Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the "visible" brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.

Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.

Detection of K-ras exon 1 mutations by constant denaturant capillary electrophoresis

Among various mutation detection methods, constant denaturant capillary electrophoresis (CDCE) is one of the most common techniques for rapid identification of known or unknown mutations. In this report, a CDCE analysis method with homemade linear polyacrylamide (LPA) kit was developed on ABI 310 genetic analyzer, the effect and relationship of various denaturing factors in CDCE analysis were investigated and K-ras gene mutations of 31 coloerctal cancer patients were detected. Results indicate that, with the increase of chemical danaturant concentration, the optimum temperature was lowered, and when the concentration of urea (formamide) was higher than 7 M (40%), the homoduplex and heteroduplex of mutant samples were separated with difficulty. Detection results of K-ras gene in colorectal samples indicated that mutations were present in eight (26%) of 31 patients; most mutations were localized in codon 12, which is thought to be a critical step and plays an important role in human colorectal carcinogenesisas. Copyright (C) 2004 John Wiley Sons, Ltd.

Rhythmic Growth-Induced Ring-Banded Spherulites with Radial Periodic Variation of Thicknesses Grown from Poly(epsilon-caprolactone) Solution with Constant Concentration

Birefringent ring-banded spherulites with radial periodic variation of thicknesses were grown from poly(epsilon-caprolactone) (PCL) solutions under conditions for which the Solution concentration was held constant during the whole development of the morphology. The as-grown ring-banded spherulites were investigated by optical (OM) and atomic force (AFM) microscopies, by transmission electron microscopy (TEM) of samples sectioned parallel to the plane of film, and also by electron diffraction (ED) and grazing incidence X-ray diffraction (GIXD) techniques.

Mass transfer kinetics of neodymium(III) extraction by calix[4]arene carboxylic acid using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamics and kinetics data are both important to explain the extraction property. In order to develop a novel separation technology superior to current extraction systems, many promising extractants have been developed including calixarene carboxylic acids. The extraction thermodynamics behavior of calix[4]arene carboxylic acids has been reported extensively. In this study, the mass transfer kinetics of neodymium(III) and the interfacial behavior of calix[4]arene carboxylic acid were investigated.

Extraction kinetics of thorium(IV) with primary amine N1923 in sulfate media using a constant interfacial cell with laminar flow

Extraction kinetics of thorium(IV) with primary amine N1923 in sulfate media has been investigated by a constant interfacial cell with laminar flow. Studies of interfacial tension and effects of the stirring rate, temperature, and specific interfacial area on mass transfer rate show that the most probable reaction zone takes place at the liquid-liquid interface. According to the experimental data correlated as a function of the concentration of the relevant species involved in the extraction reaction, the rate equation of extracting thorium has been obtained as follows: -d[Th(IV)]((o))/dt = 10(-3.10)center dot[Th(IV)](0.89)center dot[(RNH3)(2)SO4](0.74).

Extraction kinetics of cerium(IV) from sulfuric acid medium by the primary amine N1923 using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamic studies on Ce(IV) extraction with primary amine N1923 demonstrate that primary amine N1923 is an excellent extractant for separation of Ce(IV) from Re(III). In order to clarify the mechanism of extraction and to optimize the parameters in practical extraction systems used in the rare earth industry, the extraction kinetics was investigated using a constant interfacial area cell with laminar flow in the present work.RESULTS: The data indicate that the rate constant (k(ao).) becomes constant when stirring speed exceeds 250 rpm. The apparent forward extraction rate is calculated to be 10(-1.70). The activation energy (E.) was calculated to be 20.5 kJ/mol from the slope of log kao against 1000/T. The minimum bulk concentration of the extractant necessary to saturate the interface (C-min) is lower than 10(-5) mol L-1.CONCLUSION: Studies of interfacial tension and the effects of stirring rate and specific interfacial area on the extraction rate show that the extraction rate is kinetically controlled, and a mass transfer model has been proposed. The rate equation has been obtained as: -d[Ce(IV)]/dt = 10(-1.70)[Ce(IV)] [(RNH3)(2)SO4](1.376). The rate-controlling step has been evaluated from analysis of the experimental results.

Colloidal photonic crystals with a graded lattice-constant distribution

In this work, a gradient polystyrene colloidal photonic crystal was fabricated by annealing in a graded temperature field. The lattice constant of the gradient crystal gradually varied along the temperature-gradient direction. The positional bandgap wavelength as well as the attenuation of the bandgap wavelength could be tuned dependent on the position of the gradient colloidal crystal along the gradient direction because of the lattice-constant variation.

Extraction kinetics of Sc(III), Y(III), La(III) and Gd(III) from chloride medium by Cyanex 302 in heptane using the constant interfacial cell with laminar flow

The extraction kinetics of Sc, Y, La and Gd(III) from the hydrochloric acid medium using Cyanex 302 (hereafter HL) in heptane solution have been measured by the constant interfacial cell with laminar flow. Reaction regions are explored at liquid-liquid interface. Extraction regimes are deduced to be diffusion-controlled for Sc(Ill) and mixed controlled for Y, La and Gd(Ill). Extraction mechanisms are discussed according to the dimeric model of Cyanex 302 in non-polar solution. From the temperature dependence of rate measurement, the values of E-a, Delta H-+/-, Delta S-+/- and Delta G(300)(+/-) are calculated and it is found that the absolute values of these parameters keep crescent trend for Sc, Y, La and Gd(III). At the same time, it is found that it can easily achieve the mutual separation among the Sc, Y and La(III) with kinetics extraction methods.

Measuring the electronic decay constant of alkanedithiols by electrochemical impedance spectroscopy

Several methods have been used for the measurement of the electronic decay constant (beta) of organic molecules. However, each of them has some disadvantages. For the first time, electrochemical impedance spectroscopy (EIS) was used to obtain the 18 value by measuring the tunneling resistance through alkanedithiols. The tunneling resistance through alkanedithiols increases exponentially with the molecular length in terms of the mechanism of coherent nonresonant tunneling. beta was 0.51 +/- 0.01 per carbon.

Kinetics of extraction and stripping of y(III) by Cyanex 272 as an acidic extractant using a constant interfacial cell with laminar flow

The extraction and stripping kinetics of yttrium(III) with bis(2,4,4-trimethylpentyl) phosphinic acid (Cyanex 272, HA) dissolved in heptane as an acid extractant have been investigated by constant interfacial cell with laminar flow. The experimental hydrodynamic conditions have been chosen so that the contribution of diffusion to the measured rate of reaction is minimized. The plot of interfacial area on the rate has shown a linear relationship, which makes the interface the most probable local for the chemical reactions. At the same time, the extraction thermodynamic and kinetic methods are compared to determine the equilibrium extraction constant. A rate equation and the rate-determining step of the extraction and stripping of yttrium(III) have also been obtained, respectively.

A nonmonotonic dependence of standard rate constant on reorganization energy for heterogeneous electron transfer processes on electrode surface

In the present work a nonmonotonic dependence of standard rate constant (k(0)) on reorganization energy (lambda) was discovered qualitatively from electron transfer (Marcus-Hush-Levich) theory for heterogeneous electron transfer processes on electrode surface. It was found that the nonmonotonic dependence of k(0) on lambda is another result, besides the disappearance of the famous Marcus inverted region, coming from the continuum of electronic states in electrode: with the increase of lambda, the states for both Process I and Process II ET processes all vary from nonadiabatic to adiabatic state continuously, and the lambda dependence of k(0) for Process I is monotonic thoroughly, while for Process II on electrode surface the lambda dependence of k(0) could show a nonmonotonicity.

Kinetics of ytterbium(III) extraction with Cyanex 272 using a constant interfacial cell with laminar flow

Studies have been made on the kinetics of ytterbium(III) with bis-(2,4,4-trimethylpentyl) phosphinic acid (Cyanex 272, HA) in n-heptane using a constant interfacial cell with laminar flow. The stiochiometry and the equilibrium constant of the extracted complex formation reaction between Yb3+ and Cyanex 272 are determined. The extraction rate is dependent of the stirring rate. This fact together with the Ea value suggests that the mass transfer process is a mixed chemical reaction-diffusion controlled at lower temperature, whereas it is entirely diffusion controlled at higher temperature. The rate equations for the ytterbium extraction with Cyanex 272 have been obtained. The rate-determining step is also made by predictions derived from interfacial reaction models, and through the approximate solutions of the flux equation, diffusion parameters and thickness of the diffusion film have been calculated.

Mass transfer kinetics of yttrium(III) using a constant interfacial cell with laminar flow. Part II. Extraction with Cyanex 272

The yttrium(III) extraction kinetics and mechanism with bis-(2,4,4-trimethyl-pentyl) phosphinic acid (Cyanex 272, HA) dissolved in heptane have been investigated by constant interfacial cell with laminar flow. The data has been analyzed in terms of pseudo-first order constants. Studies on the effects of stirring rate, temperature, acidity in aqueous phase, and extractant concentration on the extraction rate show that the extraction regime is dependent on the extraction conditions. The plot of interfacial area on the rate has shown a linear relationship. This fact together with the strong surface activity of Cyanex 272 at heptane-water interfaces has made the interface the most probable location for the chemical reactions. The forward, reverse rate equations and extraction rate constant for the yttrium extraction with Cyanex 272 have been obtained under the experimental conditions. The rate-determining step has been also predicted from interfacial reaction models. The predictions have been found to be in good agreement with the rate equations obtained from experimental data, confirming the basic assumption that the chemical reaction is located at the liquid-liquid interface.