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.     

How the geometry of cities determines urban scaling laws

Urban scaling laws relate socio-economic, behavioural and physical variables to the population size of cities. They allow for a new paradigm of city planning and for an understanding of urban resilience and economics. The emergence of these power-law relations is still unclear. Improving our understanding of their origin will help us to better apply them in practical applications and further research their properties. In this work, we derive the basic exponents for spatially distributed variables from fundamental fractal geometric relations in cities. Sub-linear scaling arises as the ratio of the fractal dimension of the road network and of the distribution of the population embedded in three dimensions. Super-linear scaling emerges from human interactions that are constrained by the geometry of a city. We demonstrate the validity of the framework with data from 4750 European cities. We make several testable predictions, including the relation of average height of cities and population size, and the existence of a critical density above which growth changes from horizontal densification to three-dimensional growth.     

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.     

Computation of the matrix exponential and its derivatives by scaling and squaring

In this paper, a simple method based on the scaling and squaring technique for the evaluation of the matrix exponential and its derivatives is presented. A more general formulation with non‐constant first derivatives is considered here. Both higher order and mixed derivatives are investigated. The method is based directly on the property of the exponential function and does not require the use of perturbation formulae for eigenvalues and eigenvectors. The approach provides a simple and direct algorithm for the computation of the matrix exponential and its derivatives regardless of degeneracy in the spectral decomposition of the matrix argument. If the derivatives are taken with respect to the entries of the matrix argument, the first and second linearizations can be obtained directly. Copyright © 2004 John Wiley & Sons, Ltd.     

土–结构动力离心试验模型材料研究与相似关系设计

相似材料设计是保证试验模型与原型力学性质匹配的关键环节之一。依托滇中引水工程的香炉山隧洞,基于相似理论和量纲分析法,推导跨断层隧洞拟静力缩尺试验物理量的相似关系,进而以重晶石粉、河砂为骨料,以石膏、石灰为胶结材料,研制混凝土及岩体的模型相似材料,并通过一系列试验研究各组分对模型材料物理力学参数的影响。试验结果表明：高强石膏含量、水胶比可显著改变相似材料的强度、弹性模量和密度;当砂胶比取0.8~1.2时材料的强度变化较小,当砂膏比取3~12时材料的强度显著降低;以高强石膏、低强石膏、重晶石粉、河砂制配的相似材料可较好地模拟C30混凝土的弹塑性性能及脆性破坏模式;以高强石膏、石灰、河砂制配的相似材料可较好地模拟IV级、V级围岩的张拉劈裂破坏及斜剪破坏模式。该相似材料的研制过程和配比可为类似模型试验及数值模拟提供重要的参考依据。     

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.     

形变时效对FeMnSiCrNi合金形状回复率和相变温度的影响

为了进一步提高Fe-14Mn-6Si-8Cr-5Ni合金的形状记忆效应,对固溶态合金采用了形变时效的方法处理,并利用光学显微分析、X射线衍射分析和透射电子显微分析的测试手段分析了时效温度和时效时间对合金形状回复率和相变温度的影响.结果表明,固溶态合金经10%拉伸和600℃时效10 min时,形状回复率提高幅度最大,由固溶态的48%提高到84.7%,并且合金γ→ε马氏体转变的起始温度Ms由固溶态的34℃降低到13.2℃.合金的形状回复率得到提高的主要原因是合金中热诱发ε马氏体已经消失,组织为奥氏体和大量定向α’马氏体,这样的组织特征有利于应力诱发γ→ε马氏体相变以及它们的逆相变.     

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.     

Investigation of chemical ageing and its effect on static and fatigue strength of continuous fibre reinforced plastics

The long term durability of continuous glass fibre reinforced thermosets with epoxy resin at high temperature and an oxygen-environment is investigated in detail. An extensive ageing-study is performed to detect the ageing effects on the residual strength in different laminate layups and to identify the corresponding damage mechanisms. Thermal degradation is found to be the dominant damage mechanism and the weight loss is found to be the most suitable measure of damage. A new phenomenological model that is based on the time-temperature-superposition principle and a master-relation between the residual strength and weight loss is presented to model the ageing effect on the residual strength. Fatigue experiments of pre-aged specimen are performed to verify the ageing effects on the fatigue strength. A simple methodology predicting the fatigue life of pre-aged specimen from the residual static strength is demonstrated and validated experimentally for several layups.     

Planar Growth,Integration, and Applications of Semiconducting Nanowires

Silicon and other inorganic semiconductor nanowires (NWs) have been extensively investigated in the last two decades for constructing high-performance nanoelectronics, sensors, and optoelectronics. For many of these applications, these tiny building blocks have to be integrated into the existing planar electronic platform, where precise location, orientation, and layout controls are indispensable. In the advent of More-than-Moore's era, there are also emerging demands for a programmable growth engineering of the geometry, composition, and line-shape of NWs on planar or out-of-plane 3D sidewall surfaces. Here, the critical technologies established for synthesis, transferring, and assembly of NWs upon planar surface are examined; then, the recent progress of in-plane growth of horizontal NWs directly upon crystalline or patterned substrates, constrained by using nanochannels, an epitaxial interface, or amorphous thin film precursors is discussed. Finally, the unique capabilities of planar growth of NWs in achieving precise guided growth control, programmable geometry, composition, and line-shape engineering are reviewed, followed by their latest device applications in building high-performance field-effect transistors, photodetectors, stretchable electronics, and 3D stacked-channel integration.     

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.     

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.     

Two-stage double peaks ageing and its effect on stress corrosion cracking susceptibility of Al-Zn-Mg alloy

Different artificial two-stage ageing behaviors and their effect on stress corrosion cracking(SCC) susceptibility of Al-Zn-Mg alloy have been investigated. The experimental results show that two hardness peaks present on the second-stage ageing-hardening curve when the first-stage ageing is dealt with comparatively lower temperature than the conventional one. The first peak is caused by dispersive and evenly distributed G.P. zones, while η' phases and coarsened G.P. zones contribute to the second peak. Tensile strength of experimental alloy raises 9.6%(33.2 MPa) and SCC susceptibility decreases 38.9% by applying the second peak ageing regime instead of conventional T73. Al-Zn-Mg alloy obtains high strength and SCC resistance due to its finely dispersive matrix precipitates(MPts), coarsened and discontinuous grain boundary precipitates(GBPs), as well as the narrow precipitate free zone(PFZ) in the second peak ageing condition.     

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.     

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.