Ferromagnetic materials may present a complicated domain structure, due in part to the nonlocal nature of the self interactions. In this article we present a detailed study of the structure of one-dimensional magnetic domain walls in uniaxial ferromagnetic materials, and in particular, of the Neel and Bloch walls, We analyze the logarithmic tail of the Neel wall, and identify the characteristic length scales in both the Neel and Bloch walls. This analysis is used to obtain the optimal energy scaling for the Neel and Bloch walls. Our results are illustrated with numerical simulations of one-dimensional walls. A new model for the study of ferromagnetic thin films is presented.

It is well known that 1d atomistic heat transport experiences anomalous phenomenon. Temperature discontinuities and divergence of the conductivity with respect to system size suggest that, at the atomistic scale, Fourier's law does not hold in one dimensional materials. Many different thermostats exist for 1d atomistic systems, however their use is ad-hoc and requires choice of boundary conditions. A dimension reduction technique known as the Mori-Zwanzig procedure applied to infinite harmonic systems produces a type of thermostat whose equations of motion are generalized Langevin equations (GLE's) where the resulting noise term is mean zero Gaussian and stationary, satisfying the fluctuation dissipation theorem.

By using a dimension reduction procedure based on Green's function techniques, it is shown that infinite deterministic baths give rise to GLE thermostats with non-stationary noise. Numerical experiments are then performed to explore the affect of non-stationarity on the temperature profiles in non-equilibrium stationary states (NESS), and on the divergence of the conductivity. Comparisons to other simple models are also reported.

We consider a model for a system of N electrons interacting with M static nuclei withspatial coordinates RJ and a self-generated magnetic field. The energy associated with this system is (in atomic units) Esm N (Ψ,A) = XN j=1 Z R3N 1 2 |σj · (i∇j − A(rj))Ψ|2 C2 + ⟨ XN j=1 v(rj) + X 1≤j