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Mechanics of Interfacial Cracks between dissimilar Quasicrystals
We analize the steady propagation of a straight interfacial crack between two dissimilar planar quasicrystals in pure
elastic setting and infinitesimal deformation regime. A closed form solution to the balance equations is furnished. Inertia
is attributed only to the macroscopic motio
Electron dynamics in crystalline semiconductors
Electron dynamics in crystalline semiconductors is described by
distinguishing between an instantaneous velocity related to electron's momentum
and an average velocity related to its quasi-momentum in a periodic potential.
It is shown that the electron velocity used in the theory of electron transport
and free-carrier optics is the average electron velocity, not the instantaneous
velocity. An effective mass of charge carriers in solids is considered and it
is demonstrated that, in contrast to the "acceleration" mass introduced in
textbooks, it is a "velocity" mass relating carrier velocity to its
quasi-momentum that is a much more useful physical quantity. Among other
advantages, the velocity mass is a scalar for spherical but nonparabolic energy
bands , whereas the acceleration mass is not a scalar. Important
applications of the velocity mass are indicated. A two-band {\bm k}\cdot {\bm
\hp} model is introduced as the simplest example of a band structure that
still keeps track of the periodic lattice potential. It is remarked that the
two-band model, adequately describing narrow-gap semiconductors (including
zero-gap graphene), strongly resembles the special theory of relativity.
Instructive examples of the "semi-relativistic" analogy are given. The
presentation has both scientific and pedagogical aspects.Comment: 7 pages; 1 figur
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