粒径分布的分形特征及其与土壤物理性状的关系。结果表明:安达试区土壤颗粒分形维数较高,平均分别仅有48.7×10-5cm/s(Pit A)和4.30×10-6cm/s(Pit B),反映了该区土壤细颗粒含量高、土壤大孔隙数量少、土壤饱和导水率低的特征;土壤颗粒分形维数与黏粒含量呈对数正相关关系,而与粉粒和砂粒含量相关性不显著,说明在安达试区,影响土壤颗粒分形维数的主要因素是黏粒含量;羊草地土壤颗粒分形维数在土壤垂直剖面上的变异较大,说明植被生长促进了土壤质地的变异;碱斑地土壤颗粒分形维数明显大于羊草地,细颗粒含量高,饱和导水率低,说明碱斑的形成恶化了土壤物理性质;土壤颗粒分形维数可以反映安达市土壤物理性质的好坏,能作为土壤退化和生态环境恶化的评价指标。研究结果可为安达市以及松嫩平原盐碱地生态环境的修复和治理提供科学依据。

黄土丘陵区不同恢复年限草地土壤微团粒分形特征

运用分形理论研究黄土丘陵区不同恢复年限草地土壤微团粒的粒径组成、分形维数特征及与土壤理化性质关系,使分形学在土壤微团粒性状与土壤肥力特征研究中得到进一步应用,并为评价草地生态系统土壤特征及生态恢复提供新方法。结果表明:表土层分形维数随植被恢复年限的增加而减少;剖面土壤沙粒含量越高,微团粒分形维数越低,粘粒规律相反,而粉粒与分形维数相关性不显著;土壤质地由粗到细使得分形维数由小到大变化;分形维数也可有效地表征不同植被恢复年限的草地土壤结构和养分的变化趋势;分形维数与土壤容重、非活性孔度、全磷、速效钾及氨态氮之间存在正相关性,与土壤活性孔度、孔隙比、有机质、全氮、碱解氮及硝态氮表现出负相关。

青藏高原东缘高山林线乔木种群生态特征研究

青藏高原东部分布着世界最高的林线，该区域也是由欧亚北温带物种形成的林线的南界。在大面积野外踏勘的基础上，选择青藏高原东部具有典型高山林线分布的三个地点（滇西北白马雪山、川西北鹧鸪山及岷江源地区）作为研究区，从种群的结构、生存特征、分布格局及分形特征等方面对青藏高原东缘高山林线乔木种群生态学特征进行了研究，并在此基础上探讨了人类活动对林线种群生态特征及林线格局的影响。结果表明，林线区乔木树种多以单种群形式存在，林线区群落结构简单，乔木层多为单一树种组成，其生长型较之郁闭林发生了急剧的变化：树木高度急剧下降，而发展多茎多分枝的生长型。生长型的转变是高山林线乔木对恶劣自然条件的形态适应。 研究发现，在青藏高原东缘，阴坡林线乔木主要是冷杉（Abies spp.），阳坡主要由圆柏（Sabina spp.）组成，少数地方还有云杉（Picea spp.）。阴坡乔木种群结构多表现为增长型，幼苗和幼树在种群中占较大比重，种群潜在自然更新能力较强，但幼龄个体死亡率非常高，存活曲线多接近Deevey-Ⅲ型；阳坡乔木种群幼苗个体数极少，幼树相对增加。野外调查表明，人为活动较频繁的阳坡林线区幼苗数量极少甚至缺失，而受人为活动干扰较小的样地中幼苗和幼树数量明显增多，从一个侧面说明放牧等人类活动可能对林线种群的更新带来较大影响，而对卡卡沟围栏内外的样地分析也进一步证明了这一结果。 所研究林线乔木种群各龄级的空间格局在不同尺度上表现为聚集、随机和均匀分布，以聚集分布为主；各龄级在不同尺度上表现出显著的相关性，幼苗通常与另外两个龄级的关联性较密切。各龄级间显著的相关性表明不同龄级个体在空间交错分布，有利于对各种资源的充分利用，对种群的生存和发展非常有利，反映了高山生态系统恶劣生境中种群的一种适应对策。 林线乔木种群各龄级分布格局的计盒维数有差别，林线种群的计盒维数总是小于郁闭林种群的计盒维数。另外，郁闭林各龄级计盒维数通常也高于林线各龄级，表明不同海拔或者不同群落类型中的乔木树种具有不同的水平空间占据能力。林线区种群分布格局的计盒维数都很低，占据现实水平空间的程度较低，具有相对较高的生态间隙维，其潜在占据空间的能力较高，群落还可提供给种群的最大空间限度较大，但实际上由于受群落中种内、种间的竞争及林线区恶劣的生态环境条件的限制，其潜在空间占据能力可能难以表现出来。 青藏高原东缘高海拔地带以季节性游牧为主要的资源利用和生产方式，阳坡森林郁闭度低于阴坡，灌丛数量和种类较阴坡少，融雪早且积雪时间短，所以阳坡包括高山林线区成为当地牧民游牧路线的必经之地。牲畜的践踏、啃食使得幼龄乔木树种个体数量大大减少，严重阻碍了林线乔木种群的自然更新，同时种群占据空间的能力也明显降低。因此可以认为，在青藏高原东部地区，山地游牧等人为干扰叠加于恶劣的自然条件，阳坡林线的自然更新潜力受到抑制，其生存状态较之阴坡林线显著恶化，并可使阳坡林线高度逐渐降低。高山林线区森林一旦破坏在短时间内很难有效更新和恢复，因此，对于处于恶劣高山生境中的乔木种群应加强保护，同时适度控制人为干扰强度和幅度以减少其直接和间接破坏，防止阳坡林线退化并促进高山生态系统的自然恢复。 Eastern Qinghai-Tibetan Plateau has the highest timberline of the world. On the basis of field surveys and literature reviews, three typical alpine timberlines were chosen for in-depth studies, i.e., Baima Snow Mountain in northwest Yunnan, Zhegu Mountain and the waterhead area of Minjiang River in west Sichuan. Using the methodologis of population ecology, we analyzed the population structure, survival characteristics, spatial point patterns and fractal dimensions of the timberline tree populations and discussed the impacts of grazing on the structure and spatial pattern of alpine timberline. Compared with closed forests, the community structure of timberline is simpler, usually with one or two species constituting the tree layer. Differences also exist in the growth forms: the trees were significantly shorter with more stems and branches, reflecting morphological adaptation of trees to the severe conditions at timberline. In the eastern Qinghai-Tibetan Plateau, Abies spp. often formed alpine timberline in the north-facing slope while Sabina spp. and sometimes Picea spp. in the south- facing slope. The population structures of north-facing slope showed an increasing trend, with numerous seedlings and saplings. However, the survival curves tend to follow Deevy-III because of high dead ratio of young individuals. There are only few seedlings in the south-facing slope with heavy grazing, demonstrating that human disturbance may prevent regeneration at alpine timberline, which was confirmed by comparisons between fenced enclosures and control plots in the Kaka Valley. Depending on the spatial scales on consideration, the individuals of different age-classes showed clumping, random or even distribution, but mostly with clumping distribution. At all scales, individuals in different age-classes were all significantly correlated with each other while the seedlings were usually more correlated to two other age classes. This high degree of correlation among different age classes indicates that individuals of different age classes are spatially interlocked with each other, which helps sufficient utilization of various resources and is conducive to the survival and development of population. It is another adaptation strategy for trees at the severe environment. The spatial patterns of different age classes had different box dimension. In general, the box dimensions of total individuals and each age class at timberline are always smaller than that of closed forests, suggesting that space occupation capacity is not the same for populations at different altitude or in different communities. Populations on both the south- and the north-facing slopes had a very low box dimensions (far away from the max., 2), however, the lower the box dimension, the bigger the potential space provided by community. In fact, because of inner- and inter- competition as well as the severe conditions at timberline, this kind of potential ability can hardly be realized. Mountain pastoralism is the major type of as well as the only most effective way of resource uses in the high elevation regions of the eastern Qinghai-Tibetan Plateau. Due to lower canopy cover, less bushes and short snow-cover time, south-facing slopes became the favorite pastures. Damages from livestock through tramping, browsing and others have greatly reduced the number of young individuals. As a result, the potential of timberline trees to regenerate and their ability to occupy more space are greatly inhitibted. We conclude that human disturbances (mountain pastoralism) as well as harsh environmental conditions co-worked to inhibit the regeneration of tree populations in the south-facing slope and made south slopes more difficult than the north-facing slopes for trees to survive and develop, resulting a gradual retreat of timberline in the north-facing slopes. Forests at alpine timberline are susceptible to disturbance and difficult to regenerate and restore once damaged and controlling human disturbances is important for protecting the forest ecosystems at the timberline area.

子午岭林区典型植被下土壤结构及稳定性指标分析

运用分形理论,研究了子午岭林区5种天然次生植被(以6 a天然恢复弃耕地为对照)下土壤结构特征,分析了土壤水稳性团聚体分维、孔隙分维、平均重量直径等3个指标在描述土壤结构稳定性方面的差异。研究表明,相对于弃耕地,各个植被群落均能明显改善土壤结构,降低土壤水稳性团聚体分形维数,提高孔隙分形维数,增强土壤结构的稳定性。土壤水稳性团聚体分维、孔隙分维与>0.25 mm水稳性团聚体含量、土壤有机碳、容重的相关系数均达到了极显著水平,均能作为评价土壤结构稳定性的指标;而团聚体平均重量直径与土壤有机碳含量、容重相关性不显著,只与>5 mm团聚体含量和>0.25 mm团聚体含量有极显著正相关关系,因此,仅可作为大团聚体含量的评价指标。