Cross-point coordinates

Figure 12. Maxwellian zero-shear viscosity computed from cross-point coordinates versus ng for Series-I and II as well as for neat LLDPE resins.

The high frequency cross point coordinates (Gjj, Uj ) were used for calculation of the Maxwellian zero-shear viscosity, tiom from Equation 38. For the neat polymers tiqh was In agreement with ng calculated from the shear and extenslonal responses. For BL, BL-1 and especially BL-2 ngfi < ng. The presence of an apparent yield stress Is the most likely explanation for the discrepancy. 

The cross-point coordinates G = G - G" at u Wjj were determined for all coiiq>osltions then the Maxwellian viscosity n was calculated from Equation 38. The results are shown In Fig. 32 as noM vs. rig. In agreement with the previously discussed data for... 

Two types of rheological phenomena can be used for the detection of blend s miscibility (1) influence of polydispersity on the rheological functions, and (2) the inherent nature of the two-phase flow. The first type draws conclusions about miscibility from, e.g., coordinates of the relaxation spectmm maximum cross-point coordinates (G, CO ) [Zeichner and Patel, 1981] free volume gradient of viscosity a = d(lnT]) / df the initial slope of the stress growth function S = d(lnr +g)/dlnt the power-law exponent n = d(lnOj2)/dlny = S, etc. The second type involves evaluation of the extrudate swell parameter, B = D/D, strain (or form) recovery, apparent yield stress, etc. 

Cross-point coordinates (Gx, fflx) (Zeichner and Patel 1981)... 

The second dependence in Eq. (2.32) is valid when all fractions are either entangled or not. In consequence, the relaxation spectrum of a miscible polymer blend is a linear combination of the component relaxation spectra and their weight fractions, W(. A strong deviation from linearity in plots of log Hq versus Mw/Afn and log Wmax versus log r]o indicates immiscibility [87, 88]. The principle that in miscible blends polydispersity can be calculated and used to test for system miscibility was extended to other rheological functions sensitive to polydispersity, namely, the power-law exponent (n), the cross-point coordinates (G, o) ), the free volume gradient of viscosity, the initial slope of stress growth function, and so on [3]. 

The path cost computing is performed according to the distance.Let Px(j) and Py(j) the cross points coordinates.the cost is computed with n-1... 

Figure 5. A cut across the ground state (GS) and the excited state (ES) potential surfaces of the H4 system. The parameter Qp is the phase preserving nuclear coordinate connecting the H(lll) with the transition state between H(I) and H(1I) (Fig, 4). Keeping the phase of the electronic wave function constant, this coordinate leads from the ground to the excited state. At a certain point, the two surfaces must touch. At the crossing point, the wave function is degenerate.

Worth and Cederbaum [100], propose to facilitate the search for finding a conical intersection if the two states have different symmetiies If they cross along a totally symmetric nuclear coordinate, then the crossing point is a conical intersection. Even this simplifying criterion leaves open a large number of possibilities in any real system. Therefore, Worth and Cederbaum base their search on large scale nuclear motions that have been identified experimentally to be important in the evolution of the system after photoexcitation. 

Intercepts. Find those points where the cui ves of the function cross the coordinate axes. 

This formula, however, tacitly supposes that the instanton period depends monotonically on its amplitude so that the zero-amplitude vibrations in the upside-down barrier possess the smallest possible period 2nla>. This is obvious for sufficiently nonpathological one-dimensional potentials, but in two dimensions this is not necessarily the case. Benderskii et al. [1993] have found that there are certain cases of strongly bent two-dimensional PES when the instanton period has a minimum at a finite amplitude. Therefore, the cross-over temperature, formally defined as the lowest temperature at which the instanton still exists, turns out to be higher than that predicted by (4.7). At 7 > Tc the trivial solution Q= Q Q is the saddle-point coordinate) emerges instead of instanton, the action equals S = pV (where F " is the barrier height at the saddle point) and the Arrhenius dependence k oc exp( — F ") holds. 

A and A = 0.1 eV. The adiabatic ground potential energy surface is shown in Fig. 11. The present results (solid line) are in good agreement with the quantum mechanical ones (solid circles). The minimum energy crossing point (MECP) is conventionally used as the transition state and the transition probability is represented by the value at this point. This is called the MECP approximation and does not work well, as seen in Fig. 10. This means that the coordinate dependence of the nonadiabatic transmission probability on the seam surface is important and should be taken into account as is done explicitly in Eq. (18). 

The cross-peak coordinates represent two frequency values, va and vp, where va + vp=2v, and v is the proton frequency. When plotted in the coordinates v2a and v2p, the contour lineshape is transformed into a straight line segment. An extrapolation of this straight line permits the determination of the hyperfine tensors. A curve obtained by choosing some frequencies in the range will intersect the line defined by the squares of the values v2a and v2p in two points. The values where the curve intersects the experimental data are (val, vpi) and (va2, vp2), where va=A/2 + v, and vp= Vj-A/2. This gives two values of the anisotropic coupling tensor, Ar... 

Improvement Item ACEMS supervisor was not present at initial Command Post (CP). Local/National Red Cross point of contact needed at the CP to coordinate food for personnel in outlying areas. National Red Cross may be needed in the EOC (Emergency Operation Center). EPA personnel were initially unaware that the Aiken County EOC was operational. Aiken County GIS resources were not involved in UCP planning meetings. ACEMS observed additional EMS support arrive from outside Aiken County. Additional units were not coordinated with ACEMS. Large numbers of individuals at the CP did not... 

The computed results of free energy as a function of the solvent coordinate, u-ul (where ug is the value of u at the crossing point of the free energy curves at the overpotential, q =0) for Fe and are given in Fig. 9. The free energy of activation AG from the crossing point of this plot is found to be 0.6 eV, which correlates well with the experimental result of 0.59 eV. Furthermore, simple calculations using the continuum theory expression show that AG (continuum) = 0.23 eV, which is... 

The mean elution volume and total variance calculated from the e qperimental chromatograms of polystyrene and 1,2-polybutadiene on the ARL 9 0 GPC instrument are so listed in Table I. The coefficients of the effective relation, coordinates of the cross-point, paranrater % and spreading factor were computed by the schema outlined above. The results obtained are listed in Table II and III, The effective relations and calibration... 

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