The constructal unification of biological and geophysical design

Here we show that the emergence of scaling laws in inanimate (geophysical) flow systems is analogous to the emergence of allometric laws in animate (biological) flow systems, and that features of evolutionary “design” in nature can be predicted based on a principle of physics (the constructal law): “For a finite-size flow system to persist in time (to live) it must evolve in such a way that it provides easier and easier access to its currents”, meaning that the configuration and function of flow systems change over time in a predictable way that improves function, distributes imperfection, and creates geometries that best arrange high and low resistance areas or volumes. This theoretical unification of the phenomena of animate and inanimate flow design generation is illustrated with examples from biology (lung design, animal locomotion) and the physics of fluid flow (river basins, turbulent flow structure, self-lubrication). The place of this design-generation principle as a self-standing law in thermodynamics is discussed. Natural flow systems evolve by acquiring flow configuration in a definite direction in time: existing configurations are replaced by easier flowing configurations.     

Density limits imposed by the microstructure of magnetic recording media

The fundamental limit of magnetic recording density on conventional media is set by the grain size. Once this grain size limit is reached, only a reduction of the grain size allows an increased SNR and thus an increased areal density. It is shown that, whilst maintaining thermal stability, scaling demands that the required anisotropy energy density K is proportional to the areal density, or the square of the areal density if the medium thickness reaches the critical thickness (A is the exchange stiffness of the material). Recording onto materials with such a high anisotropy requires some form of a write-assist. It is furthermore shown that the grain size limit cannot be obtained with intergranular exchange present, and six different requirements are listed that constitute ideal media. An alternative path for increasing areal density of magnetic recording is to use patterned media, where each bit contains only one grain. In this case, written-in errors dominate system performance and the maximum achievable areal density is estimated to be about 6 Tbit/in². Patterned media need to exhibit narrow distributions of their physical and structural properties with standard deviations of the order of 5% or less.     

L2(Rs)中正交尺度函数和正交小波的Fourier变换紧支集的刻画

借助于Fourier变换,在较弱条件下给出了φ(x)是L²(R^s)上正交尺度函数的一个充分必要条件.进一步, 假设 {Ψ_μ } 是正交小波, 且正交小波的Fourier变换紧支集是 ∪_μsupp{ψ_μ} =∏^s_i=1[A_i, D_i] -∏^s_i=1(B_i, C_i),A_i≤B_i≤C_i≤D_i, i =1, 2,… , s. 则在最弱条件“每一个 |ψ_μ| 在ω∈∂(∏^s_i=1[A_i, D_i]) 上连续'下, 该文通过一些不等式和等式给出了正交尺度函数和正交小波的Fourier变换紧支集的刻画.文中的结论全面改进了龙瑞麟和张之华的结果.     

Adiabatic shear banding and scaling laws in chip formation with application to cutting of Ti–6Al–4V

The phenomenon of adiabatic shear banding is analyzed theoretically in the context of metal cutting. The mechanisms of material weakening that are accounted for are (i) thermal softening and (ii) material failure related to a critical value of the accumulated plastic strain. Orthogonal cutting is viewed as a unique configuration where adiabatic shear bands can be experimentally produced under well controlled loading conditions by individually tuning the cutting speed, the feed (uncut chip thickness) and the tool geometry. The role of cutting conditions on adiabatic shear banding and chip serration is investigated by combining finite element calculations and analytical modeling. This leads to the characterization and classification of different regimes of shear banding and the determination of scaling laws which involve dimensionless parameters representative of thermal and inertia effects. The analysis gives new insights into the physical aspects of plastic flow instability in chip formation. The originality with respect to classical works on adiabatic shear banding stems from the various facets of cutting conditions that influence shear banding and from the specific role exercised by convective flow on the evolution of shear bands. Shear bands are generated at the tool tip and propagate towards the chip free surface. They grow within the chip formation region while being convected away by chip flow. It is shown that important changes in the mechanism of shear banding take place when the characteristic time of shear band propagation becomes equal to a characteristic convection time. Application to Ti–6Al–4V titanium are considered and theoretical predictions are compared to available experimental data in a wide range of cutting speeds and feeds. The fundamental knowledge developed in this work is thought to be useful not only for the understanding of metal cutting processes but also, by analogy, to similar problems where convective flow is also interfering with adiabatic shear banding as in impact mechanics and perforation processes. In that perspective, cutting speeds higher than those usually encountered in machining operations have been also explored.     

半掺杂钙钛矿Pr0.5Sr0.5CoO3中磁熵变的标度律研究

对半掺杂氧化钴Pr0.5Sr0.5CoO3在居里温度附近的磁熵变进行了研究。研究表明,磁熵变的最大值依赖于外磁场强度;半高宽也与磁场强度有关;相对制冷能力与磁场强度几乎呈线性关系。另外,在不同的温度和磁场强度下测得的磁熵变能够重新标度为一条普适的曲线。依据该唯象的普适曲线,能够较准确的计算出在不同温度和磁场强度下磁熵变的大小。     

Characterizing the creep of viscoelastic materials by fractal derivative models

In this paper, we make the first attempt to apply the fractal derivative to modeling viscoelastic behavior. The methodology of scaling transformation is utilized to obtain the creep modulus and relaxation compliance for the proposed fractal Maxwell and Kelvin models. Comparing with the fractional derivatives reported in the literature, the fractal derivative as a local operator has lower calculation costs and memory storage requirements. Moreover, numerical results show that the proposed fractal models require fewer parameters, have simpler mathematical expression and result in higher accuracy than the classical integer-order derivative models. Results further confirm that the proposed fractal models can characterize the creep behavior of viscoelastic materials.     

On network form and function

Moving from the observation that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review theoretical and observational evidence on river patterns and their scale-invariant structure. Exact results complemented by numerical annealing of the basic equation in the presence of additive noise suggest that configurations at (or very close to) the global minimum of energy dissipation differ from dynamically accessible states, which have rather different scaling properties and conform much better to natural forms. Thus we argue that, at least in the fluvial landscape, Nature works through imperfect searches for dynamically accessible optimal configurations. We also show that optimal networks are spanning loopless configurations only under precise physical requirements. This is stated in a form applicable to generic networks, suggesting that other branching structures occurring in Nature (e.g. scale-free and looping) may possibly arise through optimality to selective pressures. Indeed, we show that this is the case.     

Mechanics of adhesive contact at the nanoscale: The effect of surface stress

At small length scales, the adhesion and surface effect are of great significance, both of which play important roles in the contact between two elastic solids. In this study, the classical Johnson–Kendall–Roberts (JKR) adhesive contact theory is generalized to the nanoscale at which the surface effect is considered. The influence of the surface stress on the JKR adhesive contact is investigated by employing the non-classical Boussinesq fundamental solutions. It is found that, compared with the classical theory, the pull-off force increases while the critical contact radius decreases as a result of the surface effect. Numerical results show that a relative error of 10% can be introduced in the pull-off force when the indenter radius is less than 20 nm. A detailed theoretical analysis of this interesting phenomenon is presented based on dimensional analysis, and two scaling laws for the adhesive contact at the nanoscale are constructed. These two new scaling laws reveal that the pull-off force is relevant to the elastic properties of the bulk materials, which is different from the classical adhesive contact theory. The present work is promising for the engineering applications in micro-electro-mechanical systems (MEMS) and nano-intelligent devices.