Elastic coefficients

Networks were prepared in all cases using the amount of endlinking agent necessary to give a minimum Mc. Values of Mc were calculated from the Mooney-Rivlin elasticity coefficient Cj, determined from tensile stress-strain measurements (10),... 

Experimentally-determined values of T0 for PDMS networks are plotted in Figure 3 against values of Mc calculated from the elastic coefficient C by means of equation 2. TQ was found to be accurately proportional to M, in accordance with equation 1, with the coefficient of proportionality K being about 0.30, 0.25, and 0.23 J/m2/(molecular weight unit) for the A4, A3, and randomly-linked materials, respectively. These differences are small, barely significant, but in the expected direction. Values of T0 are also shown in Figure 3 for the other materials examined. 

The interpretation of the elements of the matrix 0 is slightly more subtle, as they represent the derivatives of unknown functions fi(x) with respect to the variables x at the point x° = 1. Nevertheless, an interpretation of these parameters is possible and does not rely on the explicit knowledge of the detailed functional form of the rate equations. Note that the definition corresponds to the scaled elasticity coefficients of Metabolic Control Analysis, and the interpretation is reminiscent to the interpretation of the power-law coefficients of Section VII.C Each element 6% of the matrix measures the normalized degree of saturation, or likewise, the effective kinetic order, of a reaction v, with respect to a substrate Si at the metabolic state S°. Importantly, the interpretation of the elements of does again not hinge upon any specific mathematical representation of specific... 

ELASTICITY COEFFICIENT ELECTRIC CHARGE ELECTRIC POTENTIAL ELECTROMOTIVE EORCE ELECTROACTIVE SPECIES ELECTROCATALYSIS Electrocyclic reaction,... 

Within the elastic limit the substance returns to its original state when the stress is removed. In this case the elastic coefficient, which is stress divided by strain is constant and is known as the modulus of elasticity... 

In traditional discussions based on eq. (20), the resonance conditions have been expressed in terms of the magnetostriction coefficients. However, Du Tremolet de Lacheisserie (1995) has found that the elastic coefficients of the substrate (S 1 and S 2s) have entered his formulas of the resonance frequency. He showed that in the SMFMR method only the bY,2 and ba2 coefficients can be determined. 

The Elasticity Coefficient Is Related to an Enzyme s Responsiveness to Changes in Metabolite or Regulator Concentrations... 

FIGURE 15-35 Elasticity coefficient, e, of an enzyme with typical Michaelis-Menten kinetics. At substrate concentrations far below the Km, each increase in [S] produces a correspondingly large increase in the reaction velocity, v. For this region of the curve, the enzyme has an elasticity, e, of about 1.0. At [S] Km, increasing [S] has little effect on v s here is close to 0.0. 

The elasticity coefficient, e, of an enzyme is an experimentally determined measure of how responsive the enzyme is to changes in the concentration of a metabolite or regulator molecule. 

It is assumed that the interface is normal to the applied load. If either phase has anisotropic elastic coefficients, the generalized Young s modulus should be calculated as described by Nye [20],... 

The calculated isothermal elastic tensor for yS-HMX is compared in Table 8 to the one reported by Zaug (isentropic conditions). Uncertainties in the calculated elastic coefficients represent one standard deviation in values predicted from five contiguous two nanosecond simulation sequences from the overall ten nanosecond simulation. As mentioned above, Zaug s experiments sufficed to determine uniquely five of the thirteen elastic constants (modulo the... 

Elastic coefficients and isotropic shear modulus (G) for HMX polymorphs... 

Well-determined experimental values (see text) are in bold. cSymmetry-dictated equivalencies of the elastic coefficients for <5-FI MX (hexagonal crystal lattice) are indicated. 

Room temperature elastic tensors for a- and [Pg.318]

The last relation shows that a long macromolecule rolls up into a coil at high temperatures. The smaller the elasticity coefficient a is, the more it coils up. Another name for the model of flexible thread is the model of persistence length or the Kratky-Porod model. The quantity a/T is called the persistence length (Birshtein and Ptitsyn 1966). 

Indeed, it shows that the length of a segment or the elasticity coefficient depends on the temperature, which contradicts the proposed features of the models. 

A great deal of effort has been expended in attempts to find a distribution function for the end-to-end length of the chain (Valleau 1996). Oono et al. (1981) have shown that in the simplest approximation, the distribution function for non-dimensional quantity R2/ R2) is close to Gaussian, so the above results allow one to write down an expression for the elasticity coefficient, when the excluded-volume effect is taken into account, in the form... 

The expansion determines the terminal quantities the viscosity coefficient 7] and the elasticity coefficient u which, in their turn, determine the terminal relaxation time and steady-state compliance, correspondingly,... 

First, we shall consider in detail the characteristic quantities the viscosity coefficient rj and the elasticity coefficient i/, defined by expansion (6.11), and the value of the dynamic modulus on the plateau Ge. The latter can be calculated as the limiting value of the modulus at frequencies satisfying the relation... 

Considering that f, g, x, and u are vectors, the differentiation leads to formation of matrices. The matrix A is well known in stability analysis as the jacobian matrix it quantifies the effects of all state variables on their rates of change. A matrix similar to B turns up in metabolic control analysis, as N3v/3p [48, 108], where it denotes the immediate effects of parameter perturbations on the rates of change of all variables. If the function y is scalar and denotes a rate, then C becomes a row vector c harboring unsealed elasticity coefficients and D becomes a row vector d containing so-called n-elasticities - sensitivities of the rates with respect to the parameters [109]. The linearized system is ... 

As is seen (Table 2) filling of PTFE matrix with MWNT increases both yield strength and elasticity coefficient of material. 

It is seen from Fig. 4 and Table 3 that introduction of starting MWNT into PTFE matrix increases both yield strength and elasticity coefficient of the material. Introduction of electrochemically oxidized MWNT resulted in increase of yield strength without noticeable change of elasticity coefficient. 

Kruckeberg, A. L., Neuhaus, H. E., Feil, R.. Gottlieb, L. D., and Stitt, M. 1989. Decreased-activity mutants of phosphoglucose isomerase in the cytosol and chloroplast of Clarkia xantiana Impact on mass-action ratios and fluxes to sucrose and starch and estimation of flux control coefficients and elasticity coefficients. Biochem. J. 261, 457-467. 

Table 18 shows values of strength at break, Ob, deformation at break, 8b, and elasticity coefficient, E, of studied polymer networks. The data indicate that substitution of methyl groups by phenyl ones and variation of the distance between chain branching centers is accompanied by a significant chan-ge of deformation and strength properties of studied polymers. Note that substitution of both methyl groups by phenyl ones is accompanied by the... 

Metabolic control analysis (MCA) is a specialized theory that is concerned with particular sensitivity coefficients, elasticity coefficients and control coefficients. These coefficients tell us how a steady state of a biochemical system shifts in response to perturbation in enzyme activities or external (clamped) substrate concentration [53, 209],... 

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