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We study the stability of the critical points of the Onsager energy functional with Maier-Saupe interaction potential in general dimensions. We show that the stable critical points must be axisymmetric, which solves a problem proposed by [H. Wang, P. Hoffman, Commun. Math. Sci. 6 (2008), 949--974] and further conjectured by [P. Degond, A. Frouvelle, J.-G. Liu, Kinetic and Related Models, 15(2022), 417--465]. The main ingredients of the proof include a suitable decomposition of the second variation around the critical points and a detailed analysis of the relation between the intensity of interaction and the order parameter characterizing the anisotropy of the solution.

We present a generalization of the Maier-Saupe (MS) theory that incorporates the description of the ferroelectric nematic phase (NF) within its scope of application. The extension of the theory is carried out in a natural way, by adding to the nematic potential of MS a term proportional to cos{\theta} and to the polar order parameter , where {\theta} is the angle between the long molecular axis and the spontaneous polarization. The NF phase can be reached by cooling from the isotropic phase with or without the formation of an intermediate normal nematic phase, depending on the relative intensity of the polar and nonpolar terms of the nematic potential. For both phase sequences all the transitions are first order. The temperature dependence of the polar and nonpolar order parameters is calculated, and some results derived from the theory are compared with the experimental observations. It is argued that the theory is a valuable first approximation to describe some of the properties of ferroelectric nematics., Comment: 13 pages, 4 figures

The Maier-Leibniz Doppler-Shift technique is the most popular and accurate technique used in fission experiments to separate the yield of gamma rays from each of the two fission fragments. The technique exploits the aberration, i.e., the change in the angular distribution, of gamma rays emitted by a moving source. By measuring the speed and direction of the source with a conventional detector, as well as the yield of gamma rays at several angles from the direction of motion, the technique can be used to determine the mean multiplicities of gamma rays from each fragment. We show in this work that it is possible to extend the technique to also measure second moments of the gamma ray radiation from each fragment. In particular, given the current interest in fragment correlations in fission, we show that the covariance of the emission between the two fragments can be inferred. Experimental limitations and convergence of the new technique are discussed., Comment: 6 pages, double spaced, no figures

We present a numerical method, based on a tensor order parameter description of a nematic phase, that allows fully anisotropic elasticity. Our method thus extends the Landau-de Gennes $\mathbf{Q}$-tensor theory to anisotropic phases. A microscopic model of the nematogen is introduced (the Maier-Saupe potential in the case discussed in this paper), combined with a constraint on eigenvalue bounds of $\mathbf{Q}$. This ensures a physically valid order parameter $\mathbf{Q}$ (i.e., the eigenvalue bounds are maintained), while allowing for more general gradient energy densities that can include cubic nonlinearities, and therefore elastic anisotropy. We demonstrate the method in two specific two dimensional examples in which the Landau-de Gennes model including elastic anisotropy is known to fail, as well as in three dimensions for the cases of a hedgehog point defect, a disclination line, and a disclination ring. The details of the numerical implementation are also discussed., Comment: 37 pages, 8 figures