Landau-Lifshitz Equations

Stability in the energy space for chains of solitons of the Landau–Lifshitz equation

“…Concerning the original one, the existence of global solutions in the energy space E(R) can be achieved following arguments similar to the ones introduced by Zhou and Guo [32], or Sulem, Sulem and Bardos [30], for the Schrödinger map equation (see also [15] for more details). The uniqueness of solutions in the energy space E(R) is more involved.…”

“…In Subsection A.1, we establish the existence of smooth solutions by following the strategy developed by Sulem, Sulem and Bardos in [30] (see also [15]) for the Schrödinger map equation (see Proposition A.2 below). We then control the smooth solutions by controlling the solutions v and Ψ to the system of equations (13) and (15) (see Proposition A.3 below).…”

“…. We refer to [30] for the construction of this solution in the context of the Schrödinger map equation (see also [15]). However, its uniqueness is not immediate.…”

“…In the isotropic case λ = 0, the Landau-Lifshitz equation reduces to the one-dimensional Schrödinger map equation, which has been intensively studied in the mathematical literature (see e.g. [15,18], and the references therein).…”

Structure and hydrogen absorbing properties of ScCrMn alloy

“…The observed plateau pressures of the alloy are quite low, varying from about 0.01 kPa at 298 K to 17 kPa at 571 K. According to a general rule, the larger the lattice parameter of the alloy, the lower plateau pressure and higher stability the hydriding system has [23]. The lattice parameters of ScCrMn are close to those of ZrMnCr [24], implying similar atomic sizes between the Sc and Zr atoms in the crystal Fig. 4.…”