Principle of determinism

Acta Cryst. B39 165-170 Pauling, L. Hendricks, S.B. (1925) The crystal structures of hematite and corundum. J. Am. Chem. Soc. 47 781-790 Pauling, L. (1929) The principles of determining the structure of complex ionic crystals. J. Amer. Chem. Soc. 51 289-296 Payne, J.E. Davis, J.A. Waite,T.D. (1996) Uranium adsorption on ferrihydrite — effect of phosphate und humic add. Radiochemica Acta 74 239-243... 

Figure 14.11 Principle of determination of the thermal stability ceiling (TSC) of a polymer (see text).

FIG. 7 Principle of determining the London dispersive and specific components of adsorption Gibbs free energy between untreated carbon fiber (supplied by Soficar, T-300) and all probes, measured at 54.5 °C. 

The principle of determination of xrfrom the dependence of 6 on r has been realised in the diminishing bubble method developed by Platikanov et. al. [470,471]. From the optically measured values of the bubble radius Rb and the film contact line radius r, the values... 

Figure 3 Principle of determination of friction curve during macroscopic slip of the polymer at the wall. 

The local action principle establishes that the behavior of a particular element of a material is determined by the motion properties of that element and is independent of the behavior of any other element. The causality indifference principle together with the local action principle lead to the principle of determinism, which states that the stress of a given element of a material at time t depends only on the deformation of that element at times 0 < t. 

Rational thermodynamics proposes the construction of such equations by the use of constitutive principles [1,3] which generalize long experience accumulated during the past with proposals of special constitutive equations (cf. Sect. 1.1). Some of these constitutive principles more resemble rules or recommendations (e.g., principles of determinism or equipresence below) serving rather as a guidance. On the other hand, some constitutive principles (of admissibility below and objectivity in Sect. 3.5) seem to be sufficiently general and therefore in turn all eonstitutive equations should be in accord with them. ... 

According to the constitutive principle of determinism the response (in the actual instant) is given by deformation and temperature in the present and the past of the body (cf. also Sects. 3.5, 4.5, and Rem. 26 in Chap. 3). This means that constitutive equations give the responses (2.4) in the actual instant as functional-independent variables of which there are histories—thermokinetic processes (2.5) in the past and present (in fluids, by deflnition, the deformations which influence the response are expressible only through volume in mass conserving system cf. Rems. 3, 4 in this chapter, 30 in Chap. 3). 

For the most simple model (in fact extended model A of Sects. 2.1, 2.2) of the fluid mixture without memory, motivated by principles of determinism (with enlarged thermokinetic process by masses m, m2) and equipresence, the following are postulated for responses (2.4)... 

We call the fields (3.114)-(3.116) fulfilling the balances of mass (3.63), (3.65), momentum (3.76), moment of momentum (3.93), and energy (3.107) a thermodynamic process, because only these are of practical interest. Then we denote the fields (3.114) as the thermokinetic process and the fields (3.115) as the responses (we limit to the models with symmetric T (3.93) in more general models we must introduce also the torque M into responses (3.115), cf. Rems. 17, 32). The fields (3.116) are controlled from the outside (at least in principle). Just constitutive equations, which express the difference among materials, represent the missing equations and are relations between (3.114) and (3.115) [6, 7, 9, 10, 23, 34, 38, 40, 41, 44, 45], Referring to Sect. 2.1 we briefiy recall that constitutive equations are definitions of ideal materials which approximate real materials in the circumstances studied (i.e at chosen time and space scales). Constitutive equations may be proposed in rational thermodynamics using the constitutive principles of determinism, local action, memory, equipresence, objectivity, symmetry, and admissibility. 

Summary. A procedure really specific for the rational thermodynamics is introduced in this section in the form of several principles put forward to derive the thermodynamically consistent constitutive equations. In their most general form, the constitutive equations were proposed as functions (3.118) on the basis of the principles of determinism, local action, differential memory, and equipresence. They were further reduced to the form (3.121) considering the same material throughout the body and applying the principle of objectivity. Because of our interest in fluids only, the constitutive equations were further modified to this material type by means of the principle of material symmetry giving the final form (3.127). Two special types of fluid were defined by (3.129) and (3.130). 

Because fields (4.121) are controlled from the outside (of the mixture), constitutive equations are relations between (4.119), (4.120) according to the constitutive principle of determinism their independent variables form the thermokinetic process (4.119) giving their values as responses (4.120). For simplicity, we restrict to recent past and nearest surroundings of the considered response by constitutive principles of differential memory and local action. Constitutive equations for responses (4.120) are then functions of the following values of thermokinetic process (4.119) and their (time and space) derivatives taken in a considered instant and place of response (in referential description introduced in Sect.4.1 similarly as in Sect. 3.1, i.e. as (4.1), Py = PyOi-y, t), T = T(Ky, t)), namely... 

Principle of determining the shear stress between the EBFR and concrete surface by using cross-section analysis. 

Figure 2.6 Scheme of a capillary viscometer and principle of determination of the intrinsic viscosity of polymers. 

The measuring principle is similar to the principle of determination of the detonation velocity of explosives—the measurement of very short time intervals needed by the shock wave to travel a known distance. 

Figure 6.3 a) FTIR spectrum of the rubber-filler gel of a ternary 33/33/34 SBR/NBR/ NR blend filled with 50 phr silica. Hj) Principle of determination of the fraction of rubber components, and from the TGA curve... 

Principle of determinism The stress is determined by the history of the motion undergone by the body. 

For simplicity, we describe the equations without mass density p. Since the speciflc stress a" (x,t) is given in terms of an Eulerian description, we treat here the simplest response for that description. To satisfy the principle of determinism and the principle of local action mentioned in the previous section, the stress ai(x,t) can be written in terms of v and Vv ... 

The principle of determinism [108] belongs to the first class. It states that the stress at a given material point is determined by the entire past history of the motion in a neighborhood of the considered point. 

The solutions must be very diluted in order to obtain accurate results. Moreover, the sulfite solution must be added to the iodine solution (and not the inverse) and must have as little contact with air as possible. They are back titrations. A known volume of the sulfite solution is added to a solution of iodine in excess, slightly acidified (pH >= 3). The excess of iodine is titrated with a thiosulfate solution. This is the principle of determining sulfites in wine. 

This method uses the principle of determining residual starch from the insoluble dietary fiber residue. It consists of the enzymatic hydrolysis of starch with heat-stable a-amylase, followed by a proteolytic degradation with a protease and, finally, the hydrolysis of the starch with amyloglucosidase to yield glucose. Glucose is determined in the supernatant with glucose oxidase and peroxidase. 

Fig. 3.2.2. Sketch showing the principle of determining the overall efficiency from the cumnlative size distribntion of the feed and the cut size...

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