Second-order mixed-moment model with differentiable ansatz function in slab geometry

We study differentiable mixed-moment models (full zeroth and first moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum entropy $M_N$ models. Realizability theory for these modification of mixed moments is derived for second order. Numerical tests are performed with a kinetic first-order finite volume scheme and compared with $M_N$, classical $MM_N$ and a $P_N$ reference scheme.Comment: arXiv admin note: text overlap with arXiv:1611.01314, arXiv:1511.0271

SLED Phenomenology: Curvature vs. Volume

We assess the question whether the SLED (Supersymmetric Large Extra Dimensions) model admits phenomenologically viable solutions with 4D maximal symmetry. We take into account a finite brane width and a scale invariance (SI) breaking dilaton-brane coupling, both of which should be included in a realistic setup. Provided that the microscopic size of the brane is not tuned much smaller than the fundamental bulk Planck length, we find that either the 4D curvature or the size of the extra dimensions is unacceptably large. Since this result is independent of the dilaton-brane couplings, it provides the biggest challenge to the SLED program. In addition, to clarify its potential with respect to the cosmological constant problem, we infer the amount of tuning on model parameters required to obtain a sufficiently small 4D curvature. A first answer was recently given in [arXiv:1508.01124], showing that 4D flat solutions are only ensured in the SI case by imposing a tuning relation, even if a brane-localized flux is included. In this companion paper, we find that the tuning can in fact be avoided for certain SI breaking brane-dilaton couplings, but only at the price of worsening the phenomenological problem. Our results are obtained by solving the full coupled Einstein-dilaton system in a completely consistent way. The brane width is implemented using a well-known ring regularization. In passing, we note that for the couplings considered here the results of [arXiv:1508.01124] (which only treated infinitely thin branes) are all consistently recovered in the thin brane limit, and how this can be reconciled with the concerns about their correctness, recently brought up in [arXiv:1509.04201].Comment: 28 pages, 4 figure

A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry

We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO) method, and for time integration we use multi-step Runge-Kutta methods which are strong stability preserving and whose stages and steps can be written as convex combinations of forward Euler steps. We show that the moment vectors stay in the realizable set using these time integrators along with a maximum principle-based kinetic-level limiter, which simultaneously dampens spurious oscillations in the numerical solutions. We present numerical results both on a manufactured solution, where we perform convergence tests showing our scheme converges of the expected order up to the numerical noise from the numerical optimization, as well as on two standard benchmark problems, where we show some of the advantages of high-order solutions and the role of the key parameter in the limiter