Nanoadhesion of a Power-Law Graded Elastic Material

The Dugdale-Barenblatt model is used to analyze the adhesion of graded elastic materials at the nanoscale with Young's modulus E varying with depth z according to a power law E = E-0(z/c(0))(k) (0 < k < 1) while Poisson's ratio v remains a constant, where E-0 is a referenced Young's modulus, k is the gradient exponent and c(0) is a characteristic length describing the variation rate of Young's modulus. We show that, when the size of a rigid punch becomes smaller than a critical length, the adhesive interface between the punch and the graded material detaches due to rupture with uniform stresses, rather than by crack propagation with stress concentration. The critical length can be reduced to the one for isotropic elastic materials only if the gradient exponent k vanishes.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Indentation of power law creep solids by self-similar indenters

For creep solids obeying the power law under tension proposed by Tabor, namely sigma = b(epsilon) over dot(m), it has been established through dimensional analysis that for self-similar indenters the load F versus indentation depth h can be expressed as F(t) = bh(2)(t)[(h) over dot(t)/h(t)](m)Pi(alpha) where the dimensionless factor Pi(alpha) depends on material parameters such as m and the indenter geometry. In this article, we show that by generalizing the Tabor power law to the general three dimensional case on the basis of isotropy, this factor can be calculated so that indentation test can be used to determine the material parameters b and m appearing in the original power law. Hence indentation test can replace tension test. This could be a distinct advantage for materials that come in the form of thin films, coatings or otherwise available only in small amounts. To facilitate application values of this constant are given in tabulated form for a range of material parameters. (C) 2010 Elsevier B.V. All rights reserved.

The generalized second law of thermodynamics in generalized gravity theories

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f ( R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds.

Power law behavior of the isotope yield distributions in the multifragmentation regime of heavy ion reactions

Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, a(sym)/T, extracted in previous work and that of the pairing term, a(p)/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I = N - Z value, the corrected yields of isotopes relative to the yield of C-12 show a power law distribution Y (N, Z)/Y(C-12) similar to A(-tau) in the mass range 1 <= A <= 30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted tau value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be tau(prim) = 2.4 +/- 0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.

Spatial variability in water quality and surface sediment diatom assemblages in a complex lake basin,lake of the woods,ontario,canada

Lake of the Woods (LOW) is an international waterbody spanning the Canadian provinces of Ontario and Manitoba, and the U.S. state of Minnesota. In recent years, there has been a perception that water quality has deteriorated in northern regions of the lake, with all increase in the frequency and intensity of toxin-producing cyanobacterial blooms. However, given the lack of long-term data these trends are difficult to verify. As a first step, we examine spatial and seasonal patterns in water quality in this highly complex lake on the Canadian Shield. Further, we examine surface sediment diatom assemblages across multiple sites to determine if they track within-take differences in environmental conditions. Our results show that there are significant spatial patterns in water quality in LOW. Principal Component Analysis divides the lake into three geographic zones based primarily on algal nutrients (i.e., total phosphorus, TP), with the highest concentrations at sites proximal to Rainy River. This variation is closely tracked by sedimentary diatom assemblages, with [TP] explaining 43% of the variation in diatom assemblages across sites. The close correlation between water quality and the surface sediment diatom record indicate that paleoecological models could be used to provide data on the relative importance of natural and anthropogenic sources of nutrients to the lake.

Exploring the Origin of Power Law Distribution in Single-Molecule Conformation Dynamics: Energy Landscape Perspectives

We explored the origin of power law distribution observed in single-molecule conformational dynamics experiments. By establishing a kinetic master equation approach to study statistically the microscopic state dynamics, we show that the underlying landscape with exponentially distributed density of states leads to power law distribution of kinetics. The exponential density of states emerges when the system becomes glassy and landscape becomes rough with significant trapping.

Dielectric response of graded composites having general power-law-graded cylindrical inclusions

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation epsilon(i)(r)=c(b+r)(k) (where r is the radius of the cylindrical inclusions and c, b and k are parameters). Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile epsilon(i)(r) = cr(k) and a linear dielectric profile epsilon(i)(r) = c(b + r), analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b -> 0 and k -> 1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, epsilon(i)(r)=c(b+r)(k)e(beta r). (c) 2005 American Institute of Physics.

Effective dielectric responses of graded composites of the particles with a general power-law gradation profile

The effective dielectric response of graded spherical composites having general power-law gradient inclusions is investigated under a uniform applied electric field, where the dielectric gradation profile of the spherical inclusions is modeled by the equation epsilon(i) (r) = c(b+r)(k). Analytical solutions of the local electrical potentials are derived in terms of hyper-geometric function and the effective dielectric response of the graded composites is predicted in the dilute limit. From our result, the local potentials of graded spherical composites having both simple power-law dielectric profile epsilon(i)(r) = cr(k) and linear dielectric profile epsilon(i) (r) = c(b+r) are derived exactly by taking the limits b --> 0 and k --> 1, respectively. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded spherical composites, and it is shown that the DEDA is in excellent agreement with exact result. (C) 2005 Elsevier B.V. All rights reserved.

溶蚀岩体渗透水力学特性研究

Seepage control in karstic rock masses is one of the most important problems in domestic hydroelectric engineering and mining engineering as well as traffic engineering. At present permeability assessment and leakage analysis of multi-layer karstic rock masses are mainly qualitative, while seldom quantitative. Quantitative analyses of the permeability coefficient and seepage amount are conducted in this report, which will provide a theoretical basis for the study of seepage law and seepage control treatment of karstic rocks. Based on the field measurements in the horizontal grouting galleries of seepage control curtains on the left bank of the Shuibuya Hydropower Project on the Qingjiang river, a hydraulic model is established in this report, and the computation results will provide a scientific basis for optimization of grouting curtain engineering. Following issues are addressed in the report. (1) Based on the in-situ measurements of fissures and karstic cavities in grouting galleries, the characteristics of karstic rock mass is analyzed, and a stochastic structural model of karstic rock masses is set up, which will provide the basis for calculation of the permeability and leakage amount of karstic rock mass. (2) According to the distribution of the measured joints in the grouting galleries and the stochastic results obtained from the stochastic structural model of karstic rock mass between grouting galleries, a formula for computation of permeability tensor of fracturing system is set up, and a computation program is made with Visual Basic language. The computation results will be helpful for zoning of fissured rock masses and calculation of seepage amount as well as optimization of seepage control curtains. (3) Fractal theory is used to describe quantitatively the roughness of conduit walls of karstic systems and the sinuosity of karstic conduits. It is proposed that the roughness coefficient of kastic caves can be expressed by both fractal dimension Ds and Dr that represent respectively the extension sinuosity of karstic caves and the roughness of the conduit walls. The existing formula for calculating the seepage amount of karstic conduits is revised and programmed. The seepage amount of rock masses in the measured grouting galleries is estimated under the condition that no seepage control measures are taken before reservoir impoundment, and the results will be helpful for design and construction optimization of seepage curtains of the Shuibuya hydropower project. This report is one part of the subject "Karstic hydrogeology and the structural model and seepage hydraulics of karstic rock masses", a sub-program of "Study on seepage hydraulics of multi-layer karstic rock masses and its application in seepage control curtain engineering", which is financially supported by the Hubei Provincial key science and technology programme.