Relations between static and dynamic

The identification of relations between statics and dynamics became a constituting part in the explanation of unity of the laws of mechanics in (Lagrange, 1788). Deriving the equations of trajectories from the equation of state (1) turned out to be possible owing to the assumptions made about observance of the relativity principle of Galileo and the third law of Newton and, hence, about representability of any trajectory in the form of a continuous sequence of equilibrium states. From the representability, in turn, follow the most important properties of the Lagrange motion curves existence of the functions of states (independent of attainability path) at each point possibility to describe the curves by autonomous differential equations that have the form x = f x) dependence of the optimal configuration of any part of the curve upon its initial point only. These properties correspond to the extreme principles of the optimal control theory. 

Finally, we formulate relations between static and dynamic scattering functions. According to the definitions, the static scattering law is identical to the dynamic scattering law at zero time... 

T. Oku, M. Eto, A relation between static and dynamic Young s moduli of nuclear graphites, Ibaraki Daigaku Kogakubu Kenkyu Shuho, Fac. Eng. Ibaraki Univ. 39 (1991) 45-52. 

The flow and pressm-e distribution within cyclones and swirl tubes is more easily understood if we make clear the relation between static and dynamic... 

There seems to be some debate over the limit between static and dynamic measurements related to the question of the frequency of image registration (frames per second) at which a true real time observation is done. Obviously this judgement—if it is necessary at all— has to be made with reference to the rate of change at the surface. No attempt is made in this text to enter this discussion. Consequently, no attempt is made in this text to enter into this debate video STM will not be separated from other real time STM . 

A study of immiscible liquid/liquid displacement on model systems, paraffin oil/aqueous surfactant solutions in glass capillary tubes led to the conclusion that flow and wetting properties cannot be treated separately. Even though there is a correlation between static and dynamic contact angles, the validity of this relation is restricted to relatively low surfactant concentrations. 

Mode coupling theory provides the following rationale for the known validity of the Stokes relation between the zero frequency friction and the viscosity. According to MCT, both these quantities are primarily determined by the static and dynamic structure factors of the solvent. Hence both vary similarly with density and temperature. This calls into question the justification of the use of the generalized hydrodynamics for molecular processes. The question gathers further relevance from the fact that the time (t) correlation function determining friction (the force-force) and that determining viscosity (the stress-stress) are microscopically different. 

There are two types of electron correlation static and dynamic. The static correlation is related to the behavior of HF method at the dissociation limit of the molecule and deals with the long range behavior of this approach. On the other hand dynamic electron correlation is related to the electron repulsion term and is the reciprocal function of a distance between two electrons and thus represents short range phenomena. However, it should be noted that the electron correlation in the HF method is included in the indirect manner by the consideration of an electronic motion in an effective potential field due to the nuclei and the rest of the electrons and due to the inclusion of electron spin. Therefore, despite the known shortcomings, HF method has been extensively used in chemical calculations and has been quite successful for systems which are not extensive for electron correlation. 

Here Vp has been replaced with the pressure difference between the two points is AP, K°, and K are, respectively, the usual conductivity and the complex conductivity of the electrolyte solution in the absence of the particles, (f> is the particle volume fraction, (j)c is the volume fraction of the particle core, Vc is the volume of the particle core, volume fraction of the polyelectrolyte segments, I4 is the total volume of the polyelectrolyte segments coating one particle, and po, are respectively, the mass density of the particle core and that of the electrolyte solution, and ps is the mass density of the polyelectrolyte segment, V is the suspension volume, and p(cai) is the dynamic electrophoretic mobility of the particles. Equation (26.4) is an Onsager relation between CVP and pirn), which takes a similar form for an Onsager relation between sedimentation potential and static electrophoretic mobility (Chapter 24). 

The difference between the constant and variable parts of the structures in the reaction is similar to the analysis of the set of edges M in the sets of static and dynamic edges. These are related to the static graph S = (V, 5) with the same set of vertices Vs = V, and with the set of dynamic edges to the graph 1 = (V, >)-again with the same set of vertices Vp = V. 

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