Continuous Optimization of Adaptive Quadtree Structures

We present a novel continuous optimization method to the discrete problem of quadtree optimization. The optimization aims at achieving a quadtree structure with the highest mechanical stiffness, where the edges in the quadtree are interpreted as structural elements carrying mechanical loads. We formulate quadtree optimization as a continuous material distribution problem. The discrete design variables (i.e., to refine or not to refine) are replaced by continuous variables on multiple levels in the quadtree hierarchy. In discrete quadtree optimization, a cell is only eligible for refinement if its parent cell has been refined. We propose a continuous analogue to this dependency for continuous multi-level design variables, and integrate it in the iterative optimization process. Our results show that the continuously optimized quadtree structures perform much stiffer than uniform patterns and the heuristically optimized counterparts. We demonstrate the use of adaptive structures as lightweight infill for 3D printed parts, where uniform geometric patterns have been typically used in practice.Comment: Solid and Physical Modeling - SPM 201

Small scale aspects of warm dark matter : power spectra and acoustic oscillations

We provide a semi-analytic study of the small scale aspects of the power spectra of warm dark matter (WDM) candidates that decoupled while relativistic with arbitrary distribution functions. These are characterized by two widely different scales $k_{eq} \sim 0.01\,(\mathrm{Mpc})^{-1}$ and k_{fs}= \sqrt{3}\,k_{eq}/2\,^{1/2} with $^{1/2} \ll 1$ the velocity dispersion at matter radiation equality. Density perturbations evolve through three stages: radiation domination when the particle is relativistic and non-relativistic and matter domination. An early ISW effect during the first stage leads to an enhancement of density perturbations and a plateau in the transfer function for $k \lesssim k_{fs}$. An effective fluid description emerges at small scales which includes the effects of free streaming in initial conditions and inhomogeneities. The transfer function features \emph{WDM-acoustic oscillations} at scales $k \gtrsim 2 \,k_{fs}$. We study the power spectra for two models of sterile neutrinos with $m \sim \,\mathrm{keV}$ produced non-resonantly, at the QCD and EW scales respectively. The latter case yields acoustic oscillations on mass scales $\sim 10^{8}\,M_{\odot}$. Our results reveal a \emph{quasi-degeneracy} between the mass, distribution function and decoupling temperature suggesting caveats on the constraints on the mass of a sterile neutrino from current WDM N-body simulations and Lyman-$\alpha$ forest data. A simple analytic interpolation of the power spectra between large and small scales and its numerical implementation is given.Comment: 47 pages, 17 figures, section with comparison with Boltzmann code

Control of the magnetism and magnetic anisotropy of a single-molecule magnet with an electric field

Through systematics density functional calculations, the mechanism of the substrate induced spin reorientation transition in FePc/O-Cu(110) was explained in terms of charge transfer and rearrangement of Fe-d orbitals. Moreover, we found giant magnetoelectric effects in this system, manifested by the sensitive dependences of its magnetic moment and magnetic anisotropy energy on external electric field. In particular, the direction of magnetization of FePc/O-Cu(110) is switchable between in-plane and perpendicular axes, simply by applying an external electric field of 0.5 eV/{\AA} along the surface normal.Comment: 18 pages, 5 figure