Intraspecific scaling laws of vascular trees

A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volume–diameter and flow–length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter–length, flow–diameter and flow–volume scaling laws. The intraspecific scaling predicts the volume–diameter power relation with a theoretical exponent of 3, which is validated by the experimental measurements for the three major coronary arterial trees in swine (where a least-squares fit of these measurements has exponents of 2.96, 3 and 2.98 for the left anterior descending artery, left circumflex artery and right coronary artery trees, respectively). This scaling law as well as others agrees very well with the measured morphometric data of vascular trees in various other organs and species. This study is fundamental to the understanding of morphological and haemodynamic features in a biological vascular tree and has implications for vascular disease.     

Constructing cities,deconstructing scaling laws

Cities can be characterized and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al. have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realizations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide us enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size, regardless of the definition of the urban boundaries. However, when nonlinear correlations are present, the exponent fluctuates considerably.     

On the scaling law of throttle microliquefiers

The paper shows the derivation of the throttle-type microliquefiers¹ scaling law and similarity conditions on the grounds of a dimensional analysis theory. The computed results obtained by using the scaling law are compared with the experimental data.     

A dimensionless ordered pull-through model of the mammalian lens epithelium evidences scaling across species and explains the age-dependent changes in cell density in the human lens

We present a mathematical (ordered pull-through; OPT) model of the cell-density profile for the mammalian lens epithelium together with new experimental data. The model is based upon dimensionless parameters, an important criterion for inter-species comparisons where lens sizes can vary greatly (e.g. bovine (approx. 18 mm); mouse (approx. 2 mm)) and confirms that mammalian lenses scale with size. The validated model includes two parameters: β/α, which is the ratio of the proliferation rate in the peripheral and in the central region of the lens; and γ_GZ, a dimensionless pull-through parameter that accounts for the cell transition and exit from the epithelium into the lens body. Best-fit values were determined for mouse, rat, rabbit, bovine and human lens epithelia. The OPT model accounts for the peak in cell density at the periphery of the lens epithelium, a region where cell proliferation is concentrated and reaches a maximum coincident with the germinative zone. The β/α ratio correlates with the measured FGF-2 gradient, a morphogen critical to lens cell survival, proliferation and differentiation. As proliferation declines with age, the OPT model predicted age-dependent changes in cell-density profiles, which we observed in mouse and human lenses.     

四元数方法表示的反射和折射定律

在讨论四元数及其基本运算、Rodrigues-Hamilton参数表示的四元数和四元数变换算子的基础上,给出了标准四元数的定义。基于标准四元数,推导了四元数方法表示的光线反射和折射变换算子,并给出了对应的计算公式,为复杂光学系统以及失调光学系统的空间光线传输计算奠定了理论基础。     

Incomplete self-similarity and fatigue-crack growth

The Paris power law, which relates fatigue-crack growth rates to the applied stress-intensity range, is an example of a scaling law with the inherent property of incomplete similarity. Previous considerations of dimensions and self-similarity have suggested that the assumed materials constants in this law are also a function of specimen size. In this note, the question of the size-dependence of the Paris law is re-examined, and through comparison to a larger body of fatigue-crack growth data in steels, physical explanations why such scaling effects may exist are deduced.     

Influence of prestrain and ageing on near-threshold fatigue crack growth in fine-grained dual-phase steels

The influence of martensite content, prestraining and ageing on near-threshold fatigue crack growth in dual-phase (DP) steels was studied. The experiments were performed on fine-grained, commercially available DP-steels with volume fractions of martensite from 2–42 %. No influence of martensite volume fraction on the nominal or effective threshold values was found. Cold deformation prior to testing resulted in a decrease of both the nominal and effective thresholds, other than for DP-steels with a high martensite content where no such influence was found. A subsequent peak-ageing of either the initial or the prestrained conditions did not result in any further changes of the threshold values. Again an exception was found for the DP-steel with high martensite content where combined straining and ageing caused a lowering of the nominal level, leaving the effective value unaffected. The crack closure was determined for all structural variants and related to results from quantitative fractographic measurements.     

A dynamic model of annual foliage growth and carbon uptake in trees

The growth of trees and other plants occurs through the interactive combination of photosynthesis and carbon (and other nutrient) assimilation. Photosynthesis enables the production of carbohydrate that can then be used in growing foliage, whereby photosynthesis is enabled. We construct a mathematical model of carbon uptake and storage, which allows the prediction of the growth dynamics of trees. We find that the simplest model allows uncontrolled foliage production through the positive feedback outlined above, but that leaf shading provides an automatic saturation to carbon assimilation, and hence to foliage production. The model explains the necessity for finite leaf area production at outbreak, and it explains why foliage density reaches a constant value during a growing season, while also non-leaf tissue also continues to grow. It also explains why trees will die when their carbon stores are depleted below a certain threshold, because the cost of foliage growth and maintenance exceeds the dynamic supply of carbon by photosynthesis.     

Reversion of natural ageing and restoration of quick bake-hardening response in Al-Zn-Mg-Cu alloy

The high-strength Al-Zn-Mg-Cu alloy provides much better dent resistance and weight-reduction poten-tial compared to the conventional Al alloys used for the automobile body panels.However,natural age-ing (NA) significantly reduces the formability of Al-Zn-Mg-Cu alloy.The reversion of natural ageing has been systematically investigated by hardness test,tensile test,differential scanning calorimetry (DSC) and transmission electron microscopy (TEM).Substantial reversion of natural ageing and thus hardness de-crease occurs immediately upon thermal treatment at 120-210 ℃ in an Al-Zn-Mg-Cu alloy.Although the hardness of the most reverted state decreases with increasing temperature,the lowest hardness is still higher than the as-quenched state by 30HV.As revealed by the complementary DSC and TEM observa-tions,this is ascribed to the synchronization of the dissolution and the re-precipitation of the solutes in the NA clusters during reversion ageing.Reversion at 180-210 ℃ for less than 30 s leads to a hardness decline of 40HV.The hardening kinetics during NA after reversion is slower than that during first-time NA due to the reduced vacancy concentration.Artificial ageing at 180 ℃ for 30 min after secondary NA of less than 24 h induces intensive precipitation of plate-like pre-ηphases and a giant strength increase of 188-204 MPa.Potential use of high strength Al-Zn-Mg-Cu alloy in automobile body panels could be realized by appropriate reversion treatment improving the formability and the quick bake hardening re-sponse.     

Microneedle-assisted transdermal delivery of Zolmitriptan: effect of microneedle geometry,in vitro permeation experiments,scaling analyses and numerical simulations

Objective: The present study was aimed to investigate the effect of salient microneedle (MN) geometry parameters like length, density, shape and type on transdermal permeation enhancement of Zolmitriptan (ZMT).

Methods: Two types of MN devices viz. AdminPatch^® arrays (ADM) (0.6, 0.9, 1.2 and 1.5?mm lengths) and laboratory fabricated polymeric MNs (PM) of 0.6?mm length were employed. In the case of PMs, arrays were applied thrice at different places within a 1.77?cm² skin area (PM-3) to maintain the MN density closer to 0.6?mm ADM. Scaling analyses was done using dimensionless parameters like concentration of ZMT (C_t/C_s), thickness (h/L) and surface area of the skin (Sa/L²).

Results: Micro-injection molding technique was employed to fabricate PM. Histological studies revealed that the PM, owing to their geometry/design, formed wider and deeper microconduits when compared to ADM of similar length. Approximately 3.17- and 3.65-fold increase in ZMT flux values were observed with 1.5?mm ADM and PM-3 applications when compared to the passive studies. Good correlations were observed between different dimensionless parameters with scaling analyses. Numerical simulations, using MATLAB and COMSOL software, based on experimental data and histological images provided information regarding the ZMT skin distribution after MN application.

Discussion: Both from experimental studies and simulations, it was inferred that PM were more effective in enhancing the transdermal delivery of ZMT when compared to ADM.

Conclusions: The study suggests that MN application enhances the ZMT transdermal permeation and the geometrical parameters of MNs play an important role in the degree of such enhancement.     

Growth mode transitions and scaling behaviour at successive stages of molecular beam epitaxy

Recently developed kinetic model for homoepitaxial growth is extended to the case of heteroepitaxy (without lattice mismatch) by introducing different adatom surface mobilities in the first layer (heterodiffusion) and in all the next layers (self-diffusion). With this model the effect of two adatom mobilities as a function of the Schwoebel step-edge barrier is studied with an emphasis on the growth mode transitions. It is shown that the difference between homo- and heteroepitaxy is confined to the first few monolayers and is crucially sensitive to the ratio between the hetero- and self-diffusion coefficients: lower heterodiffusion coefficient with respect to that of self-diffusion improves essentially epitaxial growth and vice-versa. This is important for growing smooth ultrathin layers needed in modern nanotechnology. Island density kinetics in successive growing layers is studied and it is found that in smooth growth regime it acquires eventually (after deposition approx. 10 monolayers) a universal scaling form and corresponding scaling exponents have been determined.     

Nonlinear crack dynamics and scaling aspects of fracture (experimental and theoretical study)

Nonlinear dynamics of crack propagation are investigated experimentally and theoretically with the goal of clarifying the nature of limiting crack velocity, the transition from steady state to branching regimes of crack dynamics, and the dynamics of crack arrest. The theoretical explanation of limiting steady-state crack velocity and the transition to a branching regime was proposed due to the study of collective behavior of a microcrack ensemble at the crack tip area. The experimental study of crack dynamics was carried out in a preloaded plate PMMA specimen using the high-speed camera coupled with the photo-elasticity method, the point stress recording with a laser system, and the failure surface roughness measurement.     

The influence of heat treatment and strain rate on the third type strain ageing phenomenon

In this study, to further understand the effect of microstructure on the third type strain ageing (3rd SA) phenomenon, three kinds of heat treatments were conducted on cold-rolled DH-36 structural steel. The microstructures of the heat-treated specimens were observed using scanning electron microscope and compared with the as-received microstructure. The influences of heat treatment on the 3rd SA effect were analyzed. Through the analysis of the previous experimental results of DH-36 steel and Q235B steel, stress peak in the flow stress vs. temperature curves caused by the 3rd SA effect was observed at each of the indicated strain rates for the two steels. As strain rate increases, the stress peak shifts to higher temperature range. Based on the mechanism of the 3rd SA effect, e.g. the interaction of moving dislocations and diffusing solute atoms, a model was developed to quantitatively describe the strain rate effect on the 3rd SA effect.     

气泡在聚合物内长大过程的等温有限元模拟

针对气泡在聚合物熔体内的等温长大过程,建立了其几何模型和有限元模型;采用幂律型流体本构关系描述聚合物流变性质;对控制方程进行无量纲化处理,采用Galerkin方法对对流扩散有限元控制方程进行数值求解;采用隐式差分法对扩散方程中的时间导数项进行离散,并在每个时间步进行网格重划分,确保计算结果的可靠性。计算获得了聚合物内发泡剂浓度分布规律及不同的特征无量纲量对气泡长大过程的影响。     

一些相依序列的强大数律和收敛速度

本文研究了正相协序列、负相协序列、强正相依序列以及鞅差序列的强极限性质.利用负相协序列和弱鞅序列的极大值矩不等式以及随机变量的截尾方法,得到了上述相依序列的强大数定律、强收敛速度以及相应的随机变量序列上确界的可积性.本文不仅将独立情形下的强大数定律推广到以上相依序列,并且还给出了其收敛速度.     

Natural ageing of tri-layer polyethylene film: Evolution of properties and lifetime in North Africa region

The effects of natural ageing in the north Algeria of tri-layer films lay down hot greenhouse made of low-density polyethylene are presented in this work. Ageing was monitored by observing the changes of physical, mechanical and structural effects on the various greenhouse faces. It has been shown that the structural change occur on the outside face of the films, while the inside faces are protected by the dye. The study shows that the measured parameters are directly related to the criteria of evaluation of the greenhouse effectiveness. The lifetime of these films under natural conditions in north Algerian was estimated to be 10 months.     

Timing analysis of safety properties using fault trees with time dependencies and timed state-charts

Behavior in time domain is often crucial for safety critical systems. Standard fault trees cannot express time-dependent behavior. In the paper, timing analysis of safety properties using fault trees with time dependencies (FTTDs) and timed state-charts is presented. A new version of timed state-charts (TSCs) is also proposed. These state-charts can model the dynamics of technical systems, e.g. controllers, controlled objects, and people. In TSCs, activity and communication times are represented by time intervals. In the proposed approach the structure of FTTD is fixed by a human. Time properties of events and gates of FTTD are expressed by time intervals, and are calculated using TSCs. The minimal and maximal values of these time intervals of FTTD can be calculated by finding paths with minimal and maximal time lengths in TSCs, which is an NP-hard problem. In order to reduce the practical complexity of computing the FTTD time parameters, some reductions of TSCs are defined in the paper, such as sequential, alternative, loop (iteration), and parallel. Some of the reductions are intuitive, in case of others—theorems are required. Computational complexity of each reduction is not greater than linear in the size of reduced TSC. Therefore, the obtained results enable decreasing of the costs of FTTD time parameters calculation when system dynamics is expressed by TSCs. Case study of a railroad crossing with a controller that controls semaphores, gate, light-audio signal close to the gate will be analyzed.     

Industrial and occupational ergonomics in the petrochemical process industry: a regression trees approach

This work is an attempt to apply classification tree methods to data regarding accidents in a medium-sized refinery, so as to identify the important relationships between the variables, which can be considered as decision-making rules when adopting any measures for improvement. The results obtained using the CART (Classification And Regression Trees) method proved to be the most precise and, in general, they are encouraging concerning the use of tree diagrams as preliminary explorative techniques for the assessment of the ergonomic, management and operational parameters which influence high accident risk situations. The Occupational Injury analysis carried out in this paper was planned as a dynamic process and can be repeated systematically. The CART technique, which considers a very wide set of objective and predictive variables, shows new cause-effect correlations in occupational safety which had never been previously described, highlighting possible injury risk groups and supporting decision-making in these areas. The use of classification trees must not, however, be seen as an attempt to supplant other techniques, but as a complementary method which can be integrated into traditional types of analysis.     

光学晶体的生长缺陷及分析方法

介绍了光学晶体中的各种生长缺陷,分析了它们的成因以及对于光学晶体性能的影响,并介绍了相关检测方法与手段的特点和局限性.     

氧化锌纳米晶体的生长及生长机理分析

采用沉淀法生长了不同粒径且性能良好的氧化锌纳米晶体,探讨了晶粒尺寸与煅烧温度的变化关系,研究了ZnO纳米晶体的生长机理.通过实验验证了在中间产物Zn(OH)2中加入NH4HCO3后,ZnO纳米晶体实现了局域生长,很好地阻碍了晶核的过度生长,从而使生成的ZnO纳米晶体保持很小的粒径.煅烧温度较低时,ZnO纳米晶体的生长模式为正常扩散生长,煅烧温度在800℃时,发生了竞争生长现象.