Principle of local action

In more complicated material models we modify oruse further constitutive principles determinism is enlarged for densities (mass concentrations) in mixtures (cf. Sects. 2.4,3.5,4.5), and the definition of fluid used in this principle is in fact the result of constitutive principle of symmetry (see Rem. 30 in Chap. 3). Another constitutive principle is the objectivity (frame indifference) principle. Here it is trivially satisfied because motion is neglected and all quantities are objective (see Sects. 3.2,3.5). In nonuniform systems the influence of neighborhood is described in the principle of local action (cf. Sect. 3.5). In mixtures, the property of mixture invariance [32] may also be used as a constitutive principle [33]. 

Principle of local action The stress at a point is not influenced by far-field motions. Principle of frame indifference The response of a material must be described under the frame indifference (see Sect. 2.2.2). 

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 ... 

A common explanation for such phenomena is that the gradient of the deformation rate tensor affects the flow induced anisotropy and hence the stress. It follows obviously that filled (polymer) systems cannot be "simple" fluids since their behavior, by virtue of their true nature, violates the principle of "local action," which states that the stress in a fluid element is determined by the deformation history of that fluid element and is independent of the history of neighboring elements. This is the main reason for the... 

The division of the molecular volume into atomic basins follows from a deeper analysis based on the principle of stationary action. The shapes of the atomic basins, and the associated electron densities, in a functional group are very similar in different molecules. The local properties of the wave function are therefore transferable to a very good approximation, which rationalizes the basis for organic chemistry, that functional groups react similarly in different molecules. It may be shown that any observable... 

By arguing in this fashion, Stahl advocated a form of vitalism, a doctrine that holds that living bodies are alive by virtue of a vital principle. Van Helmont had also had the notion of an active spirit in bodies which worked locally in the body to produce chemical change and affect health. The importance of the idea of local action was that it enabled physicians to break away from the general pathology of the Galenists and to consider specific cures for specific illnesses. Van Helmont described a different active spirit for each of many different parts of the body. In this respect Stahls view of the local action of the soul can be seen as similar to Van Helmont s. But in his refusal to allow medicine to be explained by chemistry, Stahl broke from traditional iatro-... 

It is the non-zero value of the integral in (31), irrespective of the separation of A and B, that violates any principle of locality it appears as a direct result of applying standard quantum mechanics and seems to imply some kind of action at a distance that keeps the two spins coupled. It should be noted, however, that the postulate of Bohm and Bell - that the sytem is disintegrated by some kind of process that... 

The principle of both mechanisms of equilibrium and dynamic film elasticities is the same as a result of external disturbances (for example, local extension), a counterforce originates which returns the film to its initial state after the external action has ceased (after extension the film becomes thicker again). 

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. 

Molecular probes, such as optical or magnetic tweezers,64-71 micropipets,72 and microfibers,73-74 have been developed to manipulate single molecules and to measure their response to mechanical actions such as stretching, torsion, and compression. A force resolution down to 0.1 pN enabled quantitative measurement of the molecular forces and provided novel information on the basic principles of folding, motion, and interactions of individual molecules. Complementary to the local mechanical probes, actions of external fields were monitored on individual polymer molecules.75 77... 

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