Asymmetric Continuum: Extreme Processes in Solids and Fluids by Roman Teisseyre, Maria Teisseyre-Jeleńska

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By Roman Teisseyre, Maria Teisseyre-Jeleńska

This publication bargains with a category of simple deformations in uneven Continuum thought. It describes molecular deformations and delivery velocities in fluids, pressure deformations in solids in addition to the molecular delivery, vital in fracture approaches.
In solids, a separate challenge pertains to the displacements; their recording, e.g., through the seismometers, proves basically the lifestyles of the displacement derivatives and never a true displacement. despite the fact that, the molecular displacements and new fracture criterion together with the illness distributions and triggered traces are outlined within the e-book too.
In fluids, the shipping velocities and molecular traces describe the movement procedures. The vortex motions are outlined through the rotational delivery; this technique results in extra advanced difficulties, just like the turbulence phenomena.
The interplay approaches, together with the electrical and magnetic fields, and a few thermodynamical difficulties and quantum thought analogies aid to appreciate the intense processes

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Chap. 1). On the other hand, recent seismological observations of rotation waves by the very precise instruments, based on the Sagnac effect, were able to reveal and measure a very small spin, up to 10À9 rad/s. These recorded rotation motions are R. Teisseyre and M. 1007/978-3-642-31860-3_2, Ó Springer-Verlag Berlin Heidelberg 2014 21 22 2 Asymmetric Continuum: Basic Motions and Equations not the simple point rotations, but relate to the rotation strains. These experimental observations give grounds for a new, relatively simple theoretical approach in which the strain moments used in a classic theory are replaced by the antisymmetric part of strains.

Such fragmentations in a circular shape are typical in some material crushing under compression. For processes under constant applied load, Err þ Ezz ¼ const, we write after eqs. 4a) the wave in the cylindrical coordinates, for the field Euu :    1=2   o ro o2 o2 o2 l oFu ð2:13bÞ þ 2 Euu À q 2 Euu ¼ l þ 2 2 ror or k þ 2l oz ot row r ow  1=2 l where w ¼ u kþ2l Considering the angular squeeze deformations related to the independent axial strains, we get a completely new view on the appearance of the Euu component discovered in strain measurement related to earthquake events (Gomberg and Agnew 1996).

3 Fluids: Molecular Strains and Transport 35 ~ ½nsŠ X o2 X p o2 E o2 X p ~ ! l ¼ q ð2:26Þ oxk oxk ot2 oxk oxk ot2 k k R ~ ½ksŠ and Xp ¼ 1 xp dx. where g; q are constants and xp ¼ epks E Dx There may be some reasons to average the pure spin (molecular rotation strains) into a molecular rotation related to some Cosserat characteristic molecular length, we will return to these relations in the next chapter, however, for a constant density the considered structure as a whole can be attributed to the field X (Eq.

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