On the curvature of some free boundaries in higher dimensions

It is known that any subharmonic quadrature domain in two dimensions satisfies a natural inner ball condition, in other words there is a specific upper bound on the curvature of the boundary. This result directly applies to free boundaries appearing in obstacle type problems and in Hele-Shaw flow. In the present paper we make partial progress on the corresponding question in higher dimensions. Specifically, we prove the equivalence between several different ways to formulate the inner ball condition, and we compute the Brouwer degree for a geometrically important mapping related to the Schwarz potential of the boundary. The latter gives in particular a new proof in the two dimensional case.Comment: 27 page

String scattering off the (2+1)-dimensional rotationg black hole

The $SL(2, R)/Z$ WZW orbifold describes the (2+1)-dimensional black hole which approaches anti-de~Sitter space asymptotically. We study the $1 \rightarrow 1$ tachyon scattering off the rotating black hole background and calculate the Hawking temperature using the Bogoliubov transformation.Comment: 10 pages, LaTe

Edge Modes in the Intermediate-D and Large-D Phases of the S=2 Quantum Spin Chain with XXZ and On-Site Anisotropies

We investigate the edge modes at T=0 in the intermediate-D (ID) phase and the large-D (LD) phase of the S=2 quantum spin chain with the XXZ anisotropy and the generalized on-site anisotropies by use of the DMRG. There exists a gapless edge mode in the ID phase, while no gapless edge mode in the LD phase. These results are consistent with the physical pictures of these phases. We also show the ground-state phase diagrams obtained by use of the exact diagonalization and the level spectroscopy analysis.Comment: Submitted to "Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

Parametric study of non-periodic and hybrid auxetic bending-active gridshells

This paper presents a design method of Auxetic Bending-Active Gridshells (ABAGs), which are curved surfaces generated from the initial flat grid with 2-dimensional auxetic patterns. One of the mechanical properties of ABAGs is that a dome-like shape of a curved surface can be easily obtained by bending a grid due to negative Poisson's ratio for in-plane deformation. Shapes of auxetic patterns are relevant to Poisson's ratio. Non-periodic and/or hybrid 2-dimensional auxetic patterns are developed for designing the initial flat grid of ABAGs. Shape parameters are the sizes of each plane unit for tuning its reentrant pattern, and two types of reentrant shapes are mixed on an initial flat grid. Using the non-uniform patterns, we can obtain an asymmetric and more complex free-form surface of ABAGs than those composed of a uniform reentrant pattern. Discrete Gaussian curvature at each node on a curved surface is computed for quantitatively evaluating the properties of shapes of the obtained surfaces. Possibility of ABAGs as a new design tool is demonstrated by showing that various shapes are generated through large deformation analysis with the forced displacements at the supports

A 3-dimensional elastic beam model for form-finding of bending-active gridshells

This research is partly supported by SPIRITS program 2017 of Kyoto University.In this paper, we present a 3-dimensional elastic beam model for the form-finding and analysis of elastic gridshells subjected to bending deformation at the self-equilibrium state. Although the axial, bending, and torsional strains of the beam elements are small, the curved beams connected by hinge joints are subjected to large-deformation. The directions and rotation angles of the unit normal vectors at the nodes of the curved surfaces in addition to the translational displacements are chosen as variables. Based on the 3-dimensional elastic beam model, deformation of an element is derived from only the local geometrical relations between the orientations of elements and the unit normal vectors at nodes without resorting to a large rotation formulation in the 3-dimensional space. Deformation of a gridshell with hinge joints is also modeled using the unit normal vectors of the surface. An energy-based formulation is used for deriving the residual forces at the nodes, and the proposed model is implemented within dynamic relaxation method for form-finding and analysis of gridshells. The accuracy of the proposed method using dynamic relaxation method is confirmed in comparison to the results by finite element analysis. The results are also compared with those by optimization approach for minimizing the total potential energy derived using the proposed formulation

The universe out of a monopole in the laboratory?

To explore the possibility that an inflationary universe can be created out of a stable particle in the laboratory, we consider the classical and quantum dynamics of a magnetic monopole in the thin-shell approximation. Classically there are three types of solutions: stable, collapsing and inflating monopoles. We argue that the transition from a stable monopole to an inflating one could occur either by collision with a domain wall or by quantum tunneling.Comment: to appear in Phys. Rev. D with changing title into "Is it possible to create a universe out of a monopole in the laboratory?", text and figures revised, 21 pages, 6 figure