In a multi-dimensional domain, the slow motion behavior of internal layer solutions with spherical interfaces, referred to as bubble solutions, is analyzed for the nonlocal Allen-Cahn equation with mass conservation. This problem represents the simplest model for the phase separation of a binary mixture in the presence of a mass constraint. The bubble is shown to drift exponentially slowly acro...

This paper presents a review of the phenomenon of interlayer exchange coupling in magnetic multilayers. The emphasis is put on a pedagogical presentation of the mechanism of the phenomenon, which has been successfully explained in terms of a spin-dependent quantum confinement effect. The theoretical predictions are discussed in connection with corresponding experimental investigations.

We add a random bulk term, modeling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double-well potential. For the resulting functional we study the asymptotic properties of minimizers and minimal energy under a rescaling in space, i.e., on the macroscopic scale. By bounding the energy f...

where 2u = ( u), N > 4, λ > 0, 1 < q < 2 and μ ∈ [0,μ0], 0 < μ0 <∞. The continuous function f verifies the assumptions: (f1) f (s) = o(|s|) as s→ 0; (f2) f (s) = o(|s|) as |s| →∞; (f3) F(u0) > 0 for some u0 > 0, where F(u) = ∫ u 0 f (t) dt. According to hypotheses (f1)–(f3), the number cf = max s =0 | f (s) s | > 0 is well defined (see [1]). The continuous functions α and K verify the assumptio...

This paper presents a review of the phenomenon of interlayer exchange coupling in magnetic multilayers. The emphasis is put on a pedagogical presentation of the mechanism of the phenomenon, which has been successfully explained in terms of a spin-dependent quantum confinement effect. The theoretical predictions are discussed in connection with corresponding experimental investigations.

On the basis of Bethe ansatz solution of bosons with d-function interaction in a one-dimensional potential well, the thermodynamics equilibrium of the system in finite temperature is studied by using the strategy of Yang and Yang. The thermodynamics quantities, such as specific heat, etc., are obtained for the cases of the strong coupling and weak coupling limits respectively. © 2001 American I...

We present an analytical investigation of revival phenomena in the finite square-well potential. The classical motion, revival, and super-revival time scales are derived exactly for wave packets excited in the finite well. These time scales exhibit a richer dependence on wave-packet energy and on potential-well depth than has been found in other quantum systems: They explain, for example, the d...