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.

beta-delayed proton decays and spin assignments for Sm-133 and Yb-149

The proton-rich isotope Sm-133 was produced via the fusion evaporation reaction Ca-40 + Ru-96. Its beta-delayed proton decay was studied by p-gamma coincidence in combination with a He-jet tape transport system, and half-lives, proton energy spectra, gamma-transitions following the proton emission, as well as beta-delayed proton branching ratios to the low-lying states in the grand-daughter nucleus were determined. Comparing the observed beta-delayed proton branching ratios with statistical model calculations, the best agreement is found assuming that only one level with the spin of 3/2 in Sm-133 decays or two levels with the spins of 1/2 and 5/2 decay with similar half-lives. The configuration-constrained nuclear potential energy surfaces of Sm-133 were calculated using the Woods-Saxon-Strutinsky method, which suggests a 1/2-ground state and a 5/2(+) isomer with an excitation energy of 120 keV. Therefore, the simple(EC+beta(+)) decay scheme of Sm-133 in Eur. Phys. J.A 11,277(2001) has been revised. In addition, our previous experimental data on the beta-delayed proton decay of Yb-149 reported in Eur. Phys. J. A 12,1 ( 2 0 0 1) was also analyzed using the same method. The spin-parity of Yb-149 is suggested to be 1/2(-).

beta-delayed proton decays and spin assignments for Tb-140, Dy-141 and Dy-143

The proton-rich isotopes Tb-140 and Dy-141 were produced via the fusion evaporation reaction Ca-40+ Cd-106. Their beta-delayed proton decays were studied by p-gamma coincidence in combination with a He-jet tape transport system, and half-lives, proton energy spectra, gamma-transitions following the proton emission, as well as beta-delayed proton branching ratios to the low-lying states in the grand-daughter nuclei were determined. Comparing the experimental data with statistical model calculations, the ground-state spins of Tb-140 and Dy-141 were found to be consistent with 7 and 9/2, respectively. The configuration-constrained nuclear potential energy surfaces (NPES) of Tb-140 and Dy-141 were calculated using the Woods-Saxon-Strutinsky method, which suggest the ground-state spins and parities of Tb-140 and Dy-141 to be 7(+) and 9/2(-), respectively. In addition, the configuration-constrained NPES of Dy-143 were calculated, which predict a 1/2(+) ground state and a 11/2(-) isomer with excitation energy of 198 keV. These findings are consistent with our previous experimental data on Dy-143 reported in Eur. Phys. J. A 16, 347 (2003).

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.

Emergy Assessment of a Wheat-Maize Rotation System with Different Water Assignments in the North China Plain

Sustainable water use is seriously compromised in the North China Plain (NCP) due to the huge water requirements of agriculture, the largest use of water resources. An integrated approach which combines the ecosystem model with emergy analysis is presented to determine the optimum quantity of irrigation for sustainable development in irrigated cropping systems. Since the traditional emergy method pays little attention to the dynamic interaction among components of the ecological system and dynamic emergy accounting is in its infancy, it is hard to evaluate the cropping system in hypothetical situations or in response to specific changes. In order to solve this problem, an ecosystem model (Vegetation Interface Processes (VIP) model) is introduced for emergy analysis to describe the production processes. Some raw data, collected by investigating or observing in conventional emergy analysis, may be calculated by the VIP model in the new approach. To demonstrate the advantage of this new approach, we use it to assess the wheat-maize rotation cropping system at different irrigation levels and derive the optimum quantity of irrigation according to the index of ecosystem sustainable development in NCP. The results show, the optimum quantity of irrigation in this region should be 240-330 mm per year in the wheat system and no irrigation in the maize system, because with this quantity of irrigation the rotation crop system reveals: best efficiency in energy transformation (transformity = 6.05E + 4 sej/J); highest sustainability (renewability = 25%); lowest environmental impact (environmental loading ratio = 3.5) and the greatest sustainability index (Emergy Sustainability Index = 0.47) compared with the system in other irrigation amounts. This study demonstrates that application of the new approach is broader than the conventional emergy analysis and the new approach is helpful in optimizing resources allocation, resource-savings and maintaining agricultural sustainability.

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.

Nuclear magnetic resonance spectral assignments of 2,2 '-bis(p-aminobenzoic ester)-1,1 '-binaphthyl

H-1 and C-13 nuclear magnetic resonance (NMR) spectra of 2, 2'-bis(p-aminobenzoic ester)-1,1'-binaphthyl were assigned and confirmed using 2D H-1-H-1 COSY, C-13-H-1 HETCOR and C-13-H-1 long-range HETCOR methods. This provided a basis for NMR characterization of the similar compounds.

NMR investigation of phenolphthalein polyether ether ketone .1. The chain structure and assignments of H-1, C-13 NMR lines of PEK-C

Amorphous samples of polyether ketone with cardo(PEK-C) have been studied in the solution state by C-13, H-1 high-resolution NMR, The H-1 and C-13 1D NMR spectra were assigned using two dimensional chemical shift correlated spectroscopy, 2D homonuclear correlated(COSY) and heteronuclear correlated (HETCOR) spectroscopy present important information. In this work, the structural units of PEK-C was determined by NMR. For some peaks, these assignments are confirmed by two dimensional long-range heteronuclear correlation experiments, A little modification is made on the original C-13 peak assignments for the main chain, The symmetry and the isotacticity of the chain structure for PEK-C are obvious on NMR data.

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.