New PDF release: Continuum physics

By Peter Hertel

ISBN-10: 3642295002

ISBN-13: 9783642295003

Stability Equations -- fabric Equations -- Linear reaction conception -- Examples

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40) which state that there is no magnetic charge. 0 and 0 are constants which depend on the system of units. 40) are Maxwell’s equations. Differentiating Eq. 37) with respect to time and adding the divergence of Eq. 41) The first and the last term on the right hand side cancel, and the term in the middle vanishes as well since it is the divergence of a curl. Conservation of electric charge is a by-product of Maxwell’s equations. Since chemistry is governed by quantum theory and electromagnetism, it is no wonder why charge is conserved in chemical reactions.

Indeed, the strain tensor field describes deformation. A rigid translation or rotation of a medium does not produce strain. 2 Solid Media 39 Note that the displacement gradient @i uk is dimensionless. @k uj / to Eq. 25) may be neglected. Likewise, the square root of Eq. 30) ds was the distance between two neighbors in the relaxed state of the medium. t; x/. 29) is an approximation, it holds true for small displacement gradients, j@i uk j 1. It should not be used if large deformations of rubber-like substances are to be modeled.

Va is the average speed of particles of kind a. Particles disappear or appear in chemical reactions which are described by stoichiometric coefficients ra . In each reaction of type r there appear or disappear ra particles of kind a, depending on sign. r is the volumetric reaction rate, the number of chemical reactions of type P r per unit volume and per unit time. N a / D r r ra . Mass is conserved in each chemical reaction. Therefore, the mass density % and the mass current density %v obey the continuity equation7 %P C r %v D 0.

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Continuum physics by Peter Hertel

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