Titlebook: Mathematics of Large Eddy Simulation of Turbulent Flows; Luigi C. Berselli,Traian Iliescu,William J. Layton Book 20061st edition Springer-

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7]. Moreover, since the responses originate from on-site electronic virtual excitations, the nonlinear response time is ultrafast of the order of picosecond to femtosecond time scales. Microscopic descriptions of second order and third order it-electron virtual excitation processes are required in o

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nteraction) to form the DQW eigenstates. The resulting new states are delocalized over the DQW region. For example, two identical wells (same thickness and material composition) give rise to symmetrical and antisymmetrical z-dependent DQW wavefunctions (with respect to the center of the central barr

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ake the first and a collision will take place. After the collision, the solitons keep their shape and velocity (but in general all other parameters of solitons may alter). This fundamental property of the SIT solitons has been studied many times both theoretically and experimentally [3,6,7].

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ensively studied in the literature, such as dispersive effects, Strichartz estimates and unique continuation-type properties (which are relevant in control theory and inverse problems). A complete description is given in the case in which the underlying geometry is a manifold with periodic geodesic